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

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

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?

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

What happens when you try and fit the triomino pieces into these two grids?

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?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

How will you go about finding all the jigsaw pieces that have one peg and one hole?

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

Try this matching game which will help you recognise different ways of saying the same time interval.

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

In this matching game, you have to decide how long different events take.

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

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?

What is the least number of moves you can take to rearrange the bears so that no bear is next to a bear of the same colour?

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

What is the best way to shunt these carriages so that each train can continue its journey?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

How many models can you find which obey these rules?

Find your way through the grid starting at 2 and following these operations. What number do you end on?

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

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.

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

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?

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

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

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

Find all the numbers that can be made by adding the dots on two dice.

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

An activity making various patterns with 2 x 1 rectangular tiles.

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?

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

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