







Listing three digit combinations 
20190717 

From Larry: Using numbers 09, what are all the possible combinations of choosing 3 numbers regardless of order and no 3 numbers being used more than 2 times in the combination. So no 1,1,1, 2,2,2, 3,3,3 etc. Order does not matter. Could you please send me a listing of all those combinations? Answered by Penny Nom. 





Three digit codes 
20190714 

From Jessica: I need to find the total number of 3 digit codes using the digits 1 through 9. How many of these codes would be odd numbers, and how many even? Answered by Penny Nom. 





A three digit code 
20190714 

From Hannah: I have a briefcase with a threedigit code. I can set the code myself using digits 1 through 9, assuming that each digit can only be used once. How many possible codes are there? Answered by Penny Nom. 





4 digit codes 
20190227 

From Sophia: How many 4 digit codes can you get out of a numbered key pad ? 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. 





4 digit "combinations" 
20180518 

From Marvin: I am designing a game, and I need away of figuring this out without having to write numerically all these numbers
4 digit combinations 0 through 13 nonrepeating Answered by Penny Nom. 





Pool Digit Combinations 
20180418 

From Jacob: I need to know all the possible 3 digit combinations from the following pool of digits: 1st pool (1,2,3), 2nd pool (4,5) and the 3rd pool (7,8,9,0). Each pool has to be represented in the combinations.
The numbers can be repeated as long as they are not of the same set.
Example for not repeating: 123 is ok but not 321 or 231,132,213, etc.
The question is somehow related to Mike's but the difference is the digits are allocated into pools. Your help can assist me solve a mystery. Thanks. Answered by Penny Nom. 





What is small fourdigit whole number? 
20180415 

From Rajesh: What is small fourdigit whole number? 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. 





A four digit pass code 
20180226 

From Jessica: I was trying to fond out how many combinations could there be for a four digit pass code to a phone when no numbers are repeated? Answered by Penny Nom. 





Four multiples of 10 
20170923 

From Laudacir: Four multiples of 10 are added together.the total is a 3 digit number with three consecutive digits. What could the four number be? 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. 





Significant digits 
20170806 

From Pat: The directions for a problem are: "Solve the problem, expressing your answer
using the correct number of significant figures."
Problem
0.0043 divided by 2.04
Answer before using the correct number of significant figures is
0.002107843
Is the correct number of significant figures the number below?
2107843
Pat Answered by Penny Nom. 





A 4 digit safe combination 
20170729 

From Donna: I lost my safe combination :( it is 4 digit # with the last digit being 2.
I do not think the 1st digit is 1, 2 or 3
Can u help? Thank u :) 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. 





The smallest and largest 4 digit integers 
20170613 

From Avneetpal: Difference of the smallest and biggest 4digit number 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. 





A five digit number 
20161012 

From Massa: Explain why any four digit number is less than any five digit number? 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 tens digit of a number is five times the unit digit 
20160519 

From sanjeev: The tens digit of a number is five times the unit digit. Find the number? Answered by Penny Nom. 





A six digit code 
20160506 

From Ralph: How many combinations are possible if a "safe" has four buttons and you can use a six digit code? (these are just single press buttons..)For example, this could be one possible combination: Button 4 Button 1 Button 1 Button 3 Button 2 Button 4. Thanks! Answered by Penny Nom. 





The last two digits of a phone number 
20160403 

From Joshua: I want to find the last two digits of a phone number whose first eight numbers of a ten digit phone numbers are known. Answered by Penny Nom. 





A 2 digit number 
20160208 

From Lloyd: The sum of digits of a certain 2 digit number is 7.
Reversing its digits increases the number by 9.
Find the number Answered by Penny Nom. 





A three digit number 
20151113 

From Tina: The sum of the digits of a 3digit odd number is 13. The digit in the tens place is 4 less than the digit in the hundreds place and 3 more than the ones digit. What is the number? Answered by Penny Nom. 





A two digit number 
20150821 

From Cameron: Write the 2 digit number that matches the clues.
My number has a tens digit that is 8 more than the ones digit. Zero is not one of my digits.
My number is ________. Answered by Penny Nom. 





A two digit number 
20150605 

From Madison: Trini took some photos. The number of photos she took is a two digit number.
The sum of the digits is 11. The tens digit is 3 more than the ones digit.
How many photos did Trini take? 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. 





A second grade word problem 
20140909 

From Beth: How do I explain to my second grader how to find the answer to the problem:
My tens digit is 8 more than my ones digit. My ones digit can not be zero. Answered by Penny Nom. 





A secret number 
20140908 

From jai: it is smaller than half of 100, it is more than 4 tens and less than 5 tens, the tens digit is two more than the ones digit , together the digits have a sum of 6..... What is my secret number? Answered by Penny Nom. 





4821x14y is an 8digit number divisible by 72 
20140806 

From RAYA: if 4821x14y is an 8digit number divisible by 72. How many values can x and y take? Answered by Penny Nom. 





A six digit number 
20140630 

From anupam: hi,
my daughter asking a solution for the below question, kindly help.
Write the smallest 6 digit number wit digits ( 2,4,3,0,5,7).
plz this is an urgent requirement.
regards,
anupam Answered by Penny Nom. 





Three digit numbers 
20140515 

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





A 4 digit number 
20140404 

From LIM: "A" is a 4 digit number formed by all the numbers from 1 to 4. When "A" is divided by 9, the remainder is the biggest possible value. What is the biggest value of A? 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. 





A number with all the digits different 
20140207 

From Jon: I'm not a mathematician but just curious. Is there a name for a number of up to ten digits where each digit is different,
i.e the equivalent of an isogram in linguistics? My online banking gives me a random 8digit number each time I log on
and it is rare to get one of the type I refer to. There must be calculable odds, but I'm only allowed one question!
Thanks in advance
Jon Answered by Harley Weston. 





Units digit 
20140103 

From gracie: 9^23 units digit Answered by Penny Nom. 





A 4 digit number 
20131220 

From swathi: How many 4 digit numbers can be formed using the digit 3 only once but the digit 3 must be used in all numbers? 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. 





A two digit number 
20130904 

From JEFFERSON: The sum of the digits is 6. When the digits are interchange, the new number represented is 3 time the 10 digit of the original number. Find the original number? Answered by Penny Nom. 





Four digit combinations starting with 7 6 
20130515 

From Kaye: How do I find the rest of a four digit combination starting with 7 6? Answered by Penny Nom. 





A 2digit number 
20130513 

From A teacher: Find a “2digit number” where the sum of the 1st digit (on the Left)
and the square of the 2nd digit equal the same number. Answered by Lorraine Dame, Harley Weston. 





A 4 digit code 
20130326 

From chris: I saw a previous question about a 4 digit code type thing and I was wondering if you could email me that same type of thing.
I changed the pin number on my phone's lock screen and I tried hard to remember it, then I had to go help my mom with something and I automatically forgot it and there is no way for me to get back on my phone.
I need all of the possible 4 digit number combinations without the numbers 0, 1, or 2. It cannot be repeating, ascending, or descending.
I know you may not want to do all of them, but I really need it. Answered by Robert Dawson. 





Sixdigit passwords 
20130319 

From Judy: Hello:
Can you please explain why the answer to the following question is 10^6?
What is the number of possible sixdigit passwords when using the digits 0 through 9, with repetition allowed.
Thank you. Answered by Penny Nom. 





A 3 digit number puzzle 
20130311 

From Bonnie: My number has 3 digits. My number is not a multiple of 100. My number is a multiple of 50. My number is a factor of 1000. What is my number? Answered by Penny Nom. 





Four digit "combinations" using 0124 
20130227 

From Ayana: What are all the possible four digit combinations using 0124. Please list them for me. Thank you. Answered by Penny Nom. 





A 4 digit phone lock using the digits 4, 2, 3 and 0 
20121224 

From Ragu: I would like to know formula for searching a combination of 4 digit. eg.
I knew my Phone Lock combination is my car plate number 4230. But
this time, i used another way around instead of 4230.
But I am sure, there is only this 4 digits only. 4 & 2 & 3 & 0 Answered by Penny Nom. 





A valid UPC number 
20121222 

From Jacob: A valid UPC number , ABABABABAB C must end in a 2 after using the rule: 3A +B+3A+B+3A+B+3A+B+3A+B+C=##2. What would term C need to be in order to make the following UPC valid? 2741825293C Answered by Harley Weston. 





The last 4 digits of a cell phone number 
20121222 

From Jacob: If the last 4 digits of a cell phone number, XXXXXXABCD, are restricted where: A cannot be 0 or 1 and B cannot be 0 / how many possible 4 digit combinations are left? Answered by Penny Nom. 





Transposition error 
20121203 

From Carol: What is the correct term for when a child writes 61 instead of 16, or 83 for 38when they switch the place values of a number? Answered by Chris Fisher. 





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. 





4 digit combinations 
20121017 

From Scott: How many different 4 number combinations from 0123456789 with 2 out of the 4 odd and 2 out of the 4 even, with no numbers repeating. Thanks Answered by p. 





A four digit number 
20121009 

From cyndi: find this 4 digit number: the tens digit is 1/3 of the hundreds digit; the 2 digit number formed by the tens and ones digits i the largest prime number smaller than 40; the sum of all 4 digits is the same as the number of face on an icosahedron ? what is the number? Answered by Penny Nom. 





The units digit 
20120911 

From Shaunice: Simplify each of the following expressions and determine what the last
digit would be.
a. (24^15) 4 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. 





A 2digit number 
20120823 

From patty: Write the 2digit number that matches the clues.
My number has a tens digit that is 8 more than the ones digit. Zero is not one of my digits.
My number is Answered by Penny Nom. 





A 4 digit number 
20120809 

From May: The number is given as ABCD. The first digit is a quarter of the last digit. The second digit is one less than the first digit.
When the number ABCD is multiplied by four its digits appear in the reverse order. None of the digits are the same. What is the number. Pleas help because my child need help and I can not do this. Thank you. Answered by Penny Nom. 





Mr. Schneider's mass 
20120229 

From Khiya: Mr. Schneider's mass is 2 digits. The first digit is 3 times the second digit. Both digits are odd numbers, and his mass is greater than 35 kg. What is Mr. Schneider's mass? Answered by Penny Nom. 





Four digit combinations from 1,2, ..., 9 
20120226 

From Errol: show me a list with all four digit combination numbers from 0 9 Answered by Penny Nom. 





Can the result of the calculation be 2? 
20120209 

From Thomas: You have the digits 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9 in a random order side by side and put randomly between two digits a colon, so that a division comes into existence. Can the result of the calculation be 2? Answered by Robert Dawson and Chris Fisher. 





A two digit number 
20120129 

From Christine: Five times the sum of the digits of a two digit number equals the number. If the digits are reversed, it becomes nine more than the original number. What is the original number?
I really don't understand this question, help me please 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. 





Rounding 
20111214 

From seth: A decimal number rounded changed to 23.7 after it was rounded.
Give a decimal number that is less than 23.7 and another that is greater than 23.7 that each round to 23.7.
Explain to what place each number was rounded. Answered by Penny Nom. 





The units digit of a prime number 
20111122 

From Mike: Every prime number larger than 10 has a digit in the ones place that is included in which set of numbers below?
A. 1,3,7,9
B. 1,3,5,9
C. 0,2,4,5,6,8
D. 1,3,7 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. 





A number less than 100 
20110917 

From Sharon: I am a number less than 100. My ones digit is 6 the sum of my digit is 11. What sum am I? Answered by p. 





A four digit number 
20110916 

From gina: i am having a hard time figuring this out.. i believe the answer is 3105 but the 0 is throwing me off... i am a 4 digit number between 3100 and 3200, none of my digits are even, the sum of my digits is 9, the largest digit is in the ones place, what number am i ?? Answered by Penny Nom. 





A two digit number 
20110826 

From Felicia: Write the 2digit number that matches the clues.
My number has a tens digit that is 8 more than the ones digit.
Zero is not one of my digits Answered by Penny Nom. 





Numbers with a digit 9 
20110513 

From Veronica: How many numbers between 200 and 750 have a 9 for at least one of the digits? 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. 





A two digit number 
20110301 

From jhoanna: the sum of the digits of a two digit number is 10. The value of the number is 16 times the units digit.Find the number. Answered by Penny Nom. 





What is the 6001st digit that Sam wrote? 
20110215 

From Sarah: Sam wrote the natural numbers from 1 to 5280 in order. What is the 6001st digit that Sam wrote? Answered by Penny Nom. 





Reversing the digits 
20110208 

From rejie: if the digits are reverse , the number is 9 less than the original number.what is the equation? Answered by Penny Nom. 





An even multiple of 27 
20110201 

From parth: the 6 digit # 63x904 is an even multiple of 27 what is X Answered by Penny Nom. 





Four digits are to be randomly selected 
20110120 

From sarahbear: Suppose four digits are to be randomly selected (repetitions allowed) Find the probability that
A. 5562 is selected
B.0000 is selected
C. All four digits are the same
D. 2 is the first digit selected Answered by Penny Nom. 





A product of 1 000 000 
20101119 

From Sharron: There are many pairs of numbers that when multiplied together give a product of 1 000 000. However, there is one pair, and only one pair, of whole numbers that contain no zero digits and has a product of 1 000 000. What are these two numbers? Answered by Stephen La Rocque. 





A six digit number containing no zeros 
20101115 

From John: Find a Six digit number containing no zeros in which the first digit is three less than the third,
the third digit is three less than the fifth,and the second digit equals the sum of the last three digits. Answered by Penny Nom. 





What numbers can I be? 
20101113 

From john: my thousands digit is 2 times my ones digit.my hundreds digit is my ones digit plus 2. my tens digit is the difference between my thousands and hundreds digit what numbers can i be? 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. 





A three digit number 
20100922 

From Andrew: Both the sum and the product of its three digits are 6. The least digit is in the hundreds place and the greatest digit is in the ones place. Write it in word form: Answered by Penny Nom. 





Choose any three digits that are less than ten 
20100912 

From cecille: my son have a homework, but i don't understand the question. here's the problem:
choose any three digits that are less than ten.
make all the two digit number you can using those three digits.
add up the two digit numbers you created and divided by the
sum of the original three digits.
record your answer. then do it again with another three digits. write your observation about
the answer. Answered by Claude Tardif. 





Numbers that can be formed using the digits 1,2,3,4,5,8,9 
20100719 

From Donessa: write the number that is 2000 more than the difference between the largest and the smallest
number that can be formed using the digits 1,2,3,4,5,8,9 Answered by Tyler Wood. 





Two problems 
20100527 

From debbie:
Question from debbie, a parent:
hi, i have a daughter and she asked me a maths question I cannot solve. I was just wondering if you can give me the answers plus the working out so I could explain to my daughter,
1. The leftmost digit of a sixdigit number N is 1. If this digit is removed and then written as a rightmost digit, the number thus obtained is three times N .Find N.
2. Four friends are racing together down a flight of stairs. A goes 2 steps at a time, B 3 steps at a time. C 4 steps at a time and D 5 steps at a time. The only steps which all four tread on are the top one and the bottom one. How many stairs in the flight were stepped on exactly once? 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. 





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 three digit entry code 
20100414 

From Bryon: The entry code for the executive bathroom is a threedigit odd number
with no repeated digits. If you want to try to break in, what is the
maximum number of numbers you'll have to try?
(Remember that the threedigit numbers cannot start with zero.) Answered by Stephen La Rocque and Penny Nom. 





How many zeros? 
20100318 

From jeff: 1 light yr is 6,500 billion miles, the galaxy "Andromeda" is 2,500,000 million light yrs, how many zeros are in this equation ? Answered by Robert Dawson. 





A code on my pedometer 
20100219 

From Jacqui: Hi I need to break a code on my pedometer. I have only 3 digits 1 2 and 3 but need to fill a 5 digit code. I have tried to find answers but they seem to relate to if the digits are only used once. I can use them in any order and repeated as many times. How many possibilities are there and is there an easy way to run through them. Many thanks Answered by 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. 





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. 





A 4digit phone code 
20100121 

From pat: my daughter can`t remember her 4digit code to unlock her phone. she is pretty sure it starts with a 4. can you help us? my brain is locked up Answered by Robert Dawson. 





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. 





A 4 digit number 
20091215 

From Lisa: Billy Club was assigned the task of putting numbers on
all the playground balls used during daily recess. Billy
will number the balls using the following rules:
1. It will be a 4digit number.
2. The digit in the thousands place will be a 1 or a 2.
3. The digit in the hundreds place will be a 2, 4, or 6.
4. The digit in the tens place will be an odd number.
5. The digit in the ones place will be greater than six.
How many balls can Billy number if he follows these rules? Answered by Robert Dawson. 





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. 





A place value problem 
20091129 

From Ivy: My tens digit is 4 less than my thousands digit. My ones digit is twice my tens digit. My ten thousands digit is one less than my ones digit. My hundreds digit is the sum of my tens and thousands digit. My thousands digit is 6. Answered by Penny Nom. 





Jill and Bill 
20091104 

From Lisa: Jill and Bill are two members of the Hill family. Jill is 8 years old and Bill is 9 years old. What will Bill's age be when the total of the digits in both their ages is once again 17? Answered by Stephen La Rocque. 





In what order are the following digits? 
20090930 

From Jewell: In what order are the following digits?
0,2,3,6,7,1,9,4,5,8 Answered by Penny Nom and Claude Tardif. 





Cubes and squares 
20090916 

From Stanley: What is a three consecutive digit number like 5,6,7 , which is two less than a cube and two more than a square? Answered by Robert Dawson. 





A three digit number 
20090904 

From Mark: How many 3 digit positive integers are odd and do not contain the digit 5? Answered by Penny Nom. 





A fourdigit positive integer 
20090904 

From TRACEY: I AM A FOURDIGIT POSITIVE INTEGER SUCH THAT THE SUM OF MY DIGITS IS 18 AND MY DIGITS REVERSED ARE EXACTLY FOUR TIMES GREATER THAN MYSELF. WHAT NUMBER AM I? Answered by Robert Dawson. 





The sum of digits of 4444^4444 
20090831 

From SHIVDEEP: The sum of digits of 4444^4444 is A .The sum of digits of A is B .
Find the sum of digits of B ? Answered by Claude Tardif. 





Unlocking my suitcase 
20090821 

From Jamboree: I need to have all the possible combination of three digit between 09, i have seen the answer that there are 720 combination are there. Could you please show me all those combination numbers so that i could try it out to unlock my suitcase, will you please write it down all those combination and send it to me Answered by Victoria West. 





Units digit 
20090723 

From Jyll: How do solve for the units digit? And that, what is the units digit of the first 1000 prime numbers? Answered by Robert Dawson. 





Two questions from math class 
20090618 

From Con: Hello,
My name is Con and my son is required to answer the following questions for his maths class.
He has attempted Q1 through trial and error and has found the answer to 72453. Is this correct?
He has attempted to draw the triangles described in Q2 in a number of ways and has found that BE can not equal ED and is dependent of angle BAC. Therefore, he claims that the triangle can not be drawn/practical. Is this correct or is there a slolution?
Q1.
Digits 2, 3, 4, 5 and 7 are each used once to compose a 5digit number abcde such that 4 divides a 3digit number abc, 5 divides a 3digit number bcd and 3 divides a 3digit number cde. Find the 5digit number abcde.
Q2.
Let ABC be a triangle with AB=AC. D is a point on AC such that BC=BD. E is a point on AB such that BE = ED = AD. Find the size of the angle EAD.
Con Answered by Chris Fisher. 





The smallest 4 digit number 
20090617 

From Kat: What is the smallest 4 digit number? 0001 or 1000 Answered by Robert Dawson. 





The last non cero digit of a factorial 
20090612 

From Wilson: How can I find the last non cero digit from a factorial calculation of a big number.
For example 10! = 3628800, the last non cero digit is 8.
What is the last non cero digit of 10! ?? Answered by Robert Dawson. 





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. 





7 digit combinations 
20090511 

From CAROL: I NEED TO KNOW HOW MANY 7 DIGIT COMBINATIONS FROM 09 THERE ARE WITHOUT ANY REPEATES,
OR WHAT THOSE COMBINATIONS ARE? Answered by Penny Nom. 





Combinations and permutations 
20090507 

From Renee: We are trying to figure out the equation or how to solve the problem of how many combinations of 4 digits you can get out of 09 without repeating the numbers in a set (i.e., no 0001, 0002) begining with 0123, 0124, 0125 etc
Thanks! Answered by Stephen La Rocque. 





Fourdigit combinations 
20090418 

From Carri: How many 4digit combinations can be made out of digits 1, 2, 3, 4, & 5 using each number once? What are the combinations? Answered by Penny Nom. 





What is the original number? 
20090416 

From Yueh: A five digit number is written on a blackboard. Ron erases one of the digits and adds a newly constructed number to the original one. The result is 41751. What is the original number? Answered by Claude Tardif. 





Units digit 
20090415 

From A student: What is the unit digit of 47 to the 43rd power? Please answer as soon as possible. Thank you. Answered by Stephen La Rocque. 





Fourdigit numbers 
20090411 

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





How many times is 9 in pi? 
20090409 

From Serena: How many times is 9 in pi? Answered by Robert Dawson. 





A 5 digit push combination lock 
20090404 

From Andrew: I have a 5 digit push combo lock that i forgot the combo for. it has numbers 14 and each number can be pressed more then once ie. 11111, 36356
is there an algorithm out there that will list out the possible combinations for me? or maybe a way i could write them out myself. Answered by Penny Nom. 





0123456789 
20090325 

From Dr.: Many years ago I discovered that there are 33 numbers which,
when multiplied by 0123456789, simply rearrange the digits. Surprisingly
(to me at least) is the fact that the digits of all of those 33 numbers add up
to one of the 6 "cardinal" numbers 1, 2, 4, 5, 7, and 8. For example
6 + 2 = 8 and 62 X 0123456789 = 7654320918 etc.
Another interesting (to me) fact is that only the cardinal numbers
1, 2, 4, 5, 7, and 8 rearrange the digits in the number 9876543210.
My question is: "Is this known to anyone but me and the people I have
told?" Answered by Robert Dawson. 





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. 





The units digit of 2^95 
20090318 

From Sharvon: what is the units digit of 2^95 Answered by Robert Dawson. 





4 digit numbers from 1159 
20090310 

From David: I have the digits "1159" and need to come up with a complete list of possible fourdigit combinations. It does NOT matter the order of the two number ones (1), so this will help eliminate many possibilities.
Separately, it would also help to actually know the actual number of combinations with which I am dealing to start.
David :) Answered by Penny Nom. 





Four digit numbers 
20090310 

From Theresa: I need to know the number of 4 digit numbers that can be formed using 1234 without repeating numbers Answered by Penny Nom. 





4 digit strings starting with 7 
20090303 

From Angel: I need to no all the 4 digit combinations starting with 7 and with no repititions. Answered by Penny Nom. 





A four digit number 
20090212 

From alex: the number of tens plus the number of hundreds equals the number of thousands.
the number of ones is half the number of tens and one more than the number of hundreds the hundreds digit is 2. what is this four digit number 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. 





Dividing the digits 1  9 into two groups 
20090209 

From donna: using the numbers 1 to 9 can you arrange these into 2 groups, both of which have the same total, and no you cant turn the 6 upside down Answered by Penny Nom. 





4 digit arrangements of 7 3 6 6 
20090205 

From Carole: I need all the four digit combinations using the numbers 7 3 6 6 Answered by Penny Nom. 





The units digit is 5 
20090202 

From Ray: the number that when squared the units digit is 5 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. 





Four digit numbers using 1, 0, 2 and 8 
20090127 

From Mike: How many combinations of this four digit number 1028 can this produce only using those numbers. Example would be 0000, 0001,0002,0008,0010,0011,0012,0018,etc... Answered by Penny Nom. 





Three consecutive natural numbers 
20090126 

From abby: 1.what is the smallest fourdigit number that is the sum of the three
consecutive natural numbers? what are the three consecutive
natural numbers that give this sum?
2.what is the largest three digit number whose square root is a prime? Answered by Penny Nom. 





The tens digit of 0! + 1! + 2! + 3! + 4! .............+9999! + 10000! 
20090123 

From Kaylyn: determine the tens digit for the expression:
0! + 1! + 2! + 3! + 4! .............+9999! + 10000! Answered by Robert Dawson and Penny Nom. 





5 "digit" combinations 
20090122 

From Timothy: I was wondering how many different 5 digit combinations are possible using 09 and az and you can use the same letter or number repeatedly in the combination. Answered by Penny Nom. 





A three digit number 
20090120 

From marcha: when this three digit number is rounded to the nearest ten, the sum of its digits
is 16 the hundreds digit of this number is 8 and the ones digit is 5, what is the number? Answered by Robert Dawson. 





A four digit passcode 
20090112 

From john: i have a machine at home that has a four digit passcode and the numbers range from 1 to 4 how can i get all the ways those numbers can be used Answered by Harley Weston. 





A 4digit number 
20090105 

From Anya: It is a 4digit number
The tens are double the ones.
The thousands are double the tens.
The sum of the digits is 19.
What number is it? Answered by Penny Nom. 





The 2 rightmost digits 
20081218 

From Peter: Is there a pattern for the 2 rightmost digits of a power? For example, one problem for a math competition was what are the 2 rightmost digits of 3^1993? Answered by Robert Dawson and Victoria West. 





Student who is inverting digits 
20081209 

From Tammie: Do you have any strategies for addressing inversion of digits in two digit numbers. For example  The student the teacher is working with will write "14" and the number is 41. She has tried highlighting, practice writing numbers, and hundreds charts and finding patterns. Help! Thank you! Answered by Robert Dawson and Victoria West. 





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. 





I am a whole number less than 100 
20081203 

From Cecelia: If I am a whole number less than 100
and the sum of my digits is 4
and half of me is an odd number
What number am I?
Also am I prime or composite? Answered by Penny. 





Three digit combinations 
20081112 

From Jimmy: How many 3 digit combinations are possible using numbers 19?
How did you get that answer? Answered by Harley Weston. 





A 4 digit number 
20081106 

From Chris: numbers 0  9 form a 4 digit number with no repetition.
It would round to 3000 if rounded to the nearest thousand
The digit in the tens place is twice the value of the digit in the thousands place.
It is an odd number.
It contains the largest digit.
It contains one digit less than 2.
The digit in the hundreds place is odd.
Can you find the 2 numbers? Answered by Penny Nom. 





4 digit combinations 
20081105 

From Laura: I need to know all the number combinations possible with a 4 digit combination with double zero in the middle??? Answered by Penny Nom. 





What is the exact value of pi? 
20080927 

From mahesh: what is the exact value of pi.
22/7 is accurate value of pi, if not then how can i find out the exact pi value. Answered by Harley Weston. 





Repeating fractions 
20080909 

From Juli: My teacher recently put my math class to the test...
We were deiscussing repeating fractions and she asked
us to find out what the bar over a repeating decimal is called. I found out
it was called the vinculum. But she also said to find out what the number
under the vinculum was called. I can't seem to find it anywhere. Answered by Penny Nom. 





Hundreds, tens, and units digits 
20080905 

From Cynthia: write an expression for the value of a threedigit number whos hundreds, tens, and units digits are x, y, and z, respectively Answered by Penny Nom. 





3 digit combinatios from 09 
20080727 

From Mike: I need to know all the possible 3 digit combinations using the numbers 09.
The numbers can be repeated as long as they are not of the same set.
Example for not repeating: 123 is ok but not 321 or 231,132,213, etc.
Please help me. Thanks, Mike. Answered by Stephen La Rocque. 





The product of the digits of a four digit number 
20080726 

From Pete: I am a student preparing for a competition and this was one of the prep problems: The product of the digits of a four digit number is 6x5x4x3x2x1. how many such numbers are there with this property? Answered by Stephen La Rocque. 





Sum of Digits 
20080724 

From Warren: If 100^2525 is written in decimal notation, what is the sum of digits? 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. 





The units digit of (7*3)^21 
20080716 

From surender: what will be the unit digit of (7*3)^21?plz give me method 2 calculate such problems.thank you. Answered by Penny Nom. 





Smallest Even Number 
20080709 

From Ma.: Using the digits 0, 1, 3, 4, and 5 only once give the smallest 5digit even number Answered by Janice Cotcher. 





Zip codes, postal codes and 5 digit codes 
20080708 

From Mike: Sorry if you have answered this before but I don't understand the explanations I have seen.
How many possible combinations are in a 5 digit code (like a Zip Code). Is there an equation that can be used for this type of question? Answered by 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. 





Units digit 
20080702 

From seemachauhan: How to find unit digit of various numbers and what are unit digits? Answered by Penny Nom. 





The sum of the digits of twodigit number is 9 
20080701 

From Audrey: the sum of the digits of twodigit number is 9. if the digits are reversed, the new number if 63 greater than the original number. find the number. Answered by Penny Nom. 





A 7digit odd number 
20080626 

From Godryk: I am the smallest 7digit odd number. my ones digit is the sum of my thousands, and ten thousands digits. What number am I? Answered by Penny Nom. 





111...111 * 2003 
20080623 

From Peggy: Number a = 111...111 formed by 2003 1's. Find the sum of the digits of the number 2003 * a. Answered by Penny Nom. 





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. 





The sum of the digits of a number 
20080623 

From Ben: Question: Using mathematical induction, prove that if the sum of the digits of a number is divisible by three, then the number itself is also divisible by 3. 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 6 digit number 
20080423 

From rajiv: write the smallest 6digit number using three different digits with 6 in the ten thousands place and 1 in the hundreds place 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. 





Rearrangements of the digits in 0123456789 
20080323 

From Joe: Found a close problem but not quite.
Using digits 0123456789, how can I figure what all the different
possibilities would be without repeating any digits?
I know that there are 10! possible answers but how can I figure out what
they are? Answered by Stephen La Rocque. 





A number puzzle 
20080322 

From Cassidy: 1. Number has three digits
2. The second digit is an odd number
3. The first and third digits are even numbers
4. The number can be divided by five, six, and seven with a remainder of four.
How do you even start this type of problem? Answered by Victoria West. 





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. 





A 4 digit passcode 
20080216 

From Rob: If there is a 4 digit passcode with only 6 punch in symbols, how many possibilities are there and what are they?
symbols are: Y, X, RB, RT, LB, LT. Please get back to me, thanks for your time and help. Answered by Stephen La Rocque. 





Five digit combinations 
20080215 

From Debbie: I would like to get a list of all the possible 5 digit combinations of the numbers 12345. Answered by Penny Nom. 





A 2 digit number 
20080213 

From Jenny: The units digit of a certain twodigit number is one more than 4 times the tens digit.
The number formed by interchanging the digits is 6 more than 3 times the original number.
Find the original number. Answered by Penny Nom. 





I am a 4digit number 
20080212 

From Nickie: I am a 4digit number with no repeating digits. I am divisible by 5, my first two digits (left to right) make a number divisible by 3, and my first three digits make a number divisible by 4. Also, my digits have a sum of 19 and I have the digit 7 in the thousands place. Who am I? Answered by Penny Nom. 





A briefcase lock 
20080211 

From Alfred: A briefcase lock has 3 columns of numbers each 09. It opens with the correct combination of three numbers.
How many combinations are possible to open the lock. 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. 





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. 





A 3 digit number 
20080123 

From Adrian: Consider a 3digit number,abc,where a is not equal to c.Switch it so that it becomes cba.Subtract
the lesser from the greater to obtain rst.Switch this so that it is tsr.Prove that rst+tsr=1089 Answered by Stephen La Rocque. 





Units digit 
20080111 

From Robin: hello  my question is:
what is the units digit of (13) to 4; (17) to 2 and (29) to 3
[(13)4(17)2(29)3]
(possible answers: 9 or 7 or 5 or 3 or 1) Answered by Penny Nom. 





A 3 digit number 
20071213 

From Kim: Find the number from the following clues:
A) is is a 3 digit even whole # divisible by 5
B} Each digit is different
C) Its hundreds digit is greater than its tens digit
D) It is less that 400, divisible by 3, and has only 1 odd digit. Answered by Penny Nom. 





A math riddle 
20071127 

From Kathleen: My 4th grade daughter was given a math riddle which she is expected to answer using a problem solving strategy. The question is:
The number of my hundreds and the number of my thousands is 3. The number of my tens is 7 times the number of my thousands. All my digits are different. What am I?
I have tried to come up with an answer, but am beginning to think it is less complicated than what I have come up with. Answered by Stephen La Rocque. 





How many marshmallows did I use? 
20071121 

From gloria: the # of marshmallows i use is an even # .it is 2 digit number more than 10 less than 20 the 10th digit half of one digit.how many marshmallows did I use? Answered by Chris Langdon. 





Using the digits 1 to 9 
20071120 

From sunjoo: write the least whole number that uses the digits 1 though 9 once each. explain your answer. Answered by Penny Nom. 





A ten digit number 
20071111 

From jeff: find the greatest tendigit positive multiple of 12 using each digit once and only once Answered by Penny Nom. 





The sum of the digits of a whole number is 200 
20071106 

From Kristin: If te sum of the digits of a whole number is 200, the whole number may not have
________ digits? Answered by Penny Nom. 





The sum of the ones 
20071029 

From Hangsun: When 2 two digit numbers are added what is the greatest possible sum of the ones? Answered by Penny Nom. 





Some four digit combinations 
20071025 

From Larisa: Please tell me the answer or how to get the answer of every possible digit combination of 5173, for instance1735, 1753, 1573, 1537, 1357, 1375, etc. Answered by Stephen La Rocque. 





Show that there is no fivedigit number which 
20071004 

From Greg: show that there is no fivedigit number which uses each of the digits 1,2,3,4,5 such that the numbers formed
by the first digit is divisible by 1,
by the first two digits is divisible by 2
by the first three digits is divisible by 3,
by the first four digits is divisible by 4,
by the first five digits is divisible by 5 Answered by Stephen La Rocque, Claude Tradif and Victoria West. 





Finding the last nonzero digits of large factorials 
20071004 

From Mukesh: i have to find last five non zero digits of integer which can be very large (
upto 10^12) . i can find last non zero digit of of any factorial. Now my problem is that
i have to find last five non zero digit of factorial and also i want to general method for
last K non zero digits of factorial n. For example 10!=3628800 so last non zero digit is 8 ,last two
non zero digit is 88 .....and last five non zero digit is 36288. Answered by Victoria West. 





I have a 6 digits 
20070928 

From Kim: I have a 6 digits. My hundredthousands digit is 1 less that my ones digit, 8 more than my thousands digit, twice my tens digit, and 4 times my hundreds digit. My tenthousands digit is 0. What number am I? Answered by Stephen La Rocque. 





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. 





The largest 4digit odd number 
20070921 

From Courtney: what is the largest 4digit odd number you can make with 1  9. You can not repeat digits within a number Answered by Harley Weston. 





Three digit numbers where all digits are even 
20070914 

From Cielo: Hannah made a list of all of the three digit whole numbers where all three digit were even. How many three digit whole numbers were on Hannah's list? Answered by Penny Nom. 





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. 





Four digit combinations 
20070904 

From Natalie: Using The Numbers 7 4 5
How many different 4digit combinations are possible, you can use any of the numbers twice. Answered by Penny Nom. 





The digital lock for a cell phone 
20070829 

From Hollie: i have a four digit lock code on my cell phone and cannot remember what it is. i know that it does not contain a 2 or a 4 and none of the numbers are repeated. the numbers range from 0 to nine and the only way to figure out what the code is, is to try randomly. I was wondering if you could give me a list of possible combinations using the information i gave you to make it easier to crack the code. Answered by Penny Nom. 





A question about integers 
20070824 

From Jerry: Does there exist a positive integer such that when it is written in base 10 and its leftmost digit is crossed out, the new number is 56 times less than the original number? Answered by Stephen La Rocque and Penny Nom. 





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. 





The tens digit 
20070821 

From Arul: Hi..
Please help me on this question..
Sequence 2, 7, 22,…after the first three terms, each term is three times the previous term plus 1, a(n+1)=3an + 1. What is the sum of tens digit 33rd and tens digit of the 35 term? Answered by Penny Nom. 





The units digit of 23^45 + 67^89 
20070816 

From Christopher: What is the units digit of 23 to the 45th power plus 67 to the 89th power? Answered by Stephen La Rocque. 





who am i? 
20070808 

From Phillip: if you hold a mirror horizontally across my middle, i look the same in the mirror.if you hold a mirror between my second and third digits,i look the same in the mirror if you turn me upside down, i look the same. what 6 fourdigit numbers could i be? Answered by Penny Nom. 





4 digit number combinations that start with the digit 2 
20070805 

From tonnie: my question is what are all the 4 digit number combinations that start with the number 2? Answered by Harley Weston. 





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. 





The smallest 5digit even number 
20070626 

From charles: Using the digits 0,1,2,3,4 and 5 only once give the smallest 5digit even number Answered by Penny Nom. 





All 4 digit combinations for numbers 0 through 9 
20070621 

From Jessica: How can I find all 4 digit combinations for numbers 0 through 9? Answered by Penny Nom. 





A 5 digit key 
20070531 

From Michael: I have a 5 digit key pad lock on my truck.
I want to print out all of the combinations to try.
pad one=0 pad two =1 pad three=2 pad four=3 pad five =4.
can you help me find and print all combinations? Answered by Harley Weston. 





How many ways can I choose 4 numbers from 10? 
20070510 

From Mitch: Can you give me a list of all possible four digit combinations using 0 to 9 no repeat numbers and the numbers do not have to be entered in a special order. If you could also show me how to calulate this it would be great Answered by Stephen La Rocque. 





Who am I? 
20070424 

From Lisa: I am the largest two digit number whose units digit divides its tens digit evenly. Who am I? Answered by Stephen La Rocque. 





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. 





A four digit number 
20070328 

From Paulo: Hi , if i have to discover a keypad number of four digit , Which the closest combination of getting right?? i have this tips > i know the second and thirth number is odd . dont have the number 7 in any digit ,
Doesnt begin with 8 or 4 ... and dont have the 2 as a last number .
Thanks !! Answered by Stephen La Rocque. 





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. 





The tens digit of a really large number 
20070305 

From Sai: How can i find the tens digit of a really large number? i was gven 63^15 + 15^63 in a competitive exam. 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. 





A twodigit number is five times its units digit. 
20070221 

From Pamela: A twodigit number is five times its units digit. If the digits are reversed, the resulting number is 27 more than the original number. Find the original number. Answered by Gabriel Potter and Penny Nom. 





*** x ** = **** 
20070216 

From Dani: Use the numbers 19 only once to make the following: A three digit number times a two digit number that gives a four digit number. That is *** x ** = **** (the numbers 19 can only be used once for each star). I came up with the answer 138 x 42 = 5796 but I want to know whether this is the only solution and if not, is there a formula to come up with the answer. Thanks! I appreciate your help! Answered by Chris Fisher and Claude Tardif. 





Six digit numbers 
20070209 

From marisa: how many six digit numbers can you write using the digits 0 and 1 as many times as possible? Answered by Stephen La Rocque. 





The units digit of 9^2006 + 3^2006 
20070130 

From Ryan: What is the units digit of the sum of 9^2006 and 3^2006 Answered by Penny Nom. 





The sum of the digits of a twodigit number is 13. 
20070127 

From Liz: The sum of the digits of a twodigit number is 13. If the digits are reversed, the new number is 9 more than the original number. Find the original number. Answered by Penny Nom. 





The units digit 
20070109 

From Tyrone: This may be a dumb question, but what is the unit digit of two digits, eg: 62 or 13 or 45. Answered by Steve La Rocque and Diane Hanson. 





2 digit combinations 
20061204 

From Gary: please figure out for me what are the 2 digit combinations of numbers using numbers 0 thru 9 Answered by 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. 





My greatest digit is 9, ... 
20061117 

From Tiffany: My greatest digit is a 9, but less than 900. I'm one more than a multiple of 10 and the sum of my digits is 12. Who am I? Answered by Penny Nom. 





How can half of 12 be 7? 
20061116 

From Liz: How can half of 12 be 7? Answered by Steve La Rocque, Chris Fisher and Penny Nom. 





What is the highest number possible with 3 digits? 
20061116 

From Liz: What is the highest number possible with 3 digits? The teacher said the answer is not 999 and that the question did not say "3digit number." My answer then is 9 to the 99th power (written mathematically of course) as this uses "3 digits" and is obviously a huge number. Is this correct? Answered by Stephen La Rocque. 





The units digit of 1^5 + 2^5 + ... + 2006^5 
20061114 

From Lana: Compute the unit's digit of : 1 to the power of 5 + 2 to the power of 5 + 3 to the power of 5 + 4 to the power of 5 + 5 to the power of 5 + 6 to the power of 5 + ... + 2006 to the power of 5 . Answered by Stephen La Rocque and Penny Nom. 





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. 





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 units digit of 12^40 
20061008 

From Lana: FIND THE UNITS DIGIT OF 12 TO THE POWER OF 40. Answered by Penny Nom. 





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 threedigit number multiplied by 7, then 11, then 13 
20060917 

From Sherrie: why is it true that a threedigit number multiplied by 7, then 11, then 13 will result in the three digits repeated twice? Answered by Stephen La Rocque. 





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. 





Two characters 
20060912 

From Robert: I am looking to find out how many possible unique combinations I can have if at any time i can use only two characters of numbers or the alphabet...For ex., i can have 199 or i can have a1, a2, z1, z2 ... or i can have aa, ab, ac... i came up with possible combinations of 1295 or so... can you help? Answered by Penny. 





The last two digits 
20060722 

From Sam: You have answered this question already but you only answered to one digit.
What are the last TWO digits of:
3 to the power of 1994
7 to the power of 1994
3 to the power of 1994 + 7 to the power of 1994
7 to the power of 1994  3 to the power of 1994
Answered by Paul Betts and Penny Nom. 





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. 





How many digits are in the number 2^64? 
20060614 

From Trang: How many digits are in the number 2^{64}? Answered by Stephen La Rocque. 





We are 2 pairs of consecutive 2 digit numbers ... 
20060513 

From A perent: We are 2 pairs of consecutive 2 digit numbers that are factors of the number of feet in a mile. Who are we? Answered by Claude Tardif. 





10^100 in binary form 
20060510 

From Headmaster: How many digits has the number 10^{100} if we write it in binary form? Answered by Chris Fisher, Paul Betts and Steve La Rocque. 





8digits numbers with their digits in decreasing order 
20060509 

From Headmaster: How many 8digits number are there with their digits in decreasing order Answered by Penny Nom. 





A number theory problem 
20060505 

From DeHayward: Find the 6digit number in which the first digit is one less than the second, the third is half of the second, the fourth is 3 times the third, and the last 2 digits are the sum of the fourth and fifth. The sum of all the digits is 24. Answered by Paul Betts. 





The sum of a three digit number and its three individual digits is 429 
20060408 

From Megan: Gill has recently moved to a new house, which has a three digit number. the sum of this number and its three individual digits is 429. What is the product of the three digits which make up the house number? Answered by Chris Fisher. 





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. 





The first six million digits of PI 
20060308 

From Lori: How many threes are there in the first six million digits of PI? Also how many nines? 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 units digit 
20060305 

From Taran: My teacher asked: What is the unit's digit in the product 5 X 10 X 15 X 20 X 25? What is a "unit's digit", what are they asking for? Answered by Penny Nom. 





Counting digits 
20060130 

From Cynthia: I would like to know the easiest way to calculate the
total numbers of digits used by a printer to number the pages of a book from 1 to 250. Answered by Penny Nom. 





The number of combinations of the digits 0235588 
20051207 

From Blake: If you have the digits 0235588 how many different combinations can you possibly form with these seven digits? Answered by Penny. 





Fill in the blanks 
20051205 

From Bonnie: Distribute the numbers 1 through 9 on the lines below so that two equations are true.
_ _ x _ = _ _
_ x _ = _ _
Use each digit only once Answered by Penny Nom. 





Add one 1 at the beginning and at the end of a number 
20051113 

From Samuel: If we add one 1 at the beginning and at the end of a number, this number is increased by 14789.
What is the sum of the digits of the number? Answered by Penny Nom. 





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. 





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. 





What is the unit's digit? 
20051004 

From Alex:
Question: What is the unit's digit of the following problem?
3^{155} + 7^{412} (3 to the 155th power + 7 to the 412th power.)
Answered by Penny Nom. 





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. 





What is the ones digit of 3 to the 79 power? 
20050914 

From Candice: What is the ones digit of 3 to the 79 power? Answered by Penny Nom. 





Whats the value of the digit 7 in 756,809? 
20050914 

From Anastasia: Whats the value of the digit 7 in 756,809? Answered by Penny Nom. 





n^2+n1 has no divisors ending with 3 or 7 
20050908 

From Arne: at least it seems like for any integers n and k,
10k+3 and 10k+7 do not divide n²+n1
I tested this for every n from 0 to 3200 (which means same for the numbers from 3201 to 1)
could this be true, or is it just coincidence, or am I just totally wrong? Answered by Richard McIntosh. 





The number of four digit combinations 
20050809 

From Kevin: My 12 year old has asked me how to figure out the number of four digit combinations possible using 0 thru 9 without repeating a number? Answered by Penny. 





A two digit number 
20050809 

From Grace: I am a 2 digit number. Both of my digits are even. My tens digit is 8 more than my ones digit. What number am I? Answered by Penny Nom. 





The sum of the digits of 2^100 
20050611 

From Richard: The sum of the digits was calculated for the number 2100, then the sum of the digits was calculated for the resulting number and so on, until a single digit is left. Answered by Penny Nom. 





How many digits? 
20050607 

From Floren: The numbers 2^{1989} and 5^{1989} are written one after another. How many digits in all are there? Answered by Claude Tardif. 





The units digit 
20050518 

From Gerald: Juan wrote the first 12 powers of 2. He noticed a pattern in the digits in the units places of the results. He said he could use this pattern to predict the digits for 2 to the power of 100. Answered by Penny Nom. 





A six digit answer 
20050518 

From Angela: I have a 6 digit answer that is comprised of only 4 symbols: a square, a circle, a triangle, and an X. How many possible solutions are there and how is the best way to find out what ALL the solutions are? 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. 





The sum of the digits 
20050316 

From kelsey: What is the sum of the digits in the decimal form of 2^{1999} * 5^{2002}? Answered by Claude Tardif. 





How many three digit numbers can I make from the four cards 
20050312 

From Sue: I have four playing cards 2,3,4,5 of hearts. How many three digit numbers can I make from the four cards. 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. 





Strings of 4 digits from 1,2,...,7 
20041209 

From Tom: How many different combinations can be made of the numbers 17 in 4 string combinations in any order? EX:7235, 3517, etc...
And if you were to include the same 2 numbers in every combination, how many would that make? EX: Using 1 & 2: 1274, 5142, 2751, etc... Answered by Penny Nom. 





The last digit of a large exponent 
20041020 

From Landon: How can one determine the last digit of a large exponent by hand. I have seen several examples of how to do this by breaking it up into smaller exponents, but is there a formula or some common things to look for? Answered by Penny Nom. 





A five digit number 
20041006 

From A parent: What is the 5 digit number in which the first 2 digits are the square of the 3rd digit and the last 2 digits are the square of the digit that is one less than the third digit? The sum of all the digits is 22. Answered by Penny Nom. 





A palindrome question 
20040928 

From Lilly: 12, 21, 13, and 31 are the only doubledigit numbers whose squares are the palindromes of the squares of the palindromes of doubledigit numbers. I was wondering why it works for these numbers, and if only these numbers work this way. Answered by Chris Fisher and Penny Nom. 





The last digit of 2^28 
20040925 

From A student: I am currently enrolled in a math reasoning class and a math question I have to answer is determine the units digit in 3 28power. When I set up a table and keep cubing the numbers, I find a pattern with the last digits of the numbers that follow 1,3,9,7. My calculator gets to about the 19th power, and then I get an error. If I continued the pattern, would the units digit then be the last digit of 3 28th power, which would be a 7? Please let me know if I am solving this correctly and what a unit's digit actually is. Answered by Penny Nom. 





Four and five digit numbers 
20040921 

From Josy:
The question I have now in front of me is....Is a 4digit number always less than a 5digit number?
Hi Josy,
The digits in order are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Thus the largest four digit number is 9999. The smallet 5 digit number is 10000.
Penny
Go to Math Central
Answered by Penny Nom. 





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. 





The bar over repeating digits. 
20040907 

From Debbie: I would like to know the name given to the bar that is written over the repeating digits of a decimal. 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. 





Jack's social security number 
20040608 

From A student: Jack's social security number contains each of the nonzero digits exactly once. By examining the digits from left to right, he also found that 1 divides the first digit evenly, 2 divides the sum of the first two digirs evenly, 3 divides the sum of the first three digits evenly, and so on, until 9 divides the sum of all the digits evenly. What is Jack's social security number? Answered by Penny Nom. 





A 3 digit number divisible by 7 
20040503 

From A student: We need to arrange 1,3 and 6 to form a 3 digit number that is divisible by 7. Answered by Penny Nom. 





Setting up an equation 
20040430 

From Matt: I am trying to determine the dimensions of a 22 megapixel digital camera chip that has a 3:2 ratio. We know then, that: 3x = 2y (or 1.5x = y)
and that
xy = 22
Beyond this, I don't know how to hook those 2 seemingly unrelated facts together. Answered by Penny Nom. 





The units digit of 4^478 
20040306 

From Elizabeth: What is the units digit of 4^{478}? Answered by Penny Nom. 





Digits in the decimal expansion 
20040211 

From Leslie: In the decimal expansion of 1/17 what digit is in the 1997th place? Answered by Penny Nom. 





Three digit combinations 
20040127 

From Kevin: how many 3 digit combinations can be made with 09. i have been told only 1,000. when i asked jeeves the response was 750 without using any digit twice. i have entered a raffle and received a ticket with 4 sets of 3 digit numbers. Answered by Penny Nom. 





Four digit combinations 
20031231 

From A student: i need all 4 digit combinations using 09 please 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 digits in 349 
20030912 

From Franik: in the number 349, which number has the least value, and why? Answered by Penny Nom. 





7,473,000,000 divided by 52000 
20030906 

From A student: I am having trouble with a question. 7,473,000,000 divided by 52000. Our calculater gets 147311.5385. I come up with 143711.53846, and then the number starts to repeat itself Answered by Penny Nom. 





Four digit combinations 
20030904 

From Emma: I seriously need to find out all the four digit combinations from 0 to 9!!! My name Is Emma Dibitt and I'm going into 8th grade and I'm a student!!! Answered by Penny Nom. 





The units digit of 57 to the 28th power 
20030901 

From Maria:
If 57 is raised to the 28th power, what must be the units digit in the result? If you raise 7 to the 500th power, what is the numeral that will appear in the units digit position? 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. 





The number of three digit combinations 
20030816 

From Fred: There are four close friends having a heated discussion concerning the the number of three digit combinations using the numbers 0 through 9. The discussionÝinvolves the daily lottery.Ý Any assistance you can lend would be greatly appreciated. Answered by Penny Nom. 





Inserting a comma ever three digits 
20030725 

From Linda: when writing a large number, why do we insert a comma every three numbers instead of every two or four numbers? 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. 





Four digit palindromes 
20030505 

From Heather: How many palindromes were in between the numbers 1000 and 9999? Answered by Penny Nom. 





Three digit number 
20030310 

From Grace: What three digit positive integer is exactly 32 times the sum of its digits? Answered by Claude Tardif. 





Combinations of 1,2,3,4,5 and 6 
20030201 

From Kyle: Today I was aked a question by my geometry teacher. It was, what is the sum of all the possible combinations of the numbers 1, 2, 3, 4, 5, and 6. He said all the possible combinations were 720. I would like to know how u could do this, and what the answer is. 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. 





The units digit of 2 to the power of 31921 
20021218 

From A student: If 2 to the power of 31921 is multiplied out, what will be the units digit? Answered by Penny Nom. 





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. 





65,125 
20021204 

From Brittany: I am a threedigit number.When you reverse my digits,a larger number is formed.the product of me and the new number is 65,125.What number am I. Answered by Chris Fisher and 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. 





Rounding 27.27 
20021103 

From A parent: If you have a problem 27.27 and you need to round to the first 7 the answer would be 27 Would 27.0 be acceptable as well or is it completely wrong. Answered by Penny Nom. 





What are the digits? 
20021024 

From Ebenezer: There are three digits. The middle digit is zero and the sum of the first and last digits are is 13. When the number is reversed it is increased by 297. What are the digits? Answered by Penny Nom. 





Use each digit 19 only one time each,... 
20021019 

From Megan: Use each digit 19 only one time each, divide the numbers into 3 groups, make one 2 digit number, one 3 digit number, and one 4 digit number. There are 6 combinations of these numbers in which you can multiply the 2 digit and 3 digit number together to get the 4 digit number (using each digit 19 one time each). What are they!!!!!!!!!???????????? Answered by Claude Tardif. 





I am a 3 digit number. 
20020906 

From Jasmine: I am a 3 digit number. My last digit is 3 times my first digit. My firat digit is twice my middle digit. What numbers am I? There are at least 2 correct answers? Answered by Paul Betts. 





Counting 
20020621 

From Rachel: How many different numbers of 2 different digits each can be formed using the digits (1,3,5,7,9)?
How many triangles are formed by the vertical of a regular hexagon? Answered by Penny Nom. 





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. 





Squares of one digit numbers 
20011015 

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





The 100 chart 
20010928 

From Nich: Am I suppose to use the 100 chart for these questions. Question One: I am a 2 digit number my tens digit is 2 more than my one digit my 1 digit is between 4 & 6. What # am I ? Question Two: I am a 2 digit # I am greater than 40 but less than 60 my tens and ones digits are the same I am a odd number what am I ? Answered by Penny Nom. 





4 digit combinations 
20010922 

From Laura: I need all of the 4 digit combinations using the numbers 09. Answered by Harley Weston. 





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. 





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. 





How many 6 digit numeral combinations 
20010426 

From Bryan: How many 6 digit numeral combinations are there If you can only use 6 digits (1, 2, 3, 4, 5, 6) and no number can be used twice in the Numeral! 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. 





The repetend in repeating decimals 
20010321 

From Sharon: What is the name for the bar over the repetend in repeating decimals? Also, what is the name of the long division "house"? Answered by Penny Nom. 





Probability and a three digit number 
20010315 

From Glenn: A THREE DIGIT NUMBER IS SELECTED AT RANDOM. WHAT IS THE PROBABILITY THAT NON OF THE THREE DIGITS ARE PRIME. Answered by Harley Weston. 





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. 





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. 





Divisibility by 16 
20001212 

From Shiling: A number can be divided by 16 if and only if its 1st four digits can be divided by 16. How can you prove that? Answered by Penny Nom. 





Five digit palindromes 
20001112 

From Jacky: Positive integers such as 1287821 and 4554, in which the number is unchanged when the digits are reversed, are called palindromes. The number of fivedigit integers larger than or equal to 10,000 which are not palindromes is... a. 10 000 b. 81 000 c. 89100 d. 90 000 e. 99 100 Answered by Penny Mom. 





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. 





The units digit of 3 to the 58th power 
20000510 

From Kylie Mcalpine: the questions we have been asked are what is the units digit of the following: a) 3^{58} b) 23^{58} c) 17^{31} and the harder question of: what is the units digit of the following sum: 13^{841} + 17^{508} + 24^{617} = ??????? Answered by Paul Betts and Penny Nom. 





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. 





A three digit number 
20000113 

From Manali Shah: My son is in 5th grade, he has a math problem. There is three digit number, which is greater than 500, can be divided by 7,9 and 11, but cannot be divided by 2,4,6, and 5. Answered by Harley Weston. 





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. 





0! + 1! + 2! + 3! + ... + 2000! 
19991021 

From Melissa: My name is melissa. I am a 9th grade student I am having trouble finding out how to do this: What is the tens digit of 0! + 1! + 2! + 3! + ... + 2000! I know how to find these, but my calculator cant go any higher than 69! Is there any way i can do this problem? Answered by Penny Nom. 





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. 





A Puzzle 
19981027 

From Bruce Bragnu: We are trying to solve what SHOULD BE a simple 7th grade problem and have run into a wall. It is: ABCD ABCD ABCD ABCD  EBEA It is an addition problem. Each particular letter represents the same digit. We are looking for what number "B" represents. We have tried a multitude of solutions and have come up empty. Answered by Penny Nom. 





A Six Digit Number 
19981027 

From Craig Bedard: If a certain sixdigit number is split into two parts, one constituting the first three digits and the other the last three digits, and the two parts are added and the resultiong sum squared, it is found that the product is the original six digit number. What is the original sixdigit number? At first it seemed liked an impossible question, until it hit me...how long will it take you? Answered by Jason Stein and Dan Usselman. 





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. 





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. 





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. 





How many digits are there in 2^2520? 
19961007 

From Rita Leung: A)The number 64 is a sq., a cube, and a sixth power because 64=8*8, 4*4*4, 2*2*2*2*2*2. Find the smallest integer greater than 1 that is a sq., a cube, a 4th, 5th, 6th, 7th, 8th, 9th and 10th power. I have found that the answer is 2 to the power 2520th. B) How many digits are in the correct answer to part A? The answer is uncertain. It is either 758 or 759. Can you give me any ideas? Answered by Penny Nom. 





Repeating decimals 
19960909 

From Alice: What is the line called that is placed over the decimal to show that it is infinitely repeating? Answered by The Centralizer. 

