







How many guests were present? 
20170917 

SM pose la question : How many guests were present at an Italian dinner if every 2 guests shared a bowl of salad, every 3 guests shared a bowl of pasta, and every four guests shared a bowl of meatballs, and there were 65 bowls used altogether? Penny Nom lui répond. 





Is a large integer divisible by 2^n? 
20170328 

Sahand pose la question : You are given number x that is very large (that large that it can't be divided by hand)
can we find out that x is divisible by 2^n or not? Penny Nom lui répond. 





Divisibility of 3n^5+7n 
20161214 

Parag pose la question :
Question from Parag, a student:
if n is a natural number,then 3n^5+7n is divisible by
a)2
b)3
c)5
d)7
i got the answer but still i need a valid alternate approach. Penny Nom lui répond. 





How many boats total are in the marina? 
20150415 

Carla pose la question : In a marina, 3/4 of the boats are white, of the remainder 4/7 are blue, the rest are red. There are 9 red boats. How many boats total are in the marina? My answer is 84 because if 1/4 of the boats are divided into sevenths, that makes the whole marina a 28 part item. 3/28 are red so 84 is the total number of boats. My child thinks I am wrong. Penny Nom lui répond. 





4821x14y is an 8digit number divisible by 72 
20140806 

RAYA pose la question : if 4821x14y is an 8digit number divisible by 72. How many values can x and y take? Penny Nom lui répond. 





A 4 digit number 
20140404 

LIM pose la question : "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? Chris Fisher lui répond. 





A 2digit number 
20130513 

A teacher pose la question : 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. Lorraine Dame, Harley Weston lui répond. 





Some 6 digit numbers 
20121023 

Mason pose la question : 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? Penny Nom lui répond. 





Squares and triangles 
20111206 

Liaqath pose la question : You have squares and triangles.
Altogether there are 33 sides.
How many squares do you have?
How many triangles do you have? Penny Nom lui répond. 





An even multiple of 27 
20110201 

parth pose la question : the 6 digit # 63x904 is an even multiple of 27 what is X Penny Nom lui répond. 





Powers 
20101020 

dylan pose la question : how do you write 20736 in exponential form .same for 1728 and 50625.
is there a formula to figure out how to express large know numbers in exponential form. Penny Nom lui répond. 





(x^3 + 11x) is divisible by 6 
20100624 

PT pose la question : Given that x is a nonzero integer,
how do you show that for all values of x,
(x3 + 11x) is divisible by 6?
I know it works but how do I answer the "all values of x" part?
Thanks in advance! Robert Dawson lui répond. 





Divisibility by 3 
20100523 

Cathleen pose la question : To math central. I have to do a maths extension question that I don't understand. At first I thought I did.
It is about the dividing by three. In one part of the question, it asks me to show that the rule of division by three does not work for 23142 with a little 5 down the bottom.
What doe base 5 mean? We first thought that the little 5 down the bottom meant multiplying y the power of five.
Can you please tell me what it means so I can finish this question? Penny Nom lui répond. 





The difference of the two numbers 
20100215 

Steve pose la question : The difference of the two numbers 'abcdef ' and ' fdebca ' is divisible by 271. prove
that b = d and c = e. Claude Tardif lui répond. 





Two questions from math class 
20090618 

Con pose la question : 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 Chris Fisher lui répond. 





Divisibility 
20090617 

Sophia pose la question : Hello
Please help my son with the solutions to the following:
a) Determine the remainder when 2^2009 + 1 is divided by 17;
b) Prove that 30^99 + 61^100 is divisible by 31;
c) It is known that numbers p and 8p^2+1 are primes. Find p.
Again, your assistance is greatly appreciated.
Thanks
Sophia Robert Dawson lui répond. 





Divisibility by 11 
20080704 

Peter pose la question : For what single digit value of n is the number n53nn672 divisible by 11? Leeanne Boehm lui répond. 





The smallest number divisible by 1 to 9 
20080626 

Peggy pose la question : What is the smallest number divisible by each of the first nine counting numbers? Penny Nom lui répond. 





The sum of the digits of a number 
20080623 

Ben pose la question : 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. Penny Nom lui répond. 





Nine digit numbers 
20080521 

Alex pose la question : List of Nine digit numbers, that can be divided by nine? Janice Cotcher lui répond. 





I am a 4digit number 
20080212 

Nickie pose la question : 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? Penny Nom lui répond. 





How many combinations of 8614 are divisible by 7? 
20080122 

Rebecca pose la question : How many combinations of 8614 are divisible by 7 equally (with no remainder)? Penny Nom lui répond. 





Divisibility 
20070518 

Ashish pose la question : A number is divisible by 2^n if the last n digits of the number are divisible by 2^n.
Why? Penny Nom and Claude Tardif lui répond. 





Divisibility by 9 and 11 
20061004 

Prakai pose la question : can 818991 divisible by 9, or 11? Penny Nom lui répond. 





Divisibility by each of the first ten counting numbers 
20051017 

Simon pose la question : determine smallest positive integer that is divisible by each of the first ten counting numbers Penny Nom lui répond. 





Divisibility of a^2 + b^2 
20050516 

Ampa pose la question : given natural numbers a and b such that a^{2}+b^{2} is divisible by 21, prove that the same sum of squares is also divisible by 441. Penny Nom lui répond. 





Divisibility by 15 
20041219 

Lisa pose la question : My son was asked to find divisiblity rules for 15. We have been unable to find the answer. Does it exist? Leeanne Boehm and Denis Hanson lui répond. 





Divisibility by 7 and 11 
20041013 

Tammy pose la question : I'm stuck in class in Yr 7 And I'm finding it hard on our new topic Divisibility! When I try to find out what this means on Internet sites i can not understand the used symbols like algebra and so on. I'm stuck on the divisibility rules for the number 11! Penny lui répond. 





Divisibility by 7 
20031114 

A student pose la question : how do you test a number to see if it is divisible by 7 or not? Penny Nom lui répond. 





Divisibility by 2 or 5 or both 
20031030 

Abdu pose la question : How many positive integers less than 1,001 are divisible by either 2 or 5 or both? Penny Nom lui répond. 





39 consecutive natural numbers 
20030819 

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





The cousin of Sally's sister's boyfriend 
20030123 

Michael pose la question : Sally went to a farm to buy eggs. Returning home, she gave half of them to her sister who, in turn, gave a third of those she had gotten to her boyfriend. The latter, after eating one third of the eggs that he had gotten, gave the rest to his cousin. Given that each egg weighs 70 grams, that Sally cannot carry more than 2.5kg, and that the eggs were raw, calculate how many eggs the cousin of Sally's sister's boyfriend received. Penny Nom lui répond. 





abc,abc 
20021120 

Pam pose la question : Prove or disprove that "every number of the form abc,abc (where a, b, and c represent digits) is divisible by 7,11, and 13" Penny Nom lui répond. 





Two problems 
20021014 

Eva pose la question :
a) How many different equivalence relations can be defined on the set X={a,b,c,d}? b)Show that 6 divides the product of any 3 consecutive integers. I know it is true that 6 divides the product of any 3 consecutive integers. However, i have problem showing the proof. Leeanne Boehm and Penny Nom lui répond. 





Divisibility of 5^{ 2002} 
20020825 

Simon pose la question : I need to ask you a question if 5^{ 2002} and 3^{ 2002} are divisible by 26. Penny Nom lui répond. 





Nickles, dimes, quarters and fifty cent pieces 
20020108 

A parent pose la question : The total for all coins counted is $4,564.50 The last coin added to the pile is a 50 cent piece There are 8 times as many 50 cent pieces as there are quarters There are 6 times as many dimes as nickles How many of each are there? Penny Nom lui répond. 





Divisibility rules 
20010907 

A student pose la question : Why is it that when you add the digits of a number you can tell what the multiples of that number are. Example: 12131313111,
1+2+1+2+1+3+1+1+1=18,
therefore 12131313111 is divisble by 2, 9, 18, & 3 because those numbers are divisble by 18. Penny Nom lui répond. 





Divisibility by 16 
20001212 

Shiling pose la question : 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? Penny Nom lui répond. 





Divisibility by 9 
20001024 

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





Divisibility by 3 
20000324 

Pat Walsh pose la question : W hy does it work when you add the digits of a number then divid by three to see if the number is divisible by three Penny Nom lui répond. 





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

Rachel pose la question : 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? Claude Tardif and Denis Hanson lui répond. 





111...1222...2 
19990811 

Brad Goorman pose la question : Let N = 111...1222...2, where there are 1999 digits of 1 followed by 1999 digits of 2. Express N as the product of four integers, each of them greater than 1. Penny Nom lui répond. 





Divisibility by 9 
19990221 

Razzi pose la question : I've been having a hard time trying to solve the following problem and I was wondering if you could help me. For any positive integer a let S(a) be the sum of its digits. Prove that a is divisible by 9 if and only if there exist a positive integer b such that S(a)=S(b)=S(a+b). Chris Fisher and Harley Weston lui répond. 





Divisibility by 11 
19981028 

Pat Duggleby pose la question : I am an upgrading instructor at a dropin program in Regina. One of my students is taking General Math 30 through correspondence, and we have run into some confusing instructions. The section is about divisibility rules, and we did just fine up until the rule for Divisibility by 11. The statement is as follows:  If the difference between the sum of the oddnumbered digits and the sum of the evennumbered digits, counted from right to left, is divisible by 11, then the number is divisible by 11.  . . . Penny Nom lui répond. 





A Place Value Curiosity 
19980525 

Ed pose la question : I was visiting with an elderly gentleman this afternoon. He showed me this curiosity and then asked if I could explain it to him. Can you provide an explanation of why the 9 or multiple of 9 keeps occurring in this procedure? Choose any number, say 125 and add the digits to get 8. subtract the 8 from the 125 and the result is 117. Add the digits in 117 to get 9. Subtract the 9 from the 117 to get 108. Add the digits in 108 to get 9. If this procedure continues a 9 or a multiple of 9 reoccurs. What is the mathematical explanation behind this happening? Denis Hanson lui répond. 

