This is part of our collection of Short Problems.
You may also be interested in our longer problems on Factors, Multiples and Primes: Age 11-16.
We have put together a selection of these short problems as printable worksheets:
Printable worksheets: Age 11-14 ⭐ Printable worksheets: Age 11-14 ⭐⭐ Printable worksheets: Age 11-14 ⭐⭐⭐
Printable worksheet: Age 14-16 ⭐ Printable worksheets: Age 14-16 ⭐⭐ Printable worksheets: Age 14-16 ⭐⭐⭐ Printable worksheet solutions
1 out of 3
Which of the numbers shown is the product of exactly 3 distinct prime factors?
1 out of 3
Weekly Problem 49 - 2013
What is the value of 2000 + 1999 × 2000?
1 out of 3
Weekly Problem 24 - 2006
How many of the rearrangements of the digits 1, 3 and 5 give prime numbers?
1 out of 3
Weekly Problem 10 - 2008
If the numbers 1 to 10 are all multiplied together, how many zeros are at the end of the answer?
1 out of 3
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?
1 out of 3
How many of the numbers 1 to 20 are not the sum of two primes?
1 out of 3
The product of four different positive integers is 100. What is the sum of these four integers?
1 out of 3
Weekly Problem 26 - 2014
Which of the given numbers is divisible by 6?
1 out of 3
Charlie doesn't want his new house number to be divisible by 3 or 5. How many choices of house does he have?
1 out of 3
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?
1 out of 3
Last week, Tom and Sophie bought some stamps and they spent exactly £10. Can you work out how many stamps they bought?
1 out of 3
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?
1 out of 3
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?
1 out of 3
How many two-digit primes are there between 10 and 99 which are also prime when reversed?
1 out of 3
Can you find the missing digits, given that the number is divisible by 3, 4, 5 and 6?
2 out of 3
The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
2 out of 3
Weekly Problem 48 - 2013
What is the remainder when the number 743589 × 301647 is divided by 5?
2 out of 3
Helen buys some cakes and some buns for her party. Can you work out how many of each she buys?
2 out of 3
Weekly Problem 35 - 2006
A number has exactly eight factors, two of which are 21 and 35. What is the number?
2 out of 3
Weekly Problem 52 - 2009
How did Jenny figure out that Tom's cards added to an even number?
2 out of 3
Two numbers can be placed adjacent if one of them divides the other. Using only $1,...,10$, can you write the longest such list?
2 out of 3
How many three digit numbers formed with three different digits from 0, 1, 2, 3 and 5 are divisible by 6?
2 out of 3
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?
2 out of 3
One year there were exactly four Tuesdays and four Fridays in October. On what day of the week was Halloween.
2 out of 3
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?
2 out of 3
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?
2 out of 3
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?
2 out of 3
Can you arrange the red and blue cards so that the rules are all followed?
3 out of 3
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?
3 out of 3
In how many ways can seven of the numbers 1-9 be chosen such that they add up to a multiple of 3?
3 out of 3
What digit must replace the star to make the number a multiple of 11?
3 out of 3
How many zeros does 50! have at the end?
3 out of 3
Weekly Problem 41 - 2009
At a cinema a child's ticket costs £4.20 and an adult's ticket costs £7.70. How much did it cost this group of adults and children to see a film?
3 out of 3
Find out which two distinct primes less than $7$ will give the largest highest common factor of these two expressions.
3 out of 3
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?
3 out of 3
Weekly Problem 24 - 2017
What is the last digit of $3^{2011}$?
3 out of 3
144 divided by n leaves a remainder of 11. 220 divided by n also leaves a remainder of 11. What is n?
3 out of 3
Can you find the next time that the 29th of February will fall on a Monday?
3 out of 3
Can you work out which numbers between 1 and 2016 have exactly two of 2, 3, 4 as factors?
3 out of 3
What is the units digit in this sum of powers of 9?
1 out of 3
The four digits 5, 6, 7 and 8 are put at random in the spaces of the number : 3 _ 1 _ 4 _ 0 _ 9 2 Calculate the probability that the answer will be a multiple of 396.
1 out of 3
Chocolate bars come in boxes of 5 or boxes of 12. How many boxes do you need to have exactly 2005 chocolate bars?
1 out of 3
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?
1 out of 3
Flora has roses in three colours. What is the greatest number of identical bunches she can make, using all the flowers?
1 out of 3
Each time a class lines up in different sized groups, a different number of people are left over. How large can the class be?
1 out of 3
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?
1 out of 3
What is the smallest integer where every digit is a 3 or a 4 and it is divisible by both 3 and 4?
1 out of 3
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?
2 out of 3
How many zeros are there at the end of $3^4 \times 4^5 \times 5^6$?
2 out of 3
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?
2 out of 3
One of these numbers is the largest of nine consecutive positive integers whose sum is a perfect square. Which one is it?
2 out of 3
Ruth wants to puts stickers on the cuboid she has made from little cubes. Will she have any stickers left over?
2 out of 3
What is the sum of the digits of the largest 4-digit palindromic number which is divisible by 15?
2 out of 3
Albert Einstein is experimenting with two unusual clocks. At what time do they next agree?
2 out of 3
How many integers $n$ are there for which $n$ and $n^3+3$ are both prime?
2 out of 3
What is the last-but-one digit of 99! ?
2 out of 3
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?
2 out of 3
Weekly Problem 47 - 2017
How many numbers do I need in a list to have two squares, two primes and two cubes?
2 out of 3
Roger multiplies two consecutive integers and squares the result. Can you find the last two digits of his new number?
