Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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?

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

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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

Dotty Six is a simple dice game that you can adapt in many ways.

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

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

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?

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

Use these four dominoes to make a square that has the same number of dots on each side.

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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

What can you see? What do you notice? What questions can you ask?

Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?