We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

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?!

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

Delight your friends with this cunning trick! Can you explain how it works?

These two group activities use mathematical reasoning - one is numerical, one geometric.

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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.

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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.

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

This task follows on from Build it Up and takes the ideas into three dimensions!

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

Can you find all the ways to get 15 at the top of this triangle of numbers?

Choose any three by three square of dates on a calendar page. Circle any number on the top row, put a line through the other numbers that are in the same row and column as your circled number. Repeat. . . .

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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

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.

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

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.

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

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

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

If you have only four weights, where could you place them in order to balance this equaliser?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.