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

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

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

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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?

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

Number problems at primary level that may require resilience.

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

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?

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

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?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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

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?

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

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

Can you make square numbers by adding two prime numbers together?

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

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

Number problems at primary level to work on with others.

Can you find different ways of creating paths using these paving slabs?

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?

Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

Can you work out some different ways to balance this equation?

Can you find any two-digit numbers that satisfy all of these statements?

Got It game for an adult and child. How can you play so that you know you will always win?

Have a go at balancing this equation. Can you find different ways of doing it?

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

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.

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.

I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...

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...

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

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

If you have only four weights, where could you place them in order to balance this equaliser?

An investigation that gives you the opportunity to make and justify predictions.

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?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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