Find the frequency distribution for ordinary English, and use it to help you crack the code.

Substitution and Transposition all in one! How fiendish can these codes get?

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

A game that tests your understanding of remainders.

Some 4 digit numbers can be written as the product of a 3 digit number and a 2 digit number using the digits 1 to 9 each once and only once. The number 4396 can be written as just such a product. Can. . . .

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

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

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?

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

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?

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?

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

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

A game in which players take it in turns to choose a number. Can you block your opponent?

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

Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.

A collection of resources to support work on Factors and Multiples at Secondary level.

Have you seen this way of doing multiplication ?

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.

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" .

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...

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.

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

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.

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

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

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

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.

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

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

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

Factorial one hundred (written 100!) has 24 noughts when written in full and that 1000! has 249 noughts? Convince yourself that the above is true. Perhaps your methodology will help you find the. . . .

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?

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

The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. . . .

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

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

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

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?

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

Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.

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

Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.

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.

Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?

Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.

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. . . .

Explore the relationship between simple linear functions and their graphs.