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?

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

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?

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?

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

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?

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

Number problems at primary level to work on with others.

Number problems at primary level that may require resilience.

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

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?

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

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

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

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?

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?

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

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?

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?

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?

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?

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...

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

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

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.

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

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

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.

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

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.

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

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

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

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

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.

Explore the relationship between simple linear functions and their graphs.

Are these statements always true, sometimes true or never true?

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!?

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

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

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

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.

Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?

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

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...

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?