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?

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

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

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

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?

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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. . . .

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

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?

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

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?

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?

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?

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?

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

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.

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

Factors and Multiples game for an adult and child. How can you make sure you win this game?

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

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?

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.

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

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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

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.

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

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

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

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?

Can you complete this jigsaw of the multiplication square?

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

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?

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...

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 find a way to identify times tables after they have been shifted up or down?

Number problems at primary level that may require resilience.

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?

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

Play this game and see if you can figure out the computer's chosen number.

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

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

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

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.

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?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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?