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.

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

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?

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

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

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

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?

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?

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?

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?

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

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?

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

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

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

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

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

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 tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

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?

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

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

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

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

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.

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

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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?

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

How many different symmetrical shapes can you make by shading triangles or squares?

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

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?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

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

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?

A Sudoku that uses transformations as supporting clues.

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

How many models can you find which obey these rules?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

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?