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Weekly Problem 10 - 2008

If the numbers 1 to 10 are all multiplied together, how many zeros are at the end of the answer?

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Which of the numbers shown is the product of exactly 3 distinct prime factors?

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How many two-digit primes are there between 10 and 99 which are also prime when reversed?

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Weekly Problem 18 - 2016

The year 2010 is one in which the sum of the digits is a factor of the year itself. What is the next year that has the same property?

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The product of four different positive integers is 100. What is the sum of these four integers?

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The numbers 72, 8, 24, 10, 5, 45, 36, 15 are grouped in pairs so that each pair has the same product. Which number is paired with 10?

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Charlie doesn't want his new house number to be divisible by 3 or 5. How many choices of house does he have?

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Weekly Problem 49 - 2013

What is the value of 2000 + 1999 Ã— 2000?

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Last week, Tom and Sophie bought some stamps and they spent exactly Â£10. Can you work out how many stamps they bought?

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Weekly Problem 24 - 2006

How many of the rearrangements of the digits 1, 3 and 5 give prime numbers?

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Weekly Problem 26 - 2014

Which of the given numbers is divisible by 6?

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Can you find the missing digits, given that the number is divisible by 3, 4, 5 and 6?

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How many of the numbers 1 to 20 are not the sum of two primes?

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Four cards have a number on one side and a phrase on the back. On each card, the number does not have the property described on the back. What do the four cards have on them?

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In the multiplication table on the right, only some of the numbers have been given. What is the value of A+B+C+D+E?

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A whole number less than 100 gives remainders of 2, 3 and 4 when divided by 3, 4 and 5. What is the remainder when it is divided by 7?

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What is the smallest number of pieces grandma should cut her cake into to guarantee each grandchild gets the same amount of cake and none is left over?

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Helen buys some cakes and some buns for her party. Can you work out how many of each she buys?

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Weekly Problem 35 - 2006

A number has exactly eight factors, two of which are 21 and 35. What is the number?

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Weekly Problem 52 - 2009

How did Jenny figure out that Tom's cards added to an even number?

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Weekly Problem 48 - 2013

What is the remainder when the number 743589Ã—301647 is divided by 5?

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How many three digit numbers formed with three different digits from 0, 1, 2, 3 and 5 are divisible by 6?

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Weekly Problem 34 - 2017

An abundant number is a positive integer N such that the sum of the factors of N is larger than 2N. What is the smallest abundant number?

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The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?

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Two numbers can be placed adjacent if one of them divides the other. Using only $1,...,10$, can you write the longest such list?

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Each digit of a positive integer is 1, 2 or 3, and each of these occurs at least twice. What is the smallest such integer that is not divisible by 2 or 3?

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One year there were exactly four Tuesdays and four Fridays in October. On what day of the week was Halloween.

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Can you arrange the red and blue cards so that the rules are all followed?

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Weekly Problem 22 - 2010

Can you form this 2010-digit number...

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144 divided by n leaves a remainder of 11. 220 divided by n also leaves a remainder of 11. What is n?

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Weekly Problem 41 - 2009

At a cinema a child's ticket costs Â£4.20 and an adult's ticket costs Â£7.70. How much did is cost this group of adults and children to see a film?

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In how many ways can seven of the numbers 1-9 be chosen such that they add up to a multiple of 3?

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Find out which two distinct primes less than $7$ will give the largest highest common factor of these two expressions.

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Weekly Problem 24 - 2017

What is the last digit of $3^{2011}$?

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Given any positive integer n, Paul adds together the factors of n, apart from n itself. Which of the numbers 1, 3, 5, 7 and 9 can never be Paul's answer?

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Can you find the next time that the 29th of February will fall on a Monday?

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What digit must replace the star to make the number a multiple of 11?

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The diagram shows a large rectangle composed of 9 smaller rectangles. If each of these rectangles has integer sides, what could the area of the large rectangle be?

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Can you work out which numbers between 1 and 2016 have exactly two of 2, 3, 4 as factors?

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Peter wrote a list of all the numbers that can be formed by changing one digit of the number 200. How many of Peter's numbers are prime?

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Each time a class lines up in different sized groups, a different number of people are left over. How large can the class be?

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Flora has roses in three colours. What is the greatest number of identical bunches she can make, using all the flowers?

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A male punky fish has 9 stripes and a female punky fish has 8 stripes. I count 86 stripes on the fish in my tank. What is the ratio of male fish to female fish?

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I made a list of every number that is the units digit of at least one prime number. How many digits appear in the list?

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What is the smallest integer where every digit is a 3 or a 4 and it is divisible by both 3 and 4?

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Chocolate bars come in boxes of 5 or boxes of 12. How many boxes do you need to have exactly 2005 chocolate bars?

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How many zeros are there at the end of $3^4 \times 4^5 \times 5^6$?

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Weekly Problem 47 - 2017

How many numbers do I need in a list to have two squares, two primes and two cubes?

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What is the sum of the digits of the largest 4-digit palindromic number which is divisible by 15?

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Weekly Problem 26 - 2017

The angles in the triangle are shown in the diagram in terms of x and y. If x and y are positive integers, what is the value of x+y?

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Albert Einstein is experimenting with two unusual clocks. At what time do they next agree?

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Roger multiplies two consecutive integers and squares the result. Can you find the last two digits of his new number?

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When coins are put into piles of six 3 remain and in piles of eight 7 remain. How many remain when they are put into piles of 24?

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How many integers $n$ are there for which $n$ and $n^3+3$ are both prime?

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Ruth wants to puts stickers on the cuboid she has made from little cubes. Will she have any stickers left over?

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We are given two factors of a number with eight factors. Can you work out the other factors of the number?

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One of these numbers is the largest of nine consecutive positive integers whose sum is a perfect square. Which one is it?

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From this sum of powers, can you find the sum of the indices?

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Weekly Problem 1 - 2015

If $p$ and $q$ are prime numbers greater than $3$ and $q=p+2$, prove that $pq+1$ is divisible by $36$.

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If you take a number and add its square to its cube, how often will you get a perfect square?

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Can you find a fraction with the following properties?

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Tina has chosen a number and has noticed something about its factors. What number could she have chosen? Are there multiple possibilities?

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Weekly Problem 6 - 2010

Can you find three primes such that their product is exactly five times their sum? Do you think you have found all possibilities?

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The price of an item in pounds and pence is increased by 4%. The new price is an integer number of pounds. Can you find it?

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Weekly Problem 26 - 2008

If $n$ is a positive integer, how many different values for the remainder are obtained when $n^2$ is divided by $n+4$?

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Using the hcf and lcf of the numerators, can you deduce which of these fractions are square numbers?

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Weekly Problem 39 - 2012

For how many values of $n$ are both $n$ and $\frac{n+3}{nâˆ’1}$ integers?

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Weekly Problem 17 - 2010

The value of the factorial $n!$ is written in a different way. Can you work what $n$ must be?

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Weekly Problem 10 - 2011

Will this product give a perfect square?