







Three numbers have a sum of 45 
20200506 

From Jayden: Three numbers have a sum of 45. The greatest of the 3 numbers is 2 greater than the least number. What are the numbers? * Answered by Penny Nom. 





Four digit numbers starting with 6 
20200422 

From Judy: I need to generate a list of 4 digit numbers using 09 where the first digit is 6 and no numbers can be repeated Answered by Penny Nom. 





Sixdigit telephone numbers 
20200312 

From Lulamile: What is the probability that a sixdigit telephone number has no repeated digits? The telephone number cannot begin with a zero Answered by Penny Nom. 





Investigating y = (2)^x 
20200113 

From Gonzalo: This is not precisely a maths question, but it is formulated based on my maths curiosity. Fidgetting with my new graphic calculator, I started graphing things and had the idea to graph $y=(2)^x.$
The result surprised me, and I thought a little bit about it, stored it on the back of my brain, and promised myself to look deeper into it someday. Answered by Harley Weston. 





Two digit numbers 
20191203 

From Lacy: Using the digits zero through nine, how many twodigit numbers can be formed,which do not have a four or five? Answered by Penny Nom. 





Even 5 digit palindromes 
20191024 

From daniel: How many palindromes of 5 digits are even? Answered by Penny Nom. 





Six digit numbers from 4 digits 
20190730 

From Tab: How many six digit combinations can be made from the numbers zero, two, five, eight? With repetition of numbers Answered by Penny Nom. 





Two numbers 
20190503 

From fds: The difference of two numbers is 2, and their sum is 4. What are the two numbers? Answered by Penny Nom. 





A word problem 
20190224 

From Briana: When 4 times the number increased by 30, the answer is the same as when 70 decreased by the number. What was my number? Answered by Harley Weston. 





Adding and multiplying two numbers 
20190213 

From katie: what 2 numbers add to get 7 and multiply to get 2? Answered by Penny Nom. 





Numbering pages 
20190120 

From chungus: It takes 852 digits to number the pages of a book consecutively. How many pages are there? Answered by Penny Nom. 





Four digit numbers from 0, 1, 2 and 3 
20181130 

From A parent: how many four digit numbers can be formed using nos.0,1,2,3 if repetition is allowed? Answered by Penny Nom. 





Compatible numbers 
20180919 

From Jessica: Hello, I'm having trouble helping my daughter she is in 5th grade and I tell you her math is so much different then the math I learned in school and I been out of school for quite some time so it's a little hard for me.
Anyway her math is very confusing for me they are saying use compatible numbers to find two estimates.
I have no idea what that even mean I tried using Google but still don't get it .
The problem is 12 divided by 478 using compatible numbers to find two estimates.... please help Answered by Penny Nom. 





The sum and difference of two numbers 
20180917 

From Feni: The sum of two numbers is 4. The difference of the two numbers is 2. What are the two numbers? Answered by Penny Nom. 





The sum and difference of two numbers 
20180830 

From Saranya: Hi,
The question is to find the numbers from sum and difference.
The Sum = 14 and the difference = 2
I found in this web site some useful answers. but my kid is going second grade only. She don't know how to do a division or multiplication.
So can you please explain on how to find the answer using only the Addition and Subtraction.
Thanks in advance. Answered by Penny Nom. 





Three consecutive whole numbers 
20180622 

From whaha: the sum of three consecutive whole numbers divided by 4 is equal to 6. find the numbers. Answered by Penny Nom. 





The product of two numbers 
20180619 

From amie: the product of two numbers is 108.when the larger number is divided by the smaller number the quotient is 3. What are the number.tnx Answered by Penny Nom. 





An equation with rational coefficients 
20180526 

From Anagh: If x and y are rational number and
(x+y) + (x  2y)√2 = 2x y + (xy1) √5
Then find the value of x and y. Answered by Penny Nom. 





Gauss' Addition of whole numbers. 
20180430 

From Brad: I found this on your site. Question: what is the sum of the first 100 whole numbers??
Is there a different formula if the numbers begin at a number other than one? For example
What is the series I want to add is goes from 7  53? Answered by Harley Weston. 





The sum and difference of two numbers 
20180313 

From samima: Two numbers have a difference of 0.85 and the sum 1.What are the numbers? Answered by Penny Nom. 





Some 5 number sets 
20180302 

From Sarah: Hello! My question is:
If I have 5 columns of numbers, and I want to create all possible combinations
(or is it permutations?) How can I do that? For example all numbers in each
column may not appear in any other column. so:
column 1: 1,2,3,4,5
column 2: 6,7,8,9,10
column 3: 11,12,13,14,15
column 4: 16,17,18,19,20
column 5: 21,22,23,24,25
how may I determine all the possible ways I can get sets of 5 out if this? Thanks! Answered by Penny Nom. 





Simplify 1/2^i 
20180128 

From Deepak: How do I simplify this complex equation:
z=1/(2^i) Answered by Penny Nom. 





The sum and difference of two numbers 
20180125 

From Ali:
Hello,
I was looking at the original question that was posted and answered by
your team:
http://mathcentral.uregina.ca/QQ/database/QQ.09.07/s/donna1.html
I used the 7 and 4 as example and not looking for 39 per original
question:
A=7
B=4
7+ 4 =11 and 74 = 3
We end up with 11 +3 = 14
A= 14/2 give use 7
B = how do you solve for B or 4 with out knowing anything about 3 or any other numbers ?
Thank you
Ali Answered by Penny Nom. 





The decimal form of a fraction 
20180112 

From Tom: Prove that the decimal representation of the quotient of 2 integers must repeat (if it does not terminate). Answered by Penny Nom. 





Compatible numbers 
20180102 

From Natalie: I'm in 4th grade and two weeks ago my class learned how to use compatible numbers.
I was REALLY confused but I didn't want to say I didn't understand because I just wanted to go home.
Tomorrow we have the Topic 7 Test and I'm stuck on a problem that requires using compatible numbers.
My mom apparently hasn't heard of compatible numbers and she can't really help me too much.
Here's the problem : The local library places new books in a section with 31 shelves. Each shelf
fits 18 books. Use compatible numbers to estimate the number of books that the library can fit on
the shelves. Answered by Penny Nom. 





Retiring athletes numbers 
20171218 

From Robin: I am wondering if you can explain in layman terms how to figure out how many different ways the numbers 0099 can be arranged? The discussion that sparked this question revolved around the practice of retiring athletes numbers and how many actual number combinations there are. So if I were to use 00, 01, 02 03, 04, 05, 06, 07, 08, 09, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ....99. I say there are only 109 different numbers. I'm being told I'm wrong that there are way more than that. Please help. Thank you, Robin Answered by Penny Nom. 





27000001 
20171009 

From Tulashiram: If a× b =27000001, then what is the value of a & b ? Answered by Penny Nom. 





Two digit numbers that contain 5 
20170811 

From Irish: How many two digit numbers contain the digit 5? Answered by Penny Nom. 





Some 4 digit numbers 
20170724 

From Camille: I need all of the 4 digit combinations that starts with number 3 and digits can't be repeated Answered by Penny Nom. 





Three consecutive natural numbers 
20170611 

From Anita: Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the square of the other two by 60. Find the numbers. Answered by Penny Nom. 





4 digit codes with repeating digits 
20170601 

From Morgan: what are all possible 4 digit code repeating numbers? cuz i know that you have one website on it but, it doesn't repeat 2 numbers in a code. Answered by Harley. 





Five rational numbers between 2 and 1 
20170531 

From Prince: Five rational numbers between 2 and 1 Answered by Penny Nom. 





Rational numbers between 2 and 3 
20170408 

From Medha: Find 12 rational numbers between2 and 3 Answered by Penny Nom. 





The sum and difference of two numbers 
20170320 

From Olivia: The sum of two numbers is 87 and their difference is 29. What are the two numbers Answered by Penny Nom. 





Write these numbers from greatest to least 
20161222 

From lsaiah: write the following numbers from greatest to least
3 1/2, 7/3, 80%, 2.5, 0.94 Answered by Penny Nom. 





x^2 = 16 
20161212 

From A student: x to the second power = 16
what number solves the equation? Answered by Penny Nom. 





Four digit numbers 
20160908 

From ning: 00009999 there is ten thousand 4digit numbers. How to find the number of ways that 4 digit are the same? How to prove it by using formula? Answered by Penny Nom. 





The modulus of a complex number 
20160729 

From Cheyenne: There's a question on my Summer Assignment I cant figure out. Here it is:
Find the absolute Value of the complex number. 5i
Please help? Answered by Penny Nom. 





Writing numbers in the form a/b 
20160717 

From Edward: How to write these numbers in form of a/b: 7, 0.175, 3.25, 37/10, 16, 1/3, 2.04 Answered by Penny Nom. 





A word problem 
20160227 

From KRK: amrutha thinks of a number, multiplies it by 5 & 6, devides the result by 3
and takes away the number first thought of to get an answer 36. find out
the number Answered by Penny Nom. 





Complex numbers in standard form 
20160115 

From Michael: express the following complex numbers in standard form (2+3i)+(52i) Answered by Penny Nom. 





Sue's favourite number 
20160112 

From Maria: This is my son's homework. He is 7. Can you help?
Sue has a favourite number.
It is an even number.
It has 3 digits.
The digits add up to 15.
Find 10 numbers that could be Sue's number? Answered by favourite number. 





Is 22/7 bigger or smaller than 3.14? 
20151106 

From Natalie: Is 22/7 bigger or smaller than 3.14? Answered by Harley Weston. 





An example of an irrational number 
20151022 

From Allison: It ask me to find an example of an irrational number less than 5 and I don't
understand what the difference from a rational number and an irrational
number besides the fact that a rational number can be repeated and shown in
a simple fraction and an irrational number can't be written in a simple
fraction.
Can you help me? Answered by Penny Nom. 





Square roots 
20150921 

From mariana: I have read various articles on how to find the square root of irrational numbers and every article out there seems to be very confusing.
i read you answer to LUKOW about irrational numbers and i am still quite confused. Say i want to find the square root of 326. i know that it is between 18 and 19 because 18 is the square root of 324 and 19 is the square root of 361 im just very confused about the rest of the process. Please help! ( if possible i would appreciate two examples. thanks) Answered by Penny Nom. 





Mutually prime composite numbers 
20150109 

From nivedita: Two composite number that is mutually prime? Answered by Penny Nom. 





The units digit of a prime 
20150108 

From Patricia: Every prime number greater than 10 has a digit in the ones place that is included in which set of numbers below 1 3 7 9 or 1 3 7 or 0 2 4 5 6 8 or 1 3 5 9 Answered by Walter Whiteley. 





Missing digits in a phone number 
20150107 

From Janelle: I had a friend try and play a game on me, regarding phone numbers, so I only know the area code , and the last four digits of the phone number. Which means, there are 3 digits that I need to figure out all the possibilities to. Answered by Penny Nom. 





The sum of two numbers is 52 
20140901 

From Blake: The sum of two numbers is 52 and the difference is 10. What are the numbers? i used to be real good at this stuff? Answered by Penny Nom. 





How do I make fractions into decimals? 
20140531 

From jay: Hi,
I wanted to know how do I make fractions into decimals example 1 3/8? Answered by Penny Nom. 





The combination of 6 numbers from 1 to 355 that gives us 360 
20140529 

From Ion: Hi,
My name is Ion and I am trying to find the number of combinations of 6 numbers (angles) that would sum to 360 (degrees).
Thank you! Answered by Robert Dawson. 





Three digit numbers 
20140515 

From Mudassir: how many 3 digits numbers which at least one digit is 2 ? Answered by Penny Nom. 





Three consecutive whole numbers 
20140313 

From Abhishek: Three consecutive whole numbers are such that if they be divided by 5,3 and 4 respectively, the sum of the quotient is 40. What are the numbers? Answered by Chris Fisher. 





Four digit phone numbers 
20140225 

From Tom: Hi, I'm an online math teacher, working on lessons for my students.
This question is in their book and I can't do it...! Help!
It has to do with phone numbers, and in this problem,
we are only dealing with
the last 4 digits of the number.
It asks how many possible numbers we have
if at least one digit repeats in the last 4 digits of the number. Answered by Penny Nom. 





7 digit phone numbers 
20131208 

From Sean: Hi I was wondering how you would calculate how may 7 digit phone numbers there are with only odd digits? Answered by Penny Nom. 





Adding mixed numbers 
20131120 

From Kathy: 1 3/4 + 1 2/3= ?
5 1/2  2 5/6= ? Answered by Penny Nom. 





Two, 2digit numbers 
20130924 

From Tony: Write a problem that has two 2digit numbers.
solve your problem. Answered by Penny Nom. 





What is the value of 2((i)^(1/2))? 
20130722 

From Delilah: What is the value of 2((i)^(1/2)) ?
i.e. absolute value of 2 multiplied by square root of i. Answered by Penny Nom. 





Two numbers whose difference is 16 
20130608 

From Johan: Two numbers whose difference is 16 and whose sum is 120 Answered by Penny Nom. 





Write a rule for the sequence 
20130220 

From Angelia: Write a rule for the sequence. Then, find the unknown term. 1 3/8, 1 ¾, 2 1/8, _______, 2 7/8 Think: The pattern is increasing. Add 1/6 to find the next term. Rule: _______________ Answered by Penny Nom. 





2 1/4 x 1/8 x 1 3/4 x 12 4/9 x 3 
20121221 

From Tony: Ok my question
2 1/4 x 1/8 x 1 3/4 x 12 4/9 x 3
I just can't figure out the question ? Answered by Penny Nom. 





Some 4 digit numbers 
20121025 

From samira: How many 4digit numbers are there in which the first and last digits are the same? Answered by Penny Nom. 





Some 6 digit numbers 
20121023 

From Mason: How many different 6 digit numbers can you make using the digits 1 ,2 5, 6, 7, and 9? How many of these sixdigit numbers are divisible by 6? Answered by Penny Nom. 





Six digit numbers 
20120911 

From Fiona: using the numerals 0, 2, 3, 5, 7, 9, make as many sixdigit numbers as you can. Rearrange them into ascending order Answered by Robert Dawson. 





Kirkman schoolgirl problem 
20120818 

From Anthony: need to have the number from 115 in 6 rounds of 3 numbers without the numbers be repeating in the same row . eg round 1
1 2 3
4 5 6
7 8 9
10 11 12
13 14 15
2nd round
1 4 7
10 13 2
5 8 11
14 3 6
9 12 15 Answered by Chris Fisher. 





A number puzzle 
20120407 

From Kenya: my number is less than 25
my number of tiles will make only one rectangle
my number is odd
my number is a factor of 36 Answered by Penny Nom. 





Square numbers 
20120317 

From david: How many square numbers are there between 0 to 100? Answered by Penny Nom. 





Properties of real numbers applied to subsets 
20120201 

From Mark: Hello 
The questions that I have for you is do the properties of real numbers (such as the associative, commutative, identity, inverse, and distributive law) apply to ALL the subsets of real numbers? In other words, do all those properties work for the Natural Numbers? The Whole Numbers? And so on and so forth. I understand that they are all real numbers, but for instance: the identity is whenever you add zero to a number, you get that number back. But does that work with, say, with only the odd numbers? Zero isn't odd so can that property actually apply to JUST the odd numbers? Any consideration would be greatly appreciated! Answered by Robert Dawson. 





Triangular numbers that are square 
20111227 

From Luke: The “TnS” is a positive integer which is both Triangular number
and Square number. For example, 36 is a “TnS” number
since 36=1+2+3+4+5+6+7+8 (Triangular number)
and 36=6x6 (Square number).
What is the next “TnS” which is greater than 36? Answered by Penny Nom. 





The number of digits in a number base m 
20111222 

From Jash: Assume there is a number system of base m.
The one property of this system is: If 2 numbers written in this system, which have 'a' and 'b' as the number of digits are multiplied, then the product of the 2 numbers will have a number of digits which is a function f(a,b).
In other words, as long as the number of digits of the 2 numbers are constant, the number of digits of their product is a constant.
Find m. Answered by Robert Dawson. 





Extended real numbers 
20111212 

From Justin: Hi there, I was wondering does +infinity=+infinity in the extended real number system? Basically, I was wondering does +infinity=+infinity since infinity and any extended real number (except +infinity) are less than +infinity?
Sincerely,
Justin Answered by Robert Dawson. 





Three consecutive numbers 
20111129 

From Michael: Find three consecutive numbers such that the second number squared
is equal to the first and third added together Answered by Penny Nom. 





15 pigs and 6 pens 
20111116 

From Mike: I have 15 pigs and 6 pens, I have to put them in odd numbers, how do I do it. Answered by Chris Fisher. 





I started with Euler's identity and manipulated it 
20111114 

From anonymous: I started with Euler's identity and manipulated it
e^i*pi=1
e^i*pi=(1)^1
e^i*pi=1
e^i*i*pi=(1)^i
e^pi=(1)^i
e^pi=(1)^i
type it in in a calculator and you get e^pi=23.1406926... and
(1)^i=0.0432139183... What did I do wrong? Answered by Robert Dawson. 





Twice an even number 
20111010 

From Ron: The number of dollars that Tracy has in her pocket is an odd number.
Hal gave Tracy $2 more than she already had in her pocket.
The number of dollars Tracy now has cannot be _________.
a) $60 b) $62 c) $64 d) 68 Answered by Penny Nom. 





3digit, daily numbers 
20110929 

From Margaret: I need the list/group for a raffle that would contain the combinations
for a 3 digit (000999) daily number. There would be 100 tickets sold
with 10 3digit numbers from each numerical group beginning
from 000's, 100's 200's, 300's,...900's. No duplicates/replacement. What would be the
list of possible combinations of each group of 100 tickets, keeping each
different group/list of combinations in separate blocks of 100 tickets
without duplication. So I could use 1 list of 100 this year and the next list of
combos next year and so forth. Please help!
Example: 000,197,245,367,445,569,618,777,842,964
What would be the possible lists of each 100 tickets?
Thank you Answered by Penny Nom. 





One factor array 
20110916 

From Hana: hi my brother a 5th grade have a question. this is what it say "i have only one factor array, and i am between two numbers 12 and 16. what number am i?" Answered by Penny Nom. 





Ben's favourite numbers 
20110803 

From Luke: Ben challenges you to guess his favourite numbers by using the following three clues:
Each number is a fourdigit odd number.
Each is a palindrome
The digits of each number add up to 10
None of the numbers are divisible by 5 Answered by Robert Dawson. 





Two whole numbers 
20110511 

From yolanda: The sum of two whole numbers is 12.If the sum of the squares of those numbers is 74,what are the two numbers? Answered by Penny Nom. 





5 digit numbers using the digits 5 and 2 
20110427 

From sissy: I need a list of all possible 5 digit combinations using 5 and 2 numbers can repeat Answered by Penny Nom. 





Decreasing numbers 
20110413 

From Hadi: A number is called a "decreasing number" if each digit in the number is less than the digit to its left.
For example, 87420 is a deceasing number. How many fivedigit
decreasing numbers are there? Answered by Claude Tardif. 





8 3/8  6 1/4 
20110321 

From lenora: explain an error pattern in each of the following. 8 3/8  6 1/4 = 2 2/4 Answered by Penny Nom. 





Three consecutive odd numbers 
20110311 

From George: Write an equation three consecutive odd numbers whose sum is 75 Answered by Penny Nom. 





Three consecutive numbers 
20110131 

From parth: name 3 consecutive numbers,each less then a 100,the smallest # is divisible by 6 the next is divisibel
by 5 and the largest divisible by 4 Answered by Penny Nom. 





A mixed number 
20110130 

From Joyce: express the fraction as a mixed or whole number 94/5 Answered by Penny Nom. 





Find all the roots 
20101202 

From gagan: find all the roots of z^53z^4+2z^3+z^23z+2 Answered by Stephen La Rocque and Penny Nom. 





Ordering mixed numbers 
20101123 

From kate: what are the mixed numbers 5 7/9, 5 1/2, 5 11/18. put least to greatest? Answered by Penny Nom. 





i^i 
20101121 

From trale: Can we use e^ix=cosx+isinx for finding i^i like that: x= pi/2 =>
e^(ipi/2)=0+i then [e^(ipi/2)]^i=i^i.then we find i^i= 0,207879576....
is it true? can we give value for x for free?thank you. Answered by Harley Weston. 





What is the largest prime number? 
20101120 

From vadali: what is the largest prime number? Answered by Penny Nom. 





Fourdigit numbers using 0,3,4,5,6,and 7 
20101112 

From Katy: Using only the digits 0,3,4,5,6,and 7, how many distinct fourdigit numbers exist that are greater than 4002 and less than 6732? Answered by Stephen La Rocque. 





z^5  3z^4 + 2z^3 + z^2  3z + 2 
20101106 

From Kumar: would you please solve this problem, related to complex numbers.
Find all the roots of :
z^5  3z^4 + 2z^3 + z^2  3z + 2 Answered by Robert Dawson and Penny Nom. 





A Squared Number That's Negative 
20100922 

From David: What is the only number that when it's squared becomes negative? Answered by Stephen La Rocque. 





777777 times 111111 
20100707 

From Chew: What is 777777 times 111111 without using a calculator? Answered by Chris Fisher. 





Graphical Representation of Complex Numbers 
20100608 

From Anas: why do we write complex number a+ib as (a,b)? Answered by Janice Cotcher. 





11 trillion divided by 309,418,000 
20100605 

From Dion: I am struggling to calculate what 11 trillion divided by 309,418,000 is. Answered by Penny Nom. 





A quadratic equation with imaginary numbers 
20100603 

From Alissa: I am solving a quadratic equation and I got this far;
(x4+i)(x4i)=0
but how do I add the imaginary numbers
i know you multiply x by x and then add 4 + 4 but what do you do with the i's? Answered by Penny Nom. 





Four digit numbers 
20100522 

From tyeisha: Whats all the four digit numbers you can come up with using numbers 09 Answered by Tyler Wood. 





The sum of twice a number and 6 is 8 
20100512 

From MAE: THE SUM OF TWICE A NUMBER AND 6 IS 8 . FIND THE NUMBER Answered by Penny Nom. 





Odd numbers with no repeated digits 
20100501 

From jameka: How many odd numbers can be written from the set {2,3,4,5,6} if no digits may be used more than once? Answered by Penny Nom. 





A champagne tower 
20100416 

From gabriel: thanks for having something like this up online. My question is how do i build a Champagne Tower that has 290 glasses and 15 stories high.
Please help me out. this is for a clarity function. Answered by Robert Dawson. 





Body measurements 
20100406 

From Amirul: Recently I'm proposing my research question to my teacher for my extended essay. I'm an IB student.
My research question is regarding the estimation of human in buying trousers through reference of neck. What does the relation between the diameter of the neck and the diameter of the waist?
I want to see how far does the estimation theory is true for different type of people with different BMI(body mass index)..
But teacher said that it is golden ratio...so nothing interesting... =(
really??? But i search on net.... state that my idea seems do not have any relation with the golden ratio so far..... i just want ask you... am I able to perform in my extended essay if i continue with this research question?? Answered by Robert Dawson. 





A champagne pyramid 
20100322 

From Kathy: I have 680 champagne glasses and my pyramid can only be 15 levels high. How many glasses need to be on each level? Is there a formula I can use? Answered by Robert Dawson. 





7 odd numbers 
20100219 

From mike: Hello there,
Problem: find 7 odd numbers who sum is equal to 30.
Hint*My professor said it's possible to add 7 odd numbers and get 30 for an answer!
and he said we can use Negative and rational numbers but no decimal or fractions.
So is there anyway of solving this? Please get back to ASAP! thanks. Answered by Harley Weston and Tyler Wood. 





4digit positive numbers 
20100215 

From marjon: Find the sum of all the 4digit positive numbers with no zero digit. Answered by Penny Nom. 





Mixed numbers and multiplication 
20100208 

From Nick: Can you explain how this works, I have been going at it for hours and have a test friday and just cant get my head around the question
3 1\4 * 1/7 * 8
I have to express in lowest terms Answered by Penny Nom. 





Three digit odd numbers 
20100204 

From Rebecca: Question from rebecca, a student:
how many three digit odd numbers can be formed using the digits 1,2,3,4,5,6 without using any digit more than once? Answered by Tyler Wood. 





1/a + 1/b + 1/c < 1 
20100201 

From Mrityun: suppose a,b and c are natural numbers such that 1/a + 1/b + 1/c < 1. Prove that
1/a + 1/b + 1/c < = 41/42. Answered by Penny Nom and Claude Tardif. 





Mixed numbers 
20100113 

From Linh: Perform the indicated operations:
6 1/4 + ( 2/3) x 1 1/2 Answered by Penny Nom. 





A proof involving real numbers 
20100111 

From Amper: Let a,b is an element of real numbers, and suppose that for every x>0 we have a is lesser than or equal to b+x.
(a) Show that a is lesser than or equal to b.
(b) Show that it does not follow that a is lesser than b.
i'm feeling bad of having no idea with this, hope i you can help me. GRACIAS!! Answered by Penny Nom. 





A set of 5 numbers 
20100110 

From Marco: I need to generate in an Excel or other table all possible combinations for a set of 5 numbers with the following criteria:
1. Numbers can repeat.
2. Order does not matter.
3. Numbers may be from 09
4. The sum of all numbers is equal or less than 31.
5. The sum of all numbers is equal or greater than 10.
6. One of the numbers is 2.
7. One of the numbers is 5.
8. One of the numbers is 7.
Marco Answered by Penny Nom. 





Four digit numbers with no repeats 
20100102 

From Daniel: I want to know how many different numbers there would be between the numbers
00009999 that do not have any numbers that duplicate or repeat in the number? For example
the first number would have to be 0123 and the last would be 9876 (I think) Thanks! Answered by Penny Nom. 





Three digit numbers 
20091211 

From christopher: i need a list of all 3 digit combinations with repeat of a number thnx Answered by Penny Nom. 





Two digit numbers 
20091210 

From Jim: Can you tell me how many 2 digit numbers can be created
from the following:
1118539 Answered by Penny Nom. 





Three numbers that have the sum of 45 
20091204 

From amanda: there are three numbers that have the sum of 45.The greatest of the three numbers is 2 greater than the least number.What are the numbers?what is the formula to get the answer? Answered by Penny Nom. 





6 numbers from 12 
20091114 

From david: how many combinations of 6 numbers can there be using 12 different
numbers without using the same numbers more than once?
2, 3, 5, 8, 9, 11, 12, 14, 17, 19, 20 & 31. Answered by Penny Nom. 





A sequence of letters and numbers 
20091110 

From Maria: What is the last ten letters and numbers in the following series and how do I work it out so I can explain it to an eleven year old.
J1F8M1A0M1J0J1 Answered by Robert Dawson, Claude Tardif and Harley Weston. 





The cardinality of the prime numbers 
20091107 

From Justin: Hello there, I was just wondering since the number of primes is infinite,
are they equal to infinity or Alephnull?
Justin Answered by Robert Dawson and Victoria West. 





Tetrahedral numbers 
20091106 

From rena: consider the tetrahedral numbers 1,4,10,20, etc. Can these numbers be
described as a polynomial? If so, what is the degree of that polynomial? Answered by Stephen La Rocque. 





A number puzzle 
20091103 

From Jacqui: Write a number sentence. Use every digit once, 7, 4, 3, 6, 5,10. Insert math symbols +,  , *,/ and end up with the number 3. Use parentheses if necessary.
Jacqui Answered by Claude Tardif and Penny Nom. 





The extended real numbers 
20091102 

From Justin: Hello there, I was wondering is the set of extended real numbers a closed set or an open set?
Justin Answered by Robert Dawson. 





A number puzzle 
20090828 

From Angela: Taking 1 through 9 and using them only once subtract them to equal 33333 Answered by Chris Fisher. 





Primes 
20090625 

From Chinonyerem: If p = 2^k  1 is prime, show that k is an odd integer, except when k = 2.
[ Hint: 3/4^n  1 for all n >= 1.] Answered by Robert Dawson and Penny Nom. 





Is one Infinity larger than another in the extended real number system? 
20090624 

From Justin: Hello there, I was wondering if one infinity is larger than another in the extended real number system (just like in the transfinite ordinals and cardinals with respect to infinite sets) or are all infinities the same size in the extended real number system? Thanks sooo much for answering my question! I greatly appreciate it!
All the Best,
Justin Answered by Robert Dawson. 





Triangular Numbers 
20090616 

From Chinonyerem: Question from Chinonyerem, a student:
Each of the numbers
1 = 1, 3 = 1+2, 6 = 1+2+3, 10 = 1+2+3+4 ,...
represents the number of dots that can be arranged evenly in an equilateral
triangle:
.
. . .
. . . . . ...
. . . . . . . . . .
This led the ancient Greeks to call a number TRIANGULAR if it is the
sum of consecutive integers, beginning with 1. Prove the following facts
concerning triangular numbers:
(a) A number is triangular if and only if it is of the form n(n+1)/2 for some n >= 1
(b) The integer n is a triangular number if and only if 8n+1 is a perfect square
(c) The sum of any two consecutive triangular numbers is a perfect square
(d) If n is a triangular number, then so are 9n+1, 25n+3, and 49n+6 Answered by Penny Nom. 





A number puzzle 
20090610 

From Ann:
Hey,
I have a math problem that I can't solve which just happens to be a "mustanswer". The answer to the first problem is 25,452 and the second is 21,232. I know how to add but my teacher said that there is a pattern wherein you just have to look at the set of numbers and you already know the answer without really adding it first. Here are the condition of the problem:
1) the first, second and fourth numbers were provided by me. ( I have no idea how this works)
2) the third and the fifth numbers were given by the teacher. ( She's the one who knows the technique)
# She says that there is a "pattern."
Help me please as soon as you can. Thanks!!! Here it is:
5454 1234
+ 3636 5678 6363
4321
2323
8765
7676 1234
_______ _________
Please answer ASAP. Thank you!!! Answered by Penny Nom. 





A number puzzle 
20090517 

From Gita: Ok, we really need help for a homework problem due on Monday morning
I've been trying for 2 hours and can't figure it outif I can't I'm not sure
how my son can....We've been given a puzzle with the following rules:
The sum of each side must equal 15
We can only use the numbers 1,2,3,4,5,6,7, 8
A number can be used only once
(Hint: Think of all combinations of 3 numbers = 15)
The puzzle looks like this:
_____ _______ ______
_____ ______
_____ _______ ______ Answered by Penny Nom. 





15 pigs in 4 pens 
20090422 

From Melissa: A farmer has 15 pigs. He wants to put them all into 4 pens, have an
odd number of pigs in each pen, and have no pigs left over. Also, he
isn't thinking about having any for dinner, as they are his pets.
How does he do it? Answered by Robert Dawson. 





Fourdigit numbers 
20090411 

From jp: How many fourdigit numbers are there? Answered by Penny Nom. 





Choosing a 4 digit number at random 
20090324 

From shabkhal: If a fourdigit number is chosen at random, what is the probability that the product of the digits is 12. Answered by Harley Weston. 





wo consecutive numbers with a product of 9506 
20090225 

From sofie: find two consecutive numbers with a product of 9506 Answered by Penny Nom. 





More on cardinal numbers 
20090218 

From Justin: Hello again, I was just wondering that since the rules of Cantor's cardinal numbers in set theory do not apply to the infinity obtained by limits in calculus (ex. x>0, y=1/x=infinity), does that mean that this infinity is the largest quantity in both calculus and mathematics?
Justin Answered by Robert Dawson. 





In what base is 3x3= 10? 
20090214 

From David: In what base is 3x3= 10, 3x3=11, 3x3 = 12? is there a fast way to see this or do I have to create multiplication tables until I find the right one? Answered by Penny Nom. 





The page numbers in a book 
20090210 

From Nichole: It takes 852 digits to number the pages of a book consecutively. How many pages are there? Answered by Penny Nom. 





Missing three digits in a phone number 
20090130 

From Elmer: I have part of a phone number. the first 3 digits are 212, the last digit is four, and the three missing digits are all odd, how many numbers will I have to call to get the right number?
212 _ _ _ 4? Answered by Stephen La Rocque and Penny Nom. 





What is 301 million in word form? 
20090130 

From chyamber: What is 301 million in word form? Answered by Penny Nom. 





How many students were there 
20090125 

From sooos: After a math lecture in university, the students go to the cafeteria. EACH ONE of them buys a cheese sandwich and a cup of tea. They ALL pay $18.49. How many students were they? Answered by Chris Fisher. 





Multiplying negative numbers 
20090115 

From stephanie: hi, I'm currently working in a grade 8 class where the students are
learning about integers. the students were asked to find examples of how
integers are applied in real life. they were able to find aplications for:
adding and subtracting both positive and negative integers. however,
we could not find an example of where two negative integers would be
either divided or multiplied together in real life. For example: (2)(4)= +8.
please help. Answered by Harley Weston. 





What is a group of three numbers within a larger number? 
20081216 

From kim: My daughter brought home a question for math homework. What is a group of three numbers within a larger number? Answered by Robert Dawson and Harley Weston. 





Two numbers 
20081215 

From HERB: I am thinking of two whole numbers. When I add them , their sum is 123. When I subtract the lesser number from the greater number their difference is 45. What are my numbers? Answered by Penny Nom. 





Three onedigit numbers 
20081206 

From JOANNA: Could you please tell me what Adding Three OneDigit Numbers += 15 19 without using any number twice Answered by Penny Nom. 





Compatible numbers 
20081107 

From Erika: When working with compatible numbers, when do you choose to round up or down? For example: In the problem: 373 divided by 4, one could round 373 to 400 and keep the 4 the same, and the answer would be 100; OR, one could round 373 down to 360 and keep the 4 the same, and the answer would be 90. When given the problem as an assignment, which way dictates how one would round, up or down? Answered by Penny Nom. 





Compatible numbers 
20081030 

From Paul: Use compatible numbers to estimate the quotient of 23.52 and 11.04 Answered by Penny Nom. 





A product of positive and negative numbers 
20081003 

From kaylou: Suppose you were given 13 numbers and asked to find their product.
Seven of the numbers were positive, and the rest were negative.
Would your product be positive or negative? Why? Answered by Penny Nom. 





Compatible numbers 
20081002 

From jeff: what exactly are compatible numbers,
math problem is:
Estimate the total weight of 2 boxes that weigh 9.4 pounds and 62,6 pounds
using rounding and compatible numbers. Which estimate is closer to the actual weight and why? Answered by Harley Weston. 





Compatible numbers 
20080925 

From Katie: I am having trouble remembering how to find compatible numbers used to find the estimate in the foloowing problem. Can you please help me solve it and explain it to me? My son is in 5th grade and I need help. Thank you. Here is the problem: 2,752 / 28 estimate: 90 Answered by Penny Nom. 





Two consecutive numbers 
20080921 

From tomas: what is the two consecutive numbers with a product of 4160? Answered by Penny Nom. 





The number of digits in a really big exponent 
20080721 

From Pete: how would you find the number of digits in a really big exponent without a calculator? Answered by Penny Nom. 





???? x ? = ???? 
20080720 

From waiyan: ????
x ?
????
using 1 2 3 4 5 6 7 8 9 Answered by Janice Cotcher. 





Two numbers 
20080719 

From Jerry: while driving in my car early this morning, i 'discovered' something and want to ask if there is an equation that would fit it...
Here it goes..... take any two numbers (with the exception of two of the same numbers), multiply the first number by 2,
add the difference of the original two numbers, and the outcome will be the same as if you added the original two numbers together...
example: 3+5=8... thus, 3+3+(53)=8...
if you chose to reverse the numbers then..... 5+3=8... thus, 5+5(53)=8
i know, simple stuff.. but i just want someone to tell me what exactly this is.. is there a 'law' that describes this? Answered by Victoria West. 





equation? 
20080719 

From Jerry: while driving in my car early this morning, i 'discovered' something and want to ask if there is an equation that would fit it...
Here it goes..... take any two numbers (with the exception of two of the same numbers), multiply the first number by 2,
add the difference of the original two numbers, and the outcome will be the same as if you added the original two numbers together...
example: 3+5=8... thus, 3+3+(53)=8...
if you chose to reverse the numbers then..... 5+3=8... thus, 5+5(53)=8
i know, simple stuff.. but i just want someone to tell me what exactly this is.. is there a 'law' that describes this? Answered by Victoria West. 





Rational numbers 
20080716 

From hinal: list 12 rational numbers which lie between
a) 1 and 0
b) 3 and 3 Answered by Penny Nom. 





Two numbers whose sum is 25 and whose product is 120 
20080710 

From Michelle: Solve the following problem in at least two different ways.
Find two numbers whose sum is 25 and whose product is 120.
I know how to solve this problem by creating two equations
x+y=25 and xy=120 and then use substitution.
Are there any different ways of solving this problem? Answered by Janice Cotcher and Penny Nom. 





Probability and two digit numbers 
20080707 

From Peter: What is the probability that if you multiply two randomly selected two digit whole numbers, the result is greater that 100 and less than 200. Express your answer as a common fraction. Answered by Janice Cotcher. 





Some phone numbers 
20080630 

From star: What do you think the probability of finding the last 3 digits of a telephone number if the 1st digit begins with 7? Answered by Janice Cotcher and Harley Weston. 





Four digit combinations 
20080623 

From star: Can you you give me a list of all 4 digit combination starting with the number 7, for example 7123,7213. Answered by Penny Nom. 





How do you change bases? 
20080617 

From Peter: How do you change bases eg. 121 from base 3 to base 5? Answered by Penny Nom. 





Nine digit numbers 
20080521 

From Alex: List of Nine digit numbers, that can be divided by nine? Answered by Janice Cotcher. 





A problem with numbers 
20080518 

From Peter: When a certain number N is divided by d, the remainder is 7. If the original number N is multiplied by 5 and then divided by d, the remainder is 10, find d Answered by Stephen La Rocque and Penny Nom. 





Which is larger, 727464^512693 or 624610^518548? 
20080518 

From Yahweh: Lets say I have two very large numbers in the form of a^b:
727464^512693 and 624610^518548
I want to calculate which number is larger, but its unreasonable to type these numbers into a spreadsheet to get an answer right away. How could I determine the larger or the two numbers efficiently? Answered by Stephen La Rocque. 





Options 1 2 4 8 16 32 64 128 etc. 
20080509 

From Abraham: I have seen programs with options and I wish to create a similar program.
I have options 1 2 4 8 16 32 64 128 etc.
If I receive option 3 means option 1 and 2 are included. Option 20 means option 16 and 4 are included.
that because of the sum of those numbers is the olny way to get the given number.
I want to know if is there a way
to know which number from options are included.
How I know:
1 is Included
2 is Included
4 is Included Answered by Stephen La Rocque. 





(1i)ln(1+i) 
20080502 

From Kim: I am stuck on the expansion of (1i)ln(1+i)=(1i)[ln(square root of 2)+i(3.14/4 = 2n3.14)] Answered by Harley Weston. 





Why can't a square be twice another square? 
20080420 

From kim: why can't a square number double another one Answered by Penny Nom. 





The sum of some 5 digit numbers 
20080405 

From Tom: There are 120 fivedigit numbers that use all the digits 1 through 5 exactly once. What is the sum of these 120 numbers? Answered by Penny Nom. 





Compatible numbers 
20080404 

From dawn: Need help. Estimate the quotient. Tell what compatible numbers you used.
817divided by 4 = Answered by Penny Nom. 





Operation on the mixed numbers 
20080326 

From bradley: 1) Perform the indicated operation on the mixed numbers below; write answer in simplest form:
8 1/3 – 2 1/4
2) Perform the indicated operations on the mixed numbers below; write answer in simplest form; note;: "•" denotes multiplication:
2 1/2 • 3 2/3 • 5 3 Answered by Stephen La Rocque. 





The product of two numbers is 1,000,000,000 
20080314 

From Henry: What two numbers that don't in zero when multiplied equals 1,000,000,000 and same with 1,000,000,000,000,000,000. Answered by Penny Nom. 





Some threedigit numbers 
20080305 

From Toni: The following is a word pattern problem listed on my son's homework:
write a set of threedigit numbers that contain one odd number and three even numbers.
This confused the both of us because that would make his number a four digit number, right?
please respond. Thanks. Answered by Penny Nom. 





One number is four less than five times another number 
20080305 

From alice: One number is four less than, five times another number. The total of the two numbers is 50. What are the two numbers? Answered by Penny Nom. 





Fact family 
20080221 

From Anand: Can you think of a fact family that has only two facts? Write the fact family Answered by Penny Nom. 





7, 6, 5, 4, 3 and 2 digit numbers 
20080210 

From Edward: using the number 12345678 how many 7, 6,5,4,3 & 2 digit numbers can you make when not using any number twice in the same number Answered by Penny Nom. 





The sum of two numbers is 63 
20080207 

From kirk: The sum of two numbers is 63. The difference between the numbers is less than 10. Find all possible pairs. Answered by Penny Nom. 





Four digit numbers containing 85 
20080206 

From Vonda: How many four digit numbers contain the digit pattern 85 at least once and only once? Answered by Stephen La Rocque. 





A positive integer with 2007 digits 
20080206 

From Tom: Prove that there's a unique positive integer of 2007 digits lenght, divisible by 2^2007, and made up solely by the digits 2 and 5. Answered by Penny Nom. 





Multiplying decimal numbers 
20080205 

From alwyn: Why should when you Multiplying Decimal numbers is value becoming less and less? don't you think even decimal number is a quantity and in no chance when it multiplies its should become less or nil !!!
In fact all Multiplying and or adding the value will go up and only when you subtract and divide it should become less !! Answered by Stephen La Rocque and Penny Nom. 





Numbers and Operations 
20080202 

From Charlotte: On the TABE (Test for Adult Basic Education) test, one of the categories
is number operation. I would like to know what consist of number operation. Answered by Penny Nom. 





Choosing 10 numbers from 40 numbers 
20080118 

From Antwan: I have 40 numbers........number 140.
I want to know how many times i can chose 10 of those numbers without picking the same exact sequence twice if its even possible? Answered by Stephen La Rocque. 





The sum of two numbers is 36 
20080114 

From May: The sum of two numbers is 36.
Their product is 320.
What are the two numbers? Answered by Penny Nom. 





Negative numbers 
20071214 

From mannal: what negative integers do we use in the real world? like 30 temperature? Answered by Penny Nom. 





Improper fractions and mixed numbers 
20071212 

From Selah: How do I change an improper fraction to a mixed number? Answered by Penny Nom. 





Imaginary roots 
20071209 

From Josh: What is the correlation between imaginary roots (of a quadratic or other
polynomial equation) and the graph of the equation? As in, how can one
represent imaginary solutions graphically (and why does that work)? Answered by Harley Weston. 





Three consecutive numbers 
20071208 

From Aris: The product of 3 consecutive numbers is 1716. Find their sum. Answered by Stephen La Rocque. 





Representing different bases 
20071205 

From Sudhir: What does a number subscripted to another one denote? (I know that a number superscripted to another denotes the power, but the subscript number is something I have never seen before.) Answered by Stephen La Rocque. 





Compatible numbers 
20071119 

From Brendan: Let's say you have 291/2 and its between 281/2=14 and 301/2=15. My question is where do the
14 and the 15 come from or in other words how do you get those? Answered by Penny Nom. 





x^2 + x^3 = n^2 
20071114 

From Rapin: x and n are the whole number and less than 100 , x^2 + x^3 = n^2,
please help to solve this equation. Answered by Penny Nom. 





Whole numbers and improper fractions 
20071113 

From Jennifer: I would like to know how you convert whole numbers into improper fractions Answered by Melanie Tyrer. 





A number puzzle 
20071031 

From matthew: please help.make 200.take 4 numbers from the numbers 19,place the numbers
into a square containing 4 equal squares 1 number to each square.example
13
57 you now have 4 sets of numbers 13 ,57 ,reading across and 15 , 37. reading down
i have to find 2 or more ways of making i have to find the numbers that when added together
using this method make 200.you can only use each number once. Answered by Penny Nom. 





I am a prime number 
20071031 

From sherry: I am a prime number. I can not be shared fairly except by one group. My array can only be one row.
array can only be one row. Can you please explain this out to me so I can help my child with it.
Thanks Answered by Penny Nom. 





Compatible numbers 
20071030 

From Gary: How do I estimate the quotient. and then tell what compatible numbers were used. 703/7 Answered by Penny Nom. 





Complex numbers 
20071027 

From Dylan: My problem is to prove:
z^2 = zz* Where z is the complex number x + iy and z* is it's complex conjugate x  iy.
If the absolute value of i is 1, then it looks like: z^2 = x+y x+y = x^2 + 2xy + y^2
And zz* = x^2 + y^2. for these to be equal, 2xy = 0. This seems wrong to me. What am I doing wrong? Answered by Penny Nom. 





The largest number you can add ... 
20071026 

From Dryden: What is meant by asking what is the greatest number you can add to that number without having to regroup in any place? Answered by Penny Nom. 





4 odd numbers that equal 21 
20071015 

From gary: 4 odd numbers that equal 21 Answered by Penny Nom. 





Equivalent mixed numbers 
20071002 

From negra: an averagesized person can burn about 6 1/2 calories a minute while ridinng a bike. Which of the following is equivalent to that amount?
a) 1 2/2
b) 5 6/2
c) 6 2/4
d)6 2/6 Answered by Stephen La Rocque and Penny Nom. 





How many ten thousands makes one million? 
20071002 

From Payton: how many ten thousands makes one million? Answered by Penny Nom. 





Four digit odd numbers 
20070926 

From sonia: how many 4 digit odd numbers can be made using the digits 2, 5, 7, and 8 Answered by Penny Nom. 





A fraction that cannot be simplified 
20070917 

From Kevin: Make a fraction that cannot be simplified and has 24 as its denominator? Answered by Stephen La Rocque and Chris Langdon. 





How many two digit numbers contain at least one 7? 
20070906 

From Janet: How many two digit numbers contain at least one number seven? Answered by Penny Nom. 





Compatible numbers 
20070905 

From Beth: Estimate using compatible numbers:
2 X 3978 =
102/25 = Answered by Stephen la Rocque. 





Compatible numbers 
20070901 

From andrea: Estimate using compatible numbers. 249 /64 Answered by Harley Weston. 





How many three button codes are possible? 
20070823 

From kim: A home security device has ten buttons and is disarmed by pushing three buttons in sequence. How many three button codes are possible if each button can be pushed more than once in the code? Answered by Stephen la Rocque. 





Four digit numbers 
20070730 

From Spence: My son has a problem that he has been unable to figure out. I was asked to
try, but I am confused on how to get the last two parts. Any help would
be great.
Thanks
Spence
How many fourdigit numbers can be formed under each condition?
A) The leading digit cannot be zero: 9(10)(10)(10)=9000
B) The leading digit cannot be zero and no repetition of digits
allowed: 9(9)(8)(7)=4536
C) The leading difit cannot be zero and the number must be less
than 5000: ??
D) The leading digit cannot be zero and the number must be even:
?? Answered by Penny Nom. 





Multiplcation of two negative numbers 
20070726 

From Brett: Someone asked a question about multiplication and division of two negative numbers yielding a positive result here:
http://mathcentral.uregina.ca/qq/database/QQ.09.99/butler1.html I was not fully happy with the explanation b/c I want to give me daughter a realworld example and I can't seem to find one.
The following illustrates why multiplying negative numbers has become difficult to explain:
2 X 2 = 4
(4)(2)024
In this example we start with 2 and then want 2 more of them.
When we move across the number line from 2 to our answer, which is four, we have moved only 2 units to the right.
2 X 2 = 4
(4)(2)024
In this example we start with 2 and then want 2 more of them.
When we move across the number line from 2 to our answer, which is four, we have moved 6 units to the right.
How can the phenomenon of multiplying two negative numbers being more powerful than multiplying two positive numbers be explained?
Brett Answered by Stephen La Rocque and Harley Weston. 





(1  i)^5 
20070724 

From sofia: Compute the given arithmetic expression and give the answer in the form a + bi where a,b element in R.
1. (1  i)^5 Answered by Harley Weston. 





A complex number in polar form 
20070723 

From roland: write the given complex number z in polar form lzl(p+qi) where lp + qil=1 for 3  4i. Answered by Harley Weston. 





If A is 1 and Z is 26 
20070629 

From Sue: If A is 1 and Z is 26 is there a word that when you multiply all the numbers instead of letters adds up to a million? Answered by Chris Fisher and Harley Weston. 





The number of blocks on the face of a pyramid 
20070627 

From Heather: I was wondering if there was an equation in order to calculate the number of blocks on the face of a pyramid.
For example:
X
X X
X X X
Is there a specific formula in order to calculate that there are
6 blocks here?
Thank You,
Heather Answered by Harley Weston. 





Exponential form: x^y 
20070622 

From Kishor: whats the easy way to calculate X raised to Y where y is much greater than x. Answered by Stephen La Rocque. 





Simplifying complex denominators 
20070621 

From Krys: How do I simplify completely?
((4+i ) / (3+i ))  ((2i ) / (5i )) Answered by Stephen La Rocque. 





Compatible numbers 
20070615 

From meryl: what is a compatible number? ex.6,321/8 Answered by Penny Nom. 





Repeating decimals and rational numbers 
20070531 

From lil: Why are repeating decimals considered rational numbers? Answered by Penny Nom and Gabriel Potter. 





What is the highest known numerical value? 
20070529 

From Peg: What is the highest known numerical value? Answered by Gabriel Potter. 





Positive rational numbers 
20070522 

From Rebecca: What is the definition of positive rationals/positive rational numbers? Answered by Stephen La Rocque. 





Fractions and mixed numbers 
20070508 

From Amanda: I am having truble with this problem:
WRITE THE FRACTION 8/3 AS A MIXED NUMBER Answered by Stephen La Rocque. 





The sum of two or more consecutive integers 
20070426 

From nana: some numbers can be written as the sum of two or more consecutive integers(we consider positive integers only)
other number (eg. 4) cannot be express in this way.
let us call a number which can be expressed in this way a SOALTCI( sum of at least two consecutive integers)
a). list the first few SOALTCI and conjecture the general formula.
b). Prove that any number of the given form(in your answer (a)) is a SOALTCI Answered by Penny Nom. 





24 fourdigit numbers 
20070421 

From Megon: Of the 24 fourdigit numbers formed from the digits 1,2,3,&4 is there an easier way to find their sum other than writing them all out and totaling them by hand? Answered by Stephen La Rocque. 





Three digit numbers 
20070419 

From katelyn: How many 3 digit numbers can be created if each number is a multiple of 10? Answered by Penny Nom. 





How many different ways can she purchase candy? 
20070418 

From fathia: Stephanie can buy lemon candies for 3 cents each and chocolate candies
for 5 cents each. Stephanie has 64 cents to spend. How many different
ways can she purchase candy if she wants to spend all her money? Answered by Stephen La Rocque. 





12/(7  i) 
20070418 

From Diana: Perform the operation. Write all answers in a + bi form.
12

7  radical 1 Answered by Penny Nom. 





A subtraction problem with negative numbers 
20070412 

From Bridget: my daughter has to change a subtraction problem with negative numbers in it to an addition problem with negative numbers and then solve the problem such as:
4(2)=? Answered by Penny Nom. 





The sum of two rational numbers 
20070404 

From Fathia: Hi,
Could please help me with this question?
Prove that if a and b are rational numbers then a + b is a rational number.
Thank you, Answered by Stephen La Rocque. 





Two consecutive odd numbers 
20070319 

From Alicia: The sum of two consecutive odd numbers is divisible by 4.
Can you make similar statements about the sum of three consecutive odd
numbers and of four consecutive odd numbers?
Generalize your findings.
I tried :
n= smallest odd number
therefore the next = n, n+2 and the second =n+4 and the third = n+6
Now n+ n+2+n+4+n+6/4
Please help I am not sure of this I am just trying Answered by Penny Nom. 





Using complex numbers 
20070312 

From Kara: Do you use complex numbers in your job? Answered by Stephen La Rocque and Penny Nom. 





Seven digit account numbers 
20070309 

From Miranda: Account numbers for the Central Oil Company consist of seven digits. If the first digit cannot be 0, how many account numbers are possible? Thank you so much!!! Answered by Penny Nom. 





Four digit numbers 
20070226 

From Anton: Hello! I would like to ask you how many combinations are possible using 4 digit number. # # # # (1...9).There is no zero,numbers don't repeat,second and forth are odd.Thanks Answered by Penny Nom. 





What are the two numbers? 
20070225 

From Thomas: Two numbers have a total of 32 and a difference of 14. What are the two numbers? Answered by Stephen La Rocque. 





Exponential form of complex numbers 
20070212 

From Austin: When dealing with imaginary numbers in engineering, I am having trouble getting things into the exponential form. The equation is 1+i now I do know that re^(theta)i = r*cos(theta) + r*i*sin(theta). Just not quite understanding the order of operations. Thanks Answered by Penny Nom. 





Prime numbers 
20070116 

From A student: are the product of two prime numbers always prime? Answered by Penny Nom. 





21 pigs and only 4 pig pens 
20070111 

From Emma: i was given this pig pen problem. if there are 21 pigs and only 4 pig pens how can you distribute the pigs into the pens and have an odd number of pigs in each pen. it doesn't seem possible to me. i need help! Answered by Haley Ess. 





A word problem 
20070105 

From Harold: the sum of one number plus four less than five times another is 26. Answered by Penny Nom. 





Phone number combinations 
20070104 

From Efrain: i want to know the different combinations for numbers 7 digits the number are 09 its basically the different phone number combinations example: 5556689 or 5654896 i just want to know for many different combinations are there.... Answered by Penny Nom. 





A word problem 
20061230 

From Harold: one number is less than 5 times another number. sum of the numers is 26 Answered by Penny Nom. 





1, 3, 6, 10... 
20061215 

From Lisa: What is the nth term for the sequence, '1, 3, 6, 10...' and could you say how you got the anwser. Answered by Stephen La Rocque and Penny Nom. 





The absolute value of imaginary and complex numbers 
20061211 

From Keith: i don't get how to find the absolute value of imaginary and complex numbers here is an examples from the text book the answers are given but they don't show the work so i can follow along just show me the work please and explain how it is done
problem 3+4i Answered by Stephen La Rocque and Penny Nom. 





Four twodigit numbers 
20061202 

From Mary: I have four twodigit numbers written on my paper. The sum of these 4 numbers is less than 100.
True or False  each number is less than 25
If all the numbers on my paper are different, what is the largest (twodigit) number I could possibly have written. Answered by Stephen La Rocque. 





The sum of prime numbers 
20061128 

From Rambabu: I would like to know the sum of prime numbers below some X say 10000. Provide me with easy way to get this done Answered by Penny Nom. 





Number combinations 
20061109 

From Bob: how can I find out all the different combinations for the numbers 8168 example 8168, 8868, 1688,1886,6818 etc. how many are their. Answered by Penny Nom. 





The real numbers with decimal representations consisting of all 1s. 
20061029 

From Ivessa: Determine if the following set is countable or uncountable : the real numbers with decimal representations consisting of all 1s. Answered by Steve La Rocque and Walter Whiteley. 





Four digit combinations 
20061026 

From Sasha: CAN YOU LIST ALL OF THE POSSIBLE 4 DIGIT COMBINATION'S, THAT DO NOT START WITH 0? Answered by Stephen La Rocque. 





Three consecutive odd numbers 
20061021 

From Pige: The sum of three consecutive odd numbers is 387. Find the numbers. Answered by Penny Nom. 





Write the digits 1 to 9 on index cards, ... 
20061019 

From Kim: Write the digits 1 to 9 on index cards, arrange the cards to form three 3digit numbers (using each card only ONCE). The third number is the sum of the first two numbers ** how many different ways can you do this?? ** Answered by Penny Nom. 





The sum of two whole numbers is 72 
20061018 

From Kelin: The sum of two whole numbers is 72. Their differences is 48. What are the two numbers. Answered by Stephen La Rocque and Penny Nom. 





How many students are in the class? 
20061012 

From Lillian: There is one more boy than girls in the class, how many students in all? Answered by Stephen La Rocque. 





Four fours 
20061008 

From Prabh: Find out 10 BEDMAS problems using order of operation with only four 4's in the problem. The solution must be the digits 110.
Example 44/44=1 Answered by Stephen La Rocque. 





What number could it be? 
20060927 

From Jonathan: What number could it be?
It is between 12000 and 13000
Its hundreds, ten and ones digits are all odd
the sum of all its digits is 12. Answered by Steve La Rocque and Claude Tardif. 





A remainder of 1 
20060913 

From Juan: What is the smallest counting number which when divided by any of the numbers 2,3,4,5,6,,7,8,9 and 10, leaves a remainder of 1? Answered by Paul Betts and Claude Tardif. 





How many different threedigit numbers can you make using ... 
20060912 

From Beth: How many different threedigit numbers can you make using the numbers 2, 5, 7, 8 using the digits any number of times? Answered by Stephen La Rocque and Penny Nom. 





How many thousands are in ten million. 
20060824 

From Echoe: How many thousands are in ten million. Answered by Stephen La Rocque. 





The last digit of a sixdigit number is 2. 
20060709 

From GG: The last digit of a sixdigit number is 2. If the 2 is moved to the start of the number, the new sixdigit number is only a third of the original number. Find the original number.
Answered by Paul Betts, Chris Fisher, Penny Nom. 





As close to 841 as possible 
20060621 

From Alan: using these numbers by either add subtract division multiply come up with the answer as close to 841
100 25 10 7 6 3 Answered by Paul Betts. 





express the number 100 using the same figure 6x 
20060617 

From A student: express the number 100 using the same figure 6x Answered by Stephen La Rocque. 





how do i find i^22? 
20060612 

From Sky: how do i find i^{22}?
Sky Answered by Stephen La Rocque. 





What is the sum of the first 100 whole numbers? 
20060531 

From Jo: what is the sum of the first 100 whole numbers? Answered by Natasha Glydon, Paul Betts and Penny Nom. 





Three questions 
20060517 

From Diane:
Question:
I
What is the largest real number less than 10?
1 there is no largest real number less than 10 or
2 9
or
3 9.999...
II
Given that not (a and b) implies c.What does
(not c) imply ?
1a and b
2 (not a and b) or (a and not b)
3 (not a and b) or (a and not b)
4 a or b
III
What are the x and y intercepts of the equation
2x + 3y 6 =0 ?
1 x=3 and y=2
2 x=6 and y=2
3 3x + 2y =0
Answered by Paul Betts. 





What is the radius of the sphere? 
20060517 

From Jimmy: The surface area and volume of a sphere are both equal to the product of 4digit whole numbers and pi. What is the radius of the sphere? Answered by Stephen La Rocque. 





Four digit numbers 
20060325 

From Kenvin: i was wondering how many possibilities is there for a four digit number with the same first two numbers and the last two is not one of the first with numbers 19 Answered by Stephen La Rocque. 





Five digit numbers 
20060325 

From Tony: Can someone tell me how many unique five digit numbers can be generated using 09? Answered by Stephen La Rocque and Penny Nom. 





given that p is a prime and pa^n, prove that p^na^n 
20060324 

From Janna: given that p is a prime and pa^{n}, prove that p^{n}a^{n} Answered by Stephen La Rocque. 





A nine digit number 
20060306 

From Ryan: What is the total number of possible combinations of a nine digit number (ie., social security number) including repeating numbers? Answered by Stephen La Rocque and Penny Nom. 





The meaning of numbers 
20060303 

From John: I'm having a philosophical debate on the meaning of numbers, equations, or the world of math in general. Would it be possible if you could help me by giving me a resource that talks about it or if you have your own opinion I would be most grateful. Answered by Harley weston. 





A triangle of 50p pieces 
20060222 

From Stuart:
Ok, so i am collecting 50p pieces and arranging them on my desk in the shape of a triangle.
eg
50p
50p 50p
50p 50p 50p
50p 50p 50p 50p
I want to work out how much money I'm saving just by knowing how many rows of coins there are. If i can work out how many coins there are just by knowing how many rows I have I can just divide by 2 to find out the amount in dollars.
Answered by Penny Nom. 





sinh(i/2) 
20060209 

From Louis: How can you set up an equation to find sinh(i/2) Answered by Penny Nom. 





Write the array for 3 
20060129 

From Jamie: My son is a 5th grader and came home with a math question that I can't answer. The question stated  "Write the array for 3" I don't understand how this can be done with just one number. Answered by Penny Nom. 





GCF, LCM, primes and the ladder method 
20060107 

From Linda: How would I teach both finding the GCF and LCM with prime factors...I recall the ladder method vaguely.??? Answered by Penny Nom. 





The square root of i 
20051130 

From Kevin:
If the square root of 1 is i, what is the square root of i?
How can you find the log of a negative number?
What is the log of 1?
Answered by Claude Tardif. 





100, 000 or 100 000 
20051121 

From Jacqui: I am a parent of a grade 6 student and need to confirm that commas are no longer used when writing numbers (the Canadian method). For example, how do you write one hundred thousand? 100, 000 or 100 000 Answered by Diane Hanson and Harley Weston. 





5 digit numbers that include 5 and exclude 8 
20051104 

From Paul: figure out
how many 5 digit numbers are there that include the digit 5 and exclude the
digit 8.
show me how to do get to the answer. (23816) Answered by Paul Betts. 





A sum of 75 and a difference of 13 
20051030 

From Vicki: Find two numbers that have a difference of 13 AND A SUM OF 75? We need to learn about the formula or procedure. Answered by Penny Nom. 





Two 3digit numbers 
20051027 

From Melissa: I can't figure this out, The question is
Find the greatest possible difference of two 3digit numbers that use the digits 3, 5, 7 and 9 only once in each number.
The teacher says the answer is 62 but I can't figure out how she did it. Can you help. Answered by Claude Targif and Penny Nom. 





What number am I? 
20051027 

From Samantha: First 8 is added to me, then I am multiplied by 6. Then 40 is subtracted from me. Finally, I am divided by 10. The result is 11. What number am I? Answered by Penny Nom. 





Improper fractions 
20051021 

From Joe: Is a whole number an improper fraction. For example, is 4 an improper fraction? Is 4 an improper fraction? Is 4 the simplest form for 20/5? Are 4 and 20/5 equivalent fractions? Answered by Penny Nom. 





Divisibility by each of the first ten counting numbers 
20051017 

From Simon: determine smallest positive integer that is divisible by each of the first ten counting numbers Answered by Penny Nom. 





Whole numbers 
20051010 

From Kirk: Can the sum of two or more whole numbers be less than any of those numbers? Answered by Penny Nom. 





Four digit numbers 
20051009 

From David: I had a discussion with my father about how many four digit numbers you can make with 09. He was saying that there is 12,000 and that seems quite high for me. But can you tell me how many there are, and what exactly are they? Answered by Penny Nom. 





Three digit numbers 
20051004 

From Jordan: i need to know how many 3 digit numbers there are Answered by Penny Nom. 





Use the numbers and symbols only once to come up with the answer 
20050919 

From Kaitlyn:
Question: I have math problem that no one in my class was able to solve but the teacher said it does have an answer. We need to use the numbers and symbols only once to come up with the answer:
36 18 12 6 +  ( )
______________________________ = 41
Answered by Claude Tardif. 





What is my number? 
20050916 

From Bob: I have 6 digits.
100,000th digit is one less than my ones digit, eight greater than my 1,000's digit, twice my tens digit and four times my 100s digit. My 10,000s digit is 0
What is my number? Answered by Penny Nom. 





A two digit prime 
20050912 

From A student: The units digit of a twodigit prime number is not greater than the tens digit by 3.If the positions of the two digits are interchanged, then the new number formed is greater than the original number by more than 18. Find the value of the original prime number. Answered by Penny Nom. 





Adding positive and negative numbers 
20050903 

From Billy: 46 + 24 =
38 + 22 =
19  20 = Answered by Penny Nom. 





1,4,9,1,6,2,5,3,6,4,9,6,4,8,1 
20050830 

From Liz: Find the next four numbers to the sequence 1,4,9,1,6,2,5,3,6,4,9,6,4,8,1,___,___,___,___. Answered by Penny Nom. 





1_2_3_4_5_6_7_8_9 = 1: Fill in the blanks 
20050826 

From James: Try to replace the blanks below with + or  to make the statement correct
1_2_3_4_5_6_7_8_9 = 1 Answered by Penny Nom. 





Their sum equals their product 
20050821 

From Claudio: Find a thousand natural numbers such that their sum equals their product. Answered by Penny Nom. 





Can one place 15 integers around a circle... 
20050820 

From Hernan: Can one place 15 integers around a circle so that the sum of every 4 consecutive numbers is equal either to 1 or 3? Answered by Claude Tardif. 





Which number is greater? 
20050818 

From Dante: Which number is greater: 888....88 X 333...33 or 444.......44 x 666........67 (each of the numbers has 1989 digits)? Answered by Claude Tardif. 





Converting rational numbers 
20050807 

From Joe:
I am helping my son with his converting rational
numbers in the form of A/B where A and B are integers and
B not equal to zero
I think I am doing this right but I am not sure so
below are the problems and our answers are beside
them, please let me know if these answerers are correct
Answered by Penny Nom. 





A set of numbers whose sum is 1 
20050721 

From Santos: Does there exist a set of numbers whose sum is 1, and the sum of whose squares is less than 0,01? Answered by Paul Betts. 





Seven digit numbers 
20050623 

From Ky: How many number combinations are possible for a 7digit number? How many people in a population can exist without having to exceed the seven digit combinations and having to revert to a 8 or 9 digit number? Answered by Penny Nom. 





Primes 
20050604 

From Fede: Prove that there is not a number prime p, for which the numbers p+5 and p+10 are prime too. Answered by Penny Nom. 





The numbers p and 8p^2 +1 are prime. 
20050530 

From Antonio: The numbers p and 8p^{2} +1 are prime. Prove that the number 8p^{2}+2p+1 is also a prime number. Answered by Claude Tardif and Penny Nom. 





5+5+5=550 
20050530 

From Bill:
5+5+5=550
This is a math equation that is not true.
How can it be made to be true by using only one line? Answered by Leeanne Boehm. 





Which is larger, 31^11 or 17^14? 
20050529 

From Linda: Which number is greater 31^{11} or 17^{14} (without using
calculator). Answered by Chris Fisher and Paul Betts. 





50^99 and 99! 
20050523 

From Romel: Which number is greater, 50^{99} or 99! Answered by Claude Tardif. 





Which is smaller 2^175 or 5^75? 
20050518 

From Sarah: Which is smaller 2^{175} or 5^{75}? without using a calculator. Answered by Claude Tardif. 





A pattern of numbers 
20050421 

From Claire: We need to be able to discover the nth term in a pattern of numbers and
explain how we did it. We have arrived at the formula 1+2+3+...n=n(n+1)/2
for trios where a trio series is;
3 has the following trio (1,1,1)
4 has the following trios (2,1,1), (1,2,1), (1,1,2)
5 has the following trios (3,1,1), (1,3,1) (1,1,3) (1,2,2) (2,2,1) (2,1,2)
So the series is as follows Answered by Penny Nom. 





Some four digit numbers 
20050416 

From Lori: can u give me every possible combination of four numbers starting with the number three Answered by Penny Nom. 





Prime numbers 
20050411 

From Jesule: Given that p, p+10 and p+14 are prime numbers, find p. Answered by Claude Tardif and Chris Fisher. 





Rational functions 
20050405 

From Nicole: My name is Nicole and I am a teacher at Weyburn Comprehensive School. I am currently teaching both Math B30 and Calculus 30 at the school and I have a question about rational functions. I know that if a rational function (by definition) has common factors in the numerator and the denominator then it is not a rational function (math b30) however in calculus this common factor creates a hole in our graph. Can you explain to me why a common factor or constant does not give us a rational function? Answered by Penny Nom and Leeanne Boehm. 





When dividing a 3digit number by a 1digit number... 
20050122 

From A student: When dividing a 3digit number by a 1digit number, for what divisors can you get a remainder of 8? Answered by Penny Nom. 





Numbers that John likes 
20050116 

From Garrett: John likes 400 but not 300; he likes 100 but not 99; he likes 3600 but not 3700. Which does he like?
900
1000
1100
1200 Answered by Penny Nom. 





Six digit numbers with at least one 7 
20041227 

From Behzad: How many sixdigit numbers contain at least one 7 in their decimal expansion? Answered by Penny Nom. 





Making the number 99999 
20041222 

From Lisa: Make as many equations as possible to make the number 99999 using all of the numbers 09 but only once per equation. example 01234 + 98765 = 99999 she needs to make 150+ equations. Answered by Paul Betts. 





Some numbers less than 100 
20040917 

From Paul: for how many numbers less than 100 is the digit in the ones place half the digit in the tens place? Answered by Penny Nom. 





Half way between 
20040908 

From Ben: Find the number halfway between the number shown
751,843 Answered by Penny Nom. 





A big number 
20040826 

From Mark: If you have $999,999,999,999,999,999,999,999,999,999.99 and you find a pennie how much is that and can you give me the name of it. Answered by Penny Nom. 





A big number 
20040808 

From Carter: Can you tell me what number this is?
10,000,000,000,000,000,000,000,000,000,000,000,000
Where can I find the names for big numbers? Answered by Penny Nom. 





Four digits 
20040710 

From Rob: I am always interested to know how the for digit works. I mean, you have correctly put it that the total numbers obtain from 0000 thru 9999 are 10,000. My question is, is there any simple formula to turn this simple 4 figures of say: 1234. Answered by Penny Nom. 





Factoring integers 
20040702 

From A student: After looking at all the info I could get about NFS, I still have some questions that are unsolved:
First of all: If someone found an algorithm that has a worst case running time of N*Log(N) to factor an integer n into his divisors, would it be quicker or slower then the number field sieve algorithm?
secondly, what exactly is the time complexity of the Number Field Sieve algorithm, if I would factor an integer n? Answered by Claude Tardif. 





Aunt Lucy's letter 
20040627 

From Olivia: "Dear bob,
now that i am getting on (70 today). i want to give you some of my money, i shall give you a sum each year, starting now. you can choose which of the following schemes you would like me to use.
a) £100 now, £90 next year,£80 the yaer after and so on.
b) £10 now, £20 next year, £ 30 the next year and so on.
c) £10 now, 1.5 times as much next year, 1.5 times as much the year after that and so on.
d)£1 now, £2 next year, £ 4 the year after, £8 the year after and so on.
of course these schemes will only operate while i am alive. i look forward to hearing which scheme you choose and why!
Best wishes,
Aunt Lucy." Answered by Penny Nom and Claude Tardif. 





Divisors of 2n+1 and 3n+9 
20040602 

From Chris: Amy selected a positive integer N and wrote numbers 2xN+1 and 3xN+9 on a whiteboard. Boris looked at the two numbers on the whiteboard and wrote in his notebook a positive integer that divides each of them. Find all possible numbers that Boris could have written in his notebook. Answered by Chris Fisher and Penny Nom. 





Numbers around a circle 
20040328 

From Rebecca: my maths question is use the numbers 1,2,3,4,5,6 and 7 place each number in a circle so each line adds up to 12. There are seven circles, six on the outside and one in the middle. Each number lines up with the middle number and the outside numbers line up with the one directly across from it as if a line was going through the middle number circle. Answered by Penny Nom. 





z^2 = 3  4i 
20040326 

From John: Solve: Z^2 = 3  4i Answered by Harley Weston. 





Large exponents 
20040326 

From John: I
have encountered problem with the lack of memory every calculator
seems to have. No calculator, on or off the computer, I've found
has the amount of memory or writing space to calculate the sums I want
to solve. The sums are in great importance for my continued progress.
The sums are following:
16777216^1310270, 16777215^995328, 16777215^786432 and 16777215^480000 Answered by Claude Tardif. 





Some number problems 
20031224 

From Shruthi: 1. Write 31 using 3 five times
2. Write 100 using all the 10 digits just once
. . . Answered by Penny Nom. 





400, 100 and 2500 
20031221 

From A student: A person likes 400 but dislikes 300
He also likes l00 but dislikes 99
He also likes 2500 but
dislikes 2400
Which of the following does John like
900, 1000, 1100 or 2400
Answered by Penny Nom. 





Four digit numbers 
20031120 

From Rob: Hello, I sure hope you can answer this question. I got into a discussion at work about how many possible combinations there are for a four digit number using the numbers 0 through 9. This was in reference to a discussion about the lottery. I said there was only 10,000 possible combinations. My friend said that there was many times more, but he could not remember how to figure it out. The answer and the formula would be greatly appreciated. Answered by Penny Nom. 





The product of the page numbers 
20031107 

From Morgan and Mom: You open a book and the product of the page numbers is 12,656. What are your page numbers? Answered by Penny Nom. 





Pairs of prime numbers 
20031013 

From Nikolas: Use pairs of prime numbers to find all the numbers less than 50 that have only two prime factors. Make an organized list. Answered by Penny Nom. 





Primes 
20030923 

From Julie:
#1. Suppose you are given a number (n) and told that 1 and the number (n) divide into (n). Does that mean (n) is prime? #2. Suppose that p is a prime number greater than or equal to 3. Show that p+1 cannot be a prime number. Answered by Penny Nom. 





The Sieve of Eratosthenes 
20030918 

From Lynn: My daughter has been asked to find all the prime numbers by using the Sieve of Eratosthenes. I have no understanding what this means. Answered by Penny Nom and Claude Tardif. 





How high does the sequence of numbers go 
20030907 

From Shayna: My quetion is "How high to the sequence of numbers go"? e.g. one, ten, hundred, thousand, million, billion, trillion, and from there is my queston. Answered by Penny Nom. 





Two row arrays 
20030903 

From Madalyn: My question is, what are #'s that can not be arranged in two row arrays called? Answered by Penny Nom. 





X.9999... and X+1 
20030823 

From David: I have read your answers to the questions on rational numbers, esp. 6.9999... = ? and still have a question: The simple algebraic stunt of converting repeating decimals to rational numbers seems to work for all numbers except X.999999.... where X is any integer. The fact that the method yields the integer X+1 in each case seems to violate the completeness axiom of the real numbers, namely that there is no space on the number line which does not have an number and conversely that every geometric point on the number line is associated with a unique real number. In the case of 3.999... for example, it seems that both the number 4 and the number 3.9999.... occupy the same point on the number line. How is this possible??? Answered by Penny Nom. 





39 consecutive natural numbers 
20030819 

From A student: Prove that among any 39 consecutive natural numbers it is always possible to find one whose sum of digits is divisible by 11. Answered by Penny Nom. 





nine digit numbers 
20030723 

From John: With a nine digit number, with each of the nine digits having a possibility of 10 different numbers then what is the total number of possible mathematical variations in the nine digit number. i.e. Social Security numbers have nine digits and if each of the nine digits have a possibility of being any one of ten numbers, i.e. 0,1,2,3,4,5,6,7,8,9. Then what is the formula to calculate the maximum possible number of variations in this nine digit number and what is the mathematical maximum possible number of variations of this nine digit number? Answered by Penny Nom. 





Numbers John likes 
20030620 

From Steve: John likes 400 but not 300; he likes 100 but not 99; he likes 2500 but not 2400.
Which does he like? 900 1000 1100 1200 Answered by Penny Nom. 





The sum of two numbers is 5 and their difference is 
20030616 

From Akhil: The sum of two numbers is 5 and their difference is 11. What is the product of the two numbers? Answered by Penny Nom. 





Real numbers 
20030509 

From Sirena: what is a "real" number Answered by Penny Nom. 





Harmonic numbers 
20030319 

From Becky: Harmonic numbers are Hn = 1 + ? + 1/3 + . . . + 1/n
Use induction to prove the following theorem: For all natural numbers n, H1 + H2 + . . . + Hn = (1+n)Hn  n Answered by Penny Nom. 





1 followed by a million zeros 
20030319 

From David: What do you call the number represented by the numeral '1' followed by one million zeros? Answered by Penny Nom. 





1575 
20030313 

From Sharyn: find 6 integers that when multiplied with each other equal +1575 and when the same integers are added together equal zero. there are more positives than negatives and one of the numbers is a double digit between 10 and 20 Answered by Penny Nom. 





Harmonic numbers 
20030312 

From Becky: What can you tell me about the limit of harmonic numbers as it reaches infinity? Answered by Penny Nom. 





Hundreds, thousands, millions,... 
20030219 

From Karissa and Jasmeen: hundreds, thousands, millions,  can you help us with the rest of this sequence  we are trying to find the largest number Answered by Penny Nom. 





6 digit numbers from 0,0,2,2,4,4 
20030123 

From Amanda: How many 6 digit numbers can you make from the numbers 0,0,2,2,4,4, giving that 0 cannot come first. The number has to contain 2 twos, 2 fours, and 2 zeros. Answered by Penny Nom and Claude Tardif. 





What is larger than infinity? 
20030112 

From Dana: What is larger than infinity? Answered by Claude Tardif and Harley Weston. 





ALL of the possible 3 digit combinations of 0  9 
20021209 

From Melissa: I need to find out ALL of the possible 3 digit combinations of 0  9. Eg: 000,001,002,003. This is going to take me VERY LONG time. Any suggestions. Answered by Penny Nom. 





Making 7 
20021126 

From Bill: At one time I had the answer to this math equation but I have lost it and can't seem to regain it. I may be going at it wrong but as I recall there were the numbers 1 through 4, and the std operators, +, , /, *, and parentheses. The object was to make the four numbers with the operators equal to 7. Each number and operator may be used only once. My 9 year old loves these quizzes but I can't give it to her if I can't provide the correct answer. Answered by Claude Tardif. 





4 x abcd = dcba 
20021120 

From A student: Say you have a four digit number (e.g. abcd) and you multiply the number by 4. The answer you get will be the reverse order of the number you started with (dcba). What is the number? The four digits (a,b,c,d) cannot be the same number or cannot be repeated. Answered by Penny Nom and Claude Tardif. 





Why is 5 divided by 1/7 greater than 5 divided by 2/3? 
20021119 

From Elizabeth:
 Without performing the division, explain why 5 divided by 1/7 is a number greater than 5 divided by 2/3.
 Is the least common multiple of two prime numbers always their product? Why or why not?
Answered by Diane Hanson and Penny Nom. 





The product of two consecutive numbers is 41 more than their sum 
20021115 

From A mother: THE PRODUCT OF TWO CONSECUTIVE NUMBERS IS 41 MORE THAN THE SUM OF THE NUMBERS. WHAT ARE THE NUMBERS? Answered by Penny Nom. 





Prime numbers 
20021108 

From Lonna: Is 2 a prime number or not?? Why is 1 not considered a prime number? Answered by Penny Nom. 





7+8+9+...+1000 
20020911 

From Shirley: My question is what is the formula for adding up numbers when you don't start with number 1? For example 3 + 4 + 5 + 6 = 18. But how could you arrive at the answer without adding all the numbers? Answered by Penny Nom. 





Subsets of the Real Number System 
20020907 

From Christine: In looking for a French equivalent of the word "integer", I found that the word seems not to actually exist in French, and that Canadian schools use the term "natural number" to describe what we have been trained to call "whole numbers," while using the term "whole number" to describe what we have been trained to call "integers." Answered by Claude Tardif. 





Social security numbers 
20020906 

From Chris: How many different number combinations are there for the social security system? We know that there are only a certain ammount of combinations available and the current US population is at 281 million. The number system should include as many nine digit combinations as possible using the numbers 09 in multiple different spots. Answered by Penny Nom. 





Express 5120 as a sum of consecutive numbers 
20020825 

From Todd: Express 5120 as a sum of more than 1 consecutive number. Answered by Leeanne Boehm. 





As much greater than 47 as it is less than 105 
20020723 

From Joe: To find the number in question you need to find the number exactly halfway between 47 and 105. Another way of thinking about the number that is halfway between two other numbers is as the average of the two numbers given. Answered by Leenaan Boehm. 





Place six numbers around a triangle 
20020719 

From Monika: I need to place six numbers around a triangle, as such that one number is on each corner, and one number on each side making three numbers in one line, adding up to two hundred exactly. The number I have to use are, 40, 50, 60, 70, 80, 90. I have to use each one once, there for, each number cannot be repeated. Answered by Claude Tardif and Chris Fisher. 





Can you make up a word that adds up to 1000000? 
20020719 

From Adrie: My question is elementary and I am a student Please help me with the following conundrum, as it is driving me crazy.
'When the letters in the alphabet are given values from 1 to 26 for A to Z, can you make up a word that adds up to 1000000 ( one million )used as a multiplication?'
Like 'cat' would be 3*1*20 = 60 Answered by Claude Tardif. 





Square numbers 
20020501 

From Sally: Is one considered a square number? Answered by Penny Nom. 





a+b=10 and ab=40 
20020427 

From April: What two numbers add to ten and multiply to forty? (a+b=10, a*b=40) I think the answer includes radicals and/or imaginary numbers. Answered by Penny Nom. 





Triangular numbers 
20020426 

From Anika: Can you please tell me what a triangular number is? Answered by Penny Nom. 





An Olympiad problem 
20020423 

From Aurora: I wrote a mathematical Olympiad the other day and there was one question that I could not work out. The question was If ab = 1, bc =2, cd =3, de =4 and ea = 6, what does a + b + c + d +e = It was a multiple choice and the answers were : 43/6; 47/6; 49/6; 53/6; 61/6 The correct answer was 61/6, but how can do you get to that answer? Answered by Anrei Volodin. 





How many different account numbers are possible? 
20020418 

From Andrene: how many different account numbers are possible if the account numbers consist of a letter of the alphabet, followed by five numerical digits, and followed by another letter. Answered by Penny Nom. 





The square root of i 
20020314 

From Arlene: what is the square root of i, if i=x+yi? what is the square root of 1i? i'm getting problems like these in which I do not understand. Answered by Harley Weston. 





Mixed numbers, whole numbers and improper fractions which are less than 2. 
20020303 

From Dawn: Change each mixed number to a whole number and an improper fraction which is less than 2. 3 1/2 = 2 / Answered by Penny Nom. 





Alfredos house number 
20020221 

From Aunt Patty: Alfredos house number is between 20 and 35. The sum of the digits is less than 5. If you subtract 1 from it you would get a multiple of 3. If you add three, you get a multiple of 5. What is Alfredos house number. Answered by Penny Nom. 





Shipping charges 
20020219 

From Sohail: A mail order company charges a fixed fee for shipping merchandise that weighs 1 pound or less, plus an additional fee for each pound over 1 pound. If there shipping charge for 5 pounds is $4.80, and for 12 pounds is $6.20, find the fixed fee and the additional fee. Answered by Penny Nom. 





A farmer takes 100 animals to the market to sell. 
20020219 

From Ann: A farmer takes 100 animals to the market to sell. All are sold and $100 is earned. The prices were $5.00 per cow, $1.00 per sheep and $.05 per pig. At least one of each kind of animal was sold. How many of each kind of animal did the farmer take to market? Answered by Penny Nom. 





Square arrangements of clovers 
20020203 

From Cassie: Clyde had a strange fascination with numbers. One day he decided to mount his 4 leaf clover collection in groups of square numbers.he took a long piece of butcher paper and glue and began this arduous task.There was 1 clover,4 clovers.and then 9 clovers in the third set. what would be in the seventh set of 4 leaf clovers? Answered by Penny Nom. 





Making 24 
20020117 

From Renee: My 4th grade daughter and I need to find a simple math sentence using 5, 5, 3, & 7 to equal 24. You can add, subtract, divide or multiple. Answered by Penny Nom. 





What is a group of three numbers called in a large number? 
20020115 

From Laurie: What is a group of three numbers called in a large number? My son has this question on his 4th grade worksheet. I've taught middle school math for 7 years and nver heard of it. Answered by Paul Betts. 





Why do integers have the symbol of Z? 
20020111 

From Stephanie: Why do integers have the symbol of Z? Natural numbers have the symbol of N, whole numbers have the symbol of W. Our professor has asked us to find out why the letter Z is represented for integers. Answered by Penny Nom. 





Some functions without numbers 
20011116 

From A student: I have a worksheet that is about functions. It doesn't only use numbers. I need help to figure out the function and the solution to how the answer is solved. Answered by Claude Tardif. 





Numbering pages 
20011115 

From Lucy: A printer uses 1008 digits to number the pages of a book. How many pages are there in the book? Answered by Penny Nom. 





Negative numbers 
20011115 

From Jewel: If zero means nothing or an empty set, then how can a number be less than zero, as in negative number? My understanding of negative numbers is distance from a set point in a given direction. Thus having a negative and positive side of a line is arbritary and is related to displacement rather than value. Am I in error? Answered by Penny Nom. 





Squares of negative numbers 
20011103 

From Susana: I wanted to know if I can square a negative number..? Answered by Leeanne Boehm. 





Squares of one digit numbers 
20011015 

From Needa: What two twodigit numbers are each equal to their rightmost digit squared? Answered by Penny Nom. 





e^{ix} = cosx + isinx 
20011010 

From Peter: Given: e^{ix} = cosx + isinx  substitute x for x to find e^{ix}, simplifying your answer
 use the given and part a to find an identity for cosx making no reference to trig functions
 find an identity for sinx
 .
 .
Answered by Penny Nom. 





Six nines 
20011009 

From A mom: My middle schooler (sixth) has to calculate the integers 020 using only 6 nines. We have done all but the integer 14. He can not use decimals or double the nine like 99 or 19. the fraction 9/9 is okay. Keep in mind of course the order of operations. Answered by Claude Tardif. 





Building numbers 
20011002 

From Dorothy: Using only the numbers 1, 2. 3 & 4 and the order of operations make problems that have the answers of 1 to 50. Use each digit only once per problem. Use +, , x, (), exponents or use 2 digits to form a 2 digit number Example 1,2=21 or 12. No Division. We have been able to do all the problems except finding the answers of 7, 22, 31, 34, 42, 43 and 50. Answered by Claude Tardif. 





What are the two numbers? 
20010924 

From A student: What are the two numbers.  the sum of two numbers is 15. 6 times the smaller number is 4 times the larger number .find the two numbers.
 the sum of the two numbers is 28. 2 times the larger number is 5 times the smaller number minus 7. find the two numbers.
Answered by Claude Tardif. 





Integers 
20010909 

From A student: I am a Grade 9 student from Ontario Canada who has never understood how to do integers very well. I was wondering if you would be able to either send me some sites that will tell me how to calculate them in a simple way or if you would be able to write me back and give me some pointers. Answered by Leeanne Boehm. 





I have 6 digits. 
20010906 

From Kristan: I have 6 digits. My hundred thousands is 1 less than my 1 digit, 8 greater than my thousands digit, twice my tens digit, and 4 times my hundreds digit. My ten thousands digit is 0. What # am I? Answered by Penny Nom. 





Generating uniquie 2 digit numbers 
20010716 

From Anthony: What methodology can I use to generate uniquie 2 digit numbers from unique 7 digit numbers. Of'course the total number of 7digit numbers is not greater than 99. Answered by Penny Nom. 





6,000,000,000,000,000,000 
20010712 

From James: How would I express 6,000,000,000,000,000,000 in words? Answered by Leeanne Boehm. 





Some irrational numbers 
20010703 

From Kellie:
 Is it possible to write pi as a fraction?
 Is it possible to write the square root of 2 as a fraction.. Explain why?
Answered by Harley Weston. 





A calculation with 6 numbers 
20010616 

From Edwin: I'm asked to come with, and program (in Ansi C) an algorithm that calculates all the possible results of a calculation with 6 numbers and one result. For example: I want all calculations with the numbers 3, 3, 8, 8, 2, 9, and with a result of 786. all numbers may be used once, arithmetical operations allowed are +  / *, fractions are not allowed. The problem here is what is a fast method to do this (i.e. what's algorithm that can to this). Answered by Claude Tardif. 





Four digit numbers from 1,2,3,4,5,6,7,8 
20010531 

From Katie: Okay.......here's my question...how many different ways can you form a four digit number out of these digits..1,2,3,4,5,6,7,8? This is how my teacher said to do this.... 8*8, 7*7,6*6,5*5,4*4,3*3,2*2,1*1. then she said to add up the products and to multiply by 7. is this correct, and if not how can you figure this out. Answered by Penny Nom and Claude Tardif. 





Three goldfish 
20010530 

From Nathan: A man has three goldfish. When the youngest goldfish was born, the oldest fish was three times the middle fish's age. Nine years ago the oldest fish's age was the sum of the two other fish's ages. How old are the three goldfish? Answered by Penny Nom. 





Harmonic numbers 
20010523 

From Leslie: The harmonic numbers H_{k}, k = 1,2,3.....are defined by H_{k} = 1 + 1/2 + 1/3....1/k I am trying to prove by mathematical induction: H_{2n} >= 1 + n/2 , whenever n is a nonnegative integer. H_{8} = H_{23} >= 1 + 3/2 Can you help? Answered by Harley Weston. 





Dividing fractions 
20010509 

From Rina: I just wanted to ask if you could help me in math. See I'm having a test soon and its on Dividing Fractions and I just don't get it. My math teacher says that I'll be just fine but I failed my math quiz. I went to ask eric but they could help me so they told me to go to you. So here I am asking you if you could help me. Answered by Penny Nom. 





Neither prime nor composite 
20010508 

From Marc: what 2 numbers are neither prime nor combitative? Answered by Penny Nom. 





24 from 2, 2, 14, and 21 
20010508 

From Kimberly: using the numbers 2, 2, 14, and 21. how can you get 24 using +  X or division Answered by Claude Tardif. 





The number of occurrences of 0 is __, of 1 is __, of... 
20010417 

From Martyanne: "In this sentence the number of occurrences of 0 is __, of 1 is __, of 2 is __, of 3 is __, of 4 is __, of 5 is __, of 6 is __, if 7 is __, of 8 is __, of 9 is __."
Each blank is to be filled with a numeral of one or more digits, written in decimal notation. Answered by Claude Tardif. 





Cube roots on a calculator 
20010324 

From Will: Hi my name is Will.I have a question about the calculator TI83 Plus or the use of a scientific calculator. It is about using them to turn a cubed root to a decimal. When using that for a rational and irrational number. Rational numbers is a number that terminates or repeates. A irrational number goes on and on and uses ... (like pie). Like when you type the cube root of 8 it gives you 2, and that is a rational number. The squre root of 2 is 1.41421356... that is irrational. So why is it when you put the cube root of 16 in the calculator it says 2.5198421 that is rational it terminates at the ninth digit and my float is set for the tenth? But why when you do it by hand you get the 2 times the cube root of 2 and that is irrational? Why is that? Answered by Judi McDonald. 





Fibonacci 
20010228 

From Shona: We have been doing pattern finding with him, talking to a friend he mentioned the "Fibbinacci Series" ?, while I have tried to find a bit about it, how works etc.. what it is about, I have not really found out much, what I have I feel is way beyond him, but am still curious to know the basics of it myself. Would you be able to tell me in laymans language. Would be very much appreciated. Answered by Claude Tardif. 





Tnumbers an Ttotals 
20010227 

From Mr. M. Wiseman: Investigate the relationship between the Ttotal and the Tnumber. Answered by Penny Nom. 





Find the two numbers 
20010221 

From A grade 6 student: Find the two numbers: 5 is a common factor; 100 is a common multiple; neither number is a mulitple of the other; both are even. Answered by Penny Nom. 





Multiplying one and two digit numbers 
20010211 

From Marty: When multiplying do you put the number you are multiplying by on the top or the bottom. Example if you are multiplying by 6's would you write the problem 6 x 2 or 2 x 6 Maybe it just doesn't matter. But when you get to double digits, the double digit always goes on the top? Answered by Penny Nom. 





23 + 17 * 2 / 8 + 11 = 13 
20010202 

From David: My child is working through basic operations, and gave this problem: 23 + 17 * 2 / 8 + 11 = 13 The teacher wants the parenthesis to be put in the right places to come up with 13. Answered by Claude Tardif. 





Subsets of the natural numbers 
20010130 

From Christina: How do I explain why the set of natural numbers (N) cannot be equivalent to one of its finite subsets? Answered by Penny Nom. 





14, with 5 ODD numbers 
20010123 

From Robyn Ernst: How can you get 14, with 5 ODD numbers? Answered by Claude Tardif. 





More repeating decimals 
20010117 

From Alan: I am neither a math teacher nor a student, but I hope you will consider my question anyway. I recently was discussing repeated decimals with a friend, and went on the web to find out more about a pattern was looking for years ago. In doing so I came upon your correspondence on repeating decimals. . . . Answered by Chris Fisher and Penny Nom. 





Arranging some numbers 
20010114 

From Denise: Arrange the following numerals in two groups of four each so that each group will add to give the same sum. 1 2 3 4 5 7 8 9 Answered by Penny Nom anf Claude Tardif. 





8, 4, 2, 18, 1, 9 
20010111 

From Neyra: Place each number below in one of the blanks to create the most meaningful and realistic story possible. Answered by Claude Tardif. 





The sum of all tendigit numbers. 
20010110 

From John: Compute the sum of all tendigit numbers. Can you determine the sum of all n digit numbers? Answered by Sukanta Pati. 





Two questions 
20010104 

From Justine: first: A diagonal of a rectangle is the square root of 13 meters and the area of the rectangle is 6 meters squared. What are the dimensions of the rectangle? last: Find the ordered triple of nonzero digits (A,B,C) for which (AA)squared=BBCC where AA and BBCC are respectively, twodigit and fourdigit baseten numerals. Answered by Penny Nom. 





Why the change from commas between every 3rd digit, to spaces instead? 
20010103 

From Clarende Duby: Why the change from commas between every 3rd digit, to spaces instead? For example: Three million three hundred thirtythree thousand three hundred thirtythree written like: 3 333 333 instead of 3,333,333? Does it have something to do with standardizing mathematical notation worldwide? Answered by Harley Weston. 





Polite numbers 
20010102 

From A student: A positive whole number, greater than 1, is said to be a polite number if it can be expressed as a sum of consecutive whole numbers Find all the polite numbers less than 21. Find a pattern in the numbers that are not polite. Explain why every odd number greater than one must be polite. Answered by Penny Nom. 





Scientific notation 
20001212 

From Guy: How do I express 1.000.000 in scientific notation? Answered by Harley Weston. 





Two more problems 
20001201 

From Michael: first question: The mean of three test grades is 74. What must a fourth grade be to increase the mean to 78? final question: The product of two consecutive odd positive integers added to their sum is 119. What are these two integers? Answered by Claude Tardif. 





A complex calculation 
20001124 

From Angie: Multiply (32i)^{2}=3^{2}2(3)(2i)+(2i)^{2} Answered by Penny Nom. 





Perfect numbers 
20001031 

From A student: I was wondering if you could help me answer a question my prealgebra teacher asked in class the other day. He asked if we knew what the perfect numbers where. He told us the first number is 6 the second number is 28 but the third he did not tell us. Do you know what the third perfect number is? Answered by Paul Betts and Chris Fisher. 





Divisibility by 9 
20001024 

From Kelera: If the sum of the digits of a number is divisible by 9, then the number itself it divisible by 9. Why is that? How do you explain this? Answered by Penny Nom. 





Repeating decimals 
20001006 

From Mary O'Sullivan: I understand that with repeating decimals (those with a pattern), the number of digits repeated is put into fraction form with the same number of 9's ex. 0.4444 = 4/9 0.145145145 = 145/999 How can I explain why this is so? Some inquisitive 8th graders are anxious to find out! Answered by Penny Nom and Walter Whiteley. 





Rounding 
20000914 

From MaryAnn: How many whole numbers rounded to the hundreds place, round to 400? Can you also explain why? Answered by Penny Nom. 





Rational Numbers 
20000914 

From Josh Kuhar: How can you tell a number is rational? Answered by Harley Weston. 





4digit numbers using 7, 8, 9 and 0 
20000913 

From Ryan: Could you please help me with the following problem, How many different 4digit numbers are there that use each of the digits 7,8,9,and 0? Please list them. Answered by Penny Nom. 





A number problem 
20000902 

From Lalita Balu: Can you arrange 1234567890 to add up to 100? Answered by Penny Nom. 





Central Limit Theorem and Law of Large Numbers 
20000626 

From Jonathan Yam: The Central limit Theorem states that when sample size tends to infinity, the sample mean will be normally distributed. The Law of Large Number states that when sample size tends to infinity, the sample mean equals to population mean. Is the two statements contradictory? Answered by Paul Betts and Harley Weston. 





Names for large numbers 
20000616 

From Mireille Carthier: I am trying to find the common names (in English and French) for the big numbers as follows:  English  French  10^{6}  million  million  10^{9}  billion  milliard?  10^{12}  trillion  billion?  10^{15}  ??  trillion?  Thank you very much Answered by Claude Tardif and Harley Weston. 





Percents with mixed numbers 
20000604 

From Julie: How would you find the percent of 33 1/3 out of 90 by using fraction settup!I can do whole numbers but not mixed. This is how to do whole numbers say it was 33 of 90 33 x 90 = 2970 100 x 1 = 100 2970 divided by 100 the answer is 29.7 so how do you do it with a mixed number Answered by Penny Nom. 





Powers of i 
20000524 

From Paul Fieldhouse: What is the result of raising i to the googol power? is there a rule or pattern to raising i by increasing powers of 10? Answered by Penny Nom. 





The square root of 1 
20000519 

From Gary: i am not a student i am just some one that heard something and i can't be sure on the answer...my ? is what is the square root of 1? i think it is 1 but not sure can you let me know please thank you Answered by Harley Weston. 





Natural numbers 
20000412 

From Sara: What is a natural number??? Answered by Penny Nom. 





root(1)* root(1) 
20000320 

From Michael Moran: i squared = 1 but i squared = root(1)* root(1) = root( 1*1) = root(1) = 1 1 doesn't = 1 can you help me with my question Answered by Claude Tardif. 





Six digit numbers using 1,2,5,6,7, and 9 
20000320 

From Rachel: How many different sixdigit numbers can you make using the digits 1,2,5,6,7, and 9? How many of these six digit numbers are divisible by six? Answered by Claude Tardif and Denis Hanson. 





Rationals, irrationals and integers 
20000314 

From Erin McKeon: Why does the letter J represent the set of integers, the letter Q represent a set of rational numbers and the letter P represent a set of irrational numbers? What do each of these letters stand for? Answered by Harley Weston. 





Triangular numbers and square numbers 
20000302 

From Emily McCallum: Would someone find me some math activities using triangular numbers and square number. Especially acitivities that actually form the shapes. They need to be at the 5th grade or 6th grade level. But you can not find anything that can be tauht at these level, that fine. I just need to be able to teach this new subject or kind of math to my kids. Answered by Rick Seaman and Penny Nom. 





More on googols 
20000223 

From Kevin Brennan: Could you please give me a couple of examples of when you MATH guys would use a google. Do youu measure, like, galaxies with it ? Or was it created to keep track of Mr Gate's bank account. Answered by Penny Nom. 





Compatible numbers 
20000127 

From Angie: Use compatible numbers to estimate each product and quotient. 23*1/2 1/3*11 Answered by Penny Nom. 





Factors 
20000127 

From Pam: My son [age 9, 4th grade] has a math problem with factors. I need to know how to do the problem that involves the factor 24. I'm not even sure where to start. Answered by Harley Weston. 





Phone Number Possibilities 
20000109 

From Hamilton Weston: How do phone companies arrive at the possible number of phone numbers that can be generated for customers? Answered by Harley Weston. 





Fibonacci Numbers 
19991215 

From Gary Nelb: I'm doing a project on fibonacci numbers and I'm using different starting values and finding out if different starting values to see whether or not the ratios still get closer to phi. I was wondering, what numbers should I use. Should I use two of the same # like 2 and 2, or numbers like 1 and 2, or even something totally different. Answered by Denis Hanson. 





Bases other than 10 
19991206 

From Garret Magin: We are doing a lesson on numbers of other bases than 10. We are working with binary, octal, and Hexadecimal. I was wondering what is used to represent number of different bases other then 16? Does it just continue on with the alphabet and if so what happens when you get to Z. It would be a help if you could answer this because it is really bugging me. And none of the math teachers at my school could let me know. Answered by Claude Tardif and Patrick Maidorn. 





Whole numbers 
19991202 

From Patty: I'm in a 5th grade class, please explaine what whole numbers are..... Answered by Penny Nom. 





Critical numbers 
19991117 

From Sarah: My question is this: If f(x)=2x^{3}+4x^{2}9x+8 and the derivative is f'(x)=6x^{2}+8x9, how do I find the critical points if f'(x) is not factorable?? Answered by Penny Nom. 





Number sequences 
19991111 

From Justin Schessler: I CAN NOT figure out this sequence or how we continue this sequence... 3,2,6,5,15,14,___,___,___ Answered by Chris Fisher and Harley Weston. 





Nines and ones 
19991105 

From Greg Miller: Using the numbers 1, 1, 9, 9, only once each, how can I create an expression that equals 10 using only the basic functions of addition, subtraction, multiplication, division, and/or parentheses? Answered by Claude Tardif. 





Three numbers 
19991103 

From Walter: Three whole numbers , when added two at a time,yield the sums 75, 111, and 128. Find the smallest of these three whole #'s. Answered by Penny Nom. 





Find the missing numbers 
19991012 

From Bonnie: I must find the missing numbers and function rules n  output  7  10  12  20  39  40  24  30  16  b  87  c  we are totally confused can someone help Answered by Denis Hanson. 





A sum of two squares 
19991008 

From Marksmen: what is the smallest whole number that can be written two ways as a sum of two different perfect squares? i.e.11squared plus 3 squared is 121+ 9=130 and7 squared + 9squared=49 +81= 130. Are there any smaller? I am stumped! Answered by Claude Tardif. 





Numbers with the digit 2 in 1...1000 
19990920 

From Jessica: Is there a trick to finding out how many numbers containing the digit two is there from 1 to 1000? Answered by Walter Whiteley. 





Evens and odds 
19990504 

From Emily Hays: My name is Emily Hays, I am in the 6th grade and my teacher gave me some extra probelms to see if I could solve them. She can't find the KEY and I can't figure out the probelm so she suggested I email you guys to see if you could help us. Here's the Problem: The numbers 1,2,3...,1999 are written on the blackboard in the classroom. Evertime the teacher enters the room he chooses two numbers on the blackboard, say a & b, with a> or equal to b, then he erases them and writes the difference ab somewhere on the blackboard. After this procedure is carried on 1998 times, there will be only one number left on the blackboard. Prove the last remaining number must be even. I hope you can help us! Answered by Chris Fisher and Harley Weston. 





Large Numbers 
19990405 

From CK: Hello. I need a lesson plan for grades 4 to 7 dealing with the concept of large numbers. Specifically, how to teach scientific notation. The lesson plan has to deal with the following: the size of the universe is so huge that is is almost beyond the ability of the mind to comprehend. One way is to measure... Answered by Chris Fisher. 





Tshirts 
19990404 

From Valerie: At a discount Tshirt shop the manager marked a special batch of Tshirts that originally sold for $2.00. When all the shirts sold the shop had collected $603.77. How many shirts did they sell and what was the price per shirt? Answered by Jack LeSage and Penny Nom. 





Complex numbers/polar coordinates 
19990325 

From Kate Cegelis: What is the relationship between complex numbers and polar coordinates? Answered by Harley Weston. 





The square root of two is never supposed to end 
19990306 

From a wondering student: i am algebra II and am in the 9th grade. today we were talking about rational and irrational numbers. When we were talking about square roots my friend and i were talking and we thought of something. if you have a square with sides of length one then the diagonal of the square is the square root of 2. Now the square root of two is never supposed to end. But the diagonal of the square ends so therefore doesn't the square root of 2 end. our math teacher did not really answer our question because it was not in the lesson plan and not to many people would see where we were coming from. the answer is really bugging me and i would like to have your input. Answered by Jack LeSage and Penny Nom. 





The Board Problem 
19990215 

From Avery: Mr. Avery has 3foot boards and 4foot boards. If he puts the 3foot boards in a line, they have the same length as the 4foot boards put in a line. Altogether he has between 16 and 25 boards. How many 3foot boards does he have? Answered by Jack LeSage and Penny Nom. 





Magic Squares 
19990211 

From Katie Powell: My name is Katie Powell. I'm in the 7th grade, taking Algebra. I live in Houston, Texas. My problem is this: "Use the numbers 19 to fill in the boxes so that you get the same sum when you add vertically, horizontally or diagonally." The boxes are formed like a tictactoe  with 9 boxes  3 rows and 3 columns. Can you help? Answered by Jack LeSage. 





Grade 4 curriculum 
19990209 

From John: My daughter is in grade 4 and her math teacher has asked her to write out the number 1 to 10,000. She is currently at 4567 and is sick of it. When I complained that this was not a usefull exercise she said that the Ministry of Education curriculum requires this and gave a photocopy of the page. It states: "read and write whole number to 10,000 in standard, expanded, and written forms (eg., 9367=9000+300+60+7 = nine thousand three hundred sixtyseven). Has the teacher interpreted this the wrong way? Thanks John PS. Do you have a web address for Ontario Math and Science Teachers organization? Answered by Jack LeSage. 





Cannonballs 
19990127 

From Roger King: How many cannonballs can be stacked in a triangular pyramid? Answered by Penny Nom. 





Absolute value of i 
19990106 

From Wayne Bagley: I would like to know what is the absolute value of i. I need an answer suitable for the secondary level. Answered by Harley Weston. 





Place Value 
19990105 

From Reg: I work in a Section 27 classroom with various grades. I am looking for assistance on how to deliver a lesson on place value:decimal numbers keeping in mind that they need to see it (visual) to comprehend. I am looking for grade 46 level. Answered by Jack LeSage. 





Complex numbers and the quadratic formula 
19981225 

From Richard Peter: My age is 16, and my name is Richard. My question relates to the topic complex numbers & the quadratic formula. I would like to know how to solve quadratic equations in which the discriminant is less than 0 (i.e. we get two complex solutions to the quadratic) 3x^{2}+2x+5 = 0 and how mathematicians like euler contributed to this field. If it would be possible I would also like to know how this type of quadratic equations can be graphed? Answered by Harley Weston. 





Complex Numbers 
19981223 

From Wayne Bagley: I would like to know what is the square root of i , and i squared? I am looking for a response appropriate for secondary level students. Answered by Harley Weston. 





6.99999... = ? 
19981205 

From Tom: I have had a rather heated arguement with my students. Please settle this for me. Solve <,>, = 6.99999... __ 7 Thank you. Answered by Penny Nom. 





Triangular Numbers 
19981030 

From Matt: i would like to know about triangular numbers and it history i would also like to know about the history of prime numbers thank you Answered by Chris Fisher. 





A Number Trick 
19981026 

From Brenda Meagher: I'm a 37 year old mother and i have returned to school for personal reasons. I was faced with this question. Choose any number less than 10, multiply it by 8547, then take your answer and multiply it by 13. I chose the number 8. 8547 x 8  68376 and 68376 x 13  205128 68376  888888 Any number chosen from 1 to 9 will result in the same form of answer.If the number two is used you will end up with 222,222.etc So my question is, is there another number that will results in the answers. Answered by Harley Weston. 





Adding Fractions 
19981015 

From Lindsay: please help me!!!! Answered by Harley Weston. 





Composite Numbers 
19981007 

From Greg Murphy: What type of composite number has an odd number of factors? Answered by Harley Weston. 





Scientific Notation 
19981007 

From R. Pierce: Help! How do you express the following numbers in scientific(exponential)notation:0.00036 and 2998000000. I understand how to solve them if it was an equation, but this is confusing me. Please help me answer my questions. Thank you. Answered by Harley Weston. 





Rational and Irrational Numbers 
19980919 

From Ri: I am trying to explain rational & irrational numbers to my niece who is grade 7 and am having difficulties. Could you please explain the difference between rational & irrational numbers. Thank you Ri Answered by Penny Nom. 





Rational Numbers 
19980905 

From Kristin Mckenzie: Iam a secondary student with a math question I don't know how to do. This is the question: Explain whether each decimal number represents a rational number. (a) 0.16 (b) 0.12 (c) 3.125 (d) 0.27 (e) 0,212 112 111 2 .... (f) 0. 457 92 If it wouldn't be a problem i would really appreciate it if you sent back the instructions on how to do the question. My name is Kristin Mckenzie and my return email is lexus1999@hotmail.com Thankyou for you time Answered by Jack LeSage and Harley Weston. 





Two Problems 
19980728 

From James Pulver: How do you solve these problem? If log abc=16 and log ac=12 , find b. (The logs are log base 10.) and If a and b are real numbers, i^2 = 1 and (a+b)+5i=9+ai what is the value of b? Answered by Jack LeSage. 





Social Security Numbers 
19980707 

From Valerie Lucas: How many social security numbers are possible? the answer is 10^9 why isn't the answer 9^9? Answered by Harley Weston. 





Roman Numerals 
19980205 

From Dawn Hilgenberg: How would I read a Roman Numeral such as LXII? Does the L in front make the X equal a lesser amount? We have been discussing how to read these and I can find no information about how to read an extended Roman Numeral problem. Help!! Answered by Harley Weston. 





Divisors of 6n 
19980126 

From James: If n is a positive integer such that 2n has 28 positive divisors and 3n has 30 positive divisors, then how many positive divisors does 6n have? (a) 32 (b) 34 (c) 35 (d) 36 (e) 38 Answered by Penny Nom and Haragauri Gupta. 





The twodigit numbers from 1099 
19980121 

From Alexis Riddle: My name is Alexis. I'm a student in 8th grade and I'm taking Algebra I Honors. My question is: In a string of numbers, two adjacent digits are considered as a twodigit number. For instance, the string 11012 contains the numbers 10, 11, and 12. What is the number of digits in the smallest string that contains all of the twodigit numbers from 1099? Please help and thank you for any assistance you can give me. Answered by Penny Nom. 





Find the Numbers. 
19971228 

From Sandy C: The sum of the squares of two numbers is 53. Twice the greater, minus the lesser is 11. Find the numbers. Answered by Penny Nom. 





Driving me CRAZY. 
19971117 

From Billy Tran: Write a two digit number (both digits different and neither equal to zero) and then express the same number but now composed of the same two digits in reverse order with some mathematical symbol (+, , *, /, roots, !, or exponents). for example: 25 = 5^2. Now give me another. Hope you get this, cause its driving me CRAZY Answered by Penny Nom. 





Negative Primes. 
19971110 

From Leah Zucker and Paul Michael: I have received the following question via email from my granddaughter: "Can negative numbers (like 7) be prime? If not, why not?" Answered by Chris Fisher. 





Multiplying imaginary numbers. 
19971103 

From Jim Catton: Here is the question: (square root 2) x (square root 8) My algebra suggests two possibilities . . .
Answered by Walter Whiteley, Chris Fisfer and Harley Weston. 





Billions and more! 
19970915 

From Mahabir B. Gupta: I would like to know how you americans write the number 1 billion. Do you say "One thousand million"..can you answer by giving me examples? 1,000,000> 1 million 1,000,000,000>1 billion Why is it that in spanish it is different? Answered by Penny Nom. 





Triangular Numbers. 
19970908 

From Rachel: Show visually that the square number 16 is the sum of two triangular numbers. Which two? Answered by Penny Nom. 





Prime Numbers 
19970904 

From Jack Bedard: Hi. I have a real stupid question What are prime numbers? My name is Jack Bedard and I am in grade 5. Answered by Penny Nom. 





Repeating Decimals 
19970124 

From Grant Reed: Is there a way to tell that the repeating decimal for 1/17 has no more than 16 repeating digits? Answered by Penny Nom. 





Term definitions 
19960918 

From M. Seltzer: A 7th grade algebra student would like the definition of the terms proper factor and perfect number. Answered by The Centralizer. 





How do you find out if a number is a composite or prime? 
19960916 

From Trish Feenstra: Hi my name is Trish Feenstra. In grade 8. How do you find out if a number is a composite or prime if it is big like 37 529? Reply soon got a test on Friday the 13th Answered by Denis Hanson. 





Thousands, millions, billions and trillions 
19960822 

From Blaine: What are the names of the periods in groups of numbers like 123,456,789. I need to know the names of them for school. I already know the first ones: units thousands millions billions trillions. Answered by Penny Nom and Diane Hanson. 





Prime numbers 
19960222 

From Charles Hewitt: I would apprecaite it if you could share with me any algorithm to determine whether a number is prime. Answered by Penny Nom. 





Complex numbers 
19951022 

From Jacquie: Why should we teach complex numbers in high school? Answered by Harley Weston. 





2^(2^1954) estil premier? 
20051004 

From Un eleve: 2^{(21945)}+1 estil premier? Answered by Claude Tardif. 





Avec les chiffres 1 3 4 6... 
20050414 

From Ambre et Miel: avec les chiffres 1 3 4 6 utilisé une seule fois chacun soit en div multipl addit ousoustr je dois avoir 24 comme résultat Answered by Claude Tardif. 





Combien y aura t il de 9 dans la réponse? 
20000617 

From Marie: J'ai lu une énigme mais je n'ai pas la réponse."si l'on divise 123 456 789 par 999 999 999, combien y aura t il de 9 dans la réponse?" Answered by Claude Tardif. 

