







More on the last 2 digits of a^k = N 
20200807 

From Jay: I've seen solution methods for finding the last 2 digits
of a^k = N, where a and k are known. My question
is:
What if the number N is known and the last 2
digits are, say, ...62. Is there a way to find, for
any given a, the value of k which will result in a
number where the last 2 digits are ...62? and if
that is possible, then do the same for
a number with the last n digits (say 7 or 53 or
something)? Answered by Harley Weston. 





Some strings of 4 digits 
20200626 

From Judy: I wrote previously and need more help. I need to generate a list of 4 digit. Numbers using 09 with no repetitions
I know that there is a 6 followed by a 2. Order does matter
Thank you in advance for your help. Answered by Penny Nom. 





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. 





How many numbers from the set have the sum of its digits equal to 2? 
20191024 

From Marcel: Hello. My question is the following: Given the set {1,2...........10exp2019}, how many numbers from the set have the sum of its digits equal to 2?
I got some of them : 2 20 200 2000 20000 .......2. 10exp2018 11 110 1100 11000 110000....101 1010 10100 101000 1010000....10011 10010 100100 1001000 1010000.....10001 100010 1000100 10001000,,,,,,100001 1000010 10000100.......
My problem is that I have difficulty in finding a strategy to obtain the exact quantity of numbers. Please help me, thanks Answered by Penny Nom. 





Arranging 10 digits 
20191009 

From Laxmi: 1)The integers 0 to 9 are arranged along a straight line in some order.a) find a possible arrangement in which the sum of any three adjacent numbers is less than 15.b)is there an arrangement of this kind 0 is not included in the numbers. Answered by Penny Nom. 





The number of integers that satisfy some conditions 
20190910 

From Ryu: Using only the digits 0 1 2 3 4 5 6 7 8 9 without repetition, how many integers are:
(a) Greater than 999, less than 10,000, start with an even digit and are even?
(b) Greater than 999, less than 10,000, start with an odd digit and are odd?
(c) Greater than 999, less than 10,000, start with an even digit and are odd?
(d) Greater than 999, less than 10,000, start with an odd digit and are even? 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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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 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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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 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. 





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. 





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. 





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 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. 





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. 





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 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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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 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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 

