As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?

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

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

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?

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?

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

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

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

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

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

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

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?

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

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?

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

One day five small animals in my garden were going to have a sports day. They decided to have a swimming race, a running race, a high jump and a long jump.

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.

Some children were playing a game. Make a graph or picture to show how many ladybirds each child had.

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

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?

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

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?

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

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?

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

These pieces of wallpaper need to be ordered from smallest to largest. Can you find a way to do it?

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.

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?

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

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.

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?

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

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