Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.

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

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

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?

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?

Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

Can you beat the computer in the challenging strategy game?

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

7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

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?

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Practise your diamond mining skills and your x,y coordination in this homage to Pacman.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

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

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Imagine picking up a bow and some arrows and attempting to hit the target a few times. Can you work out the settings for the sight that give you the best chance of gaining a high score?

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.

Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?

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

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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?

Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?

Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

Can you fit the tangram pieces into the outlines of these people?

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?