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

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

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?

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?

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

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?

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

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?

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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?

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

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

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!

Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

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?

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

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

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

Meg and Mo need to hang their marbles so that they balance. Use the interactivity to experiment and find out what they need to do.

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

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?

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

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?

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

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.

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

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

Mo has left, but Meg is still experimenting. Use the interactivity to help you find out how she can alter her pouch of marbles and still keep the two pouches balanced.

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

Meg and Mo still need to hang their marbles so that they balance, but this time the constraints are different. Use the interactivity to experiment and find out what they need to do.

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.

A game for 1 person to play on screen. Practise your number bonds whilst improving your memory

How many different triangles can you make which consist of the centre point and two of the points on the edge? Can you work out each of their angles?

Can you beat the computer in the challenging strategy game?

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

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?

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?

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?

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?