
Whenever two chameleons of different colours meet they change colour to the third colour. Describe the shortest sequence of meetings in which all the chameleons change to green if you start with 12. . . .

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

Investigate 1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n and 2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n for different values of n.

A combination mechanism for a safe comprises thirty-two tumblers numbered from one to thirty-two in such a way that the numbers in each wheel total 132... Could you open the safe?

What is the sum of all the digits in all the integers from one to one million?

The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?

Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?

There are exactly 3 ways to add 4 odd numbers to get 10. Find all the ways of adding 8 odd numbers to get 20. To be sure of getting all the solutions you will need to be systematic. What about. . . .

You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre jug is full of wine, the others are empty. Can you divide the wine into three equal quantities?

This challenge is to make up YOUR OWN alphanumeric. Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

Using the 8 dominoes make a square where each of the columns and rows adds up to 8

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Find the values of the nine letters in the sum: FOOT + BALL = GAME
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

Each symbol has a numerical value. The total for the symbols is written at the end of each row and column. Can you find the missing total that should go where the question mark has been put?

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was. . . .

In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

Here is a chance to play a version of the classic Countdown Game.

Different combinations of the weights available allow you to make different totals. Which totals can you make?

If you wrote all the possible four digit numbers made by using each of the digits 2, 4, 5, 7 once, what would they add up to?
This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 35?

Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

Find a great variety of ways of asking questions which make 8.

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?
How can we help students make sense of addition and subtraction of negative numbers?

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

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.

The country Sixtania prints postage stamps with only three values 6 lucres, 10 lucres and 15 lucres (where the currency is in lucres).Which values cannot be made up with combinations of these postage. . . .
An account of some magic squares and their properties and and how to construct them for yourself.

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.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

There are nasty versions of this dice game but we'll start with the nice ones...

In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?

This Sudoku, based on differences. Using the one clue number can you find the solution?

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

Special clue numbers related to the difference between numbers in two adjacent cells and values of the stars in the "constellation" make this a doubly interesting problem.

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
Find out about Magic Squares in this article written for students. Why are they magic?!