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

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

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?

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

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

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

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

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!

Can you find all the different triangles on these peg boards, and find their angles?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

How many different triangles can you make on a circular pegboard that has nine pegs?

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

An environment which simulates working with Cuisenaire rods.

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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

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?

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

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?

Can you find all the different ways of lining up these Cuisenaire rods?

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

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

Find out what a "fault-free" rectangle is and try to make some of your own.

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

Try out the lottery that is played in a far-away land. What is the chance of winning?

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

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

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?

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

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.

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

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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?

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

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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?

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 put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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?