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

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...

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

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

Can you explain the strategy for winning this game with any target?

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

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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

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

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

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

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.

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

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

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

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?

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.

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

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

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

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

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...

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 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?

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.

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

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

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?

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

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.

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.

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

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.

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.

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

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 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?

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

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

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

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

Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?

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

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

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

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.