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 listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

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?

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?

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

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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 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?

How many models can you find which obey these rules?

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?

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?

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....?

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

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

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

These practical challenges are all about making a 'tray' and covering it with paper.

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

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?

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?

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?

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

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

The Zargoes use almost the same alphabet as English. What does this birthday message say?

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?

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

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

Two sudokus in one. Challenge yourself to make the necessary connections.

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

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.

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

Two sudokus in one. Challenge yourself to make the necessary connections.

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

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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

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

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?

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?

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.

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. . . .

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

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