Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?

Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?

Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

This article for teachers describes how number arrays can be a useful representation for many number concepts.

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Follow this recipe for sieving numbers and see what interesting patterns emerge.

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

Given the products of adjacent cells, can you complete this Sudoku?

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

Given the products of diagonally opposite cells - can you complete this Sudoku?

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

Is there an efficient way to work out how many factors a large number has?

What is the smallest number of answers you need to reveal in order to work out the missing headers?

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

The clues for this Sudoku are the product of the numbers in adjacent squares.

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

Can you work out how many lengths I swim each day?

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

Number problems at primary level that may require resilience.

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

Find the highest power of 11 that will divide into 1000! exactly.

Can you find any perfect numbers? Read this article to find out more...

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

Can you work out what size grid you need to read our secret message?

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?

6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?

A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N?

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

56 406 is the product of two consecutive numbers. What are these two numbers?

Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.

Find the number which has 8 divisors, such that the product of the divisors is 331776.