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?
A toy has a regular tetrahedron, a cube and a base with triangular
and square hollows. If you fit a shape into the correct hollow a
bell rings. How many times does the bell ring in a complete game?
Try this interactive strategy game for 2
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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
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?
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?
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?
What is the best way to shunt these carriages so that each train
can continue its journey?
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?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
One face of a regular tetrahedron is painted blue and each of the
remaining faces are painted using one of the colours red, green or
yellow. How many different possibilities are there?
A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
How can you paint the faces of these eight cubes so they can be put
together to make a 2 x 2 cube that is green all over AND a 2 x 2
cube that is yellow all over?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
Investigate the number of paths you can take from one vertex to
another in these 3D shapes. Is it possible to take an odd number
and an even number of paths to the same vertex?
A game has a special dice with a colour spot on each face. These
three pictures show different views of the same dice. What colour
is opposite blue?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Can you cut up a square in the way shown and make the pieces into a
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
Can you fit the tangram pieces into the outlines of the candle and sundial?
What is the greatest number of squares you can make by overlapping
A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.
Can you fit the tangram pieces into the outline of Little Ming?
Can you work out what kind of rotation produced this pattern of
pegs in our pegboard?
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?
Can you fit the tangram pieces into the outline of Granma T?
What is the relationship between these first two shapes? Which
shape relates to the third one in the same way? Can you explain
Here are more buildings to picture in your mind's eye. Watch out -
they become quite complicated!
Can you fit the tangram pieces into the outline of Mai Ling?
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Can you fit the tangram pieces into the outline of these rabbits?
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?
An extension of noughts and crosses in which the grid is enlarged
and the length of the winning line can to altered to 3, 4 or 5.
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you work out what is wrong with the cogs on a UK 2 pound coin?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outlines of the chairs?
Can you make a 3x3 cube with these shapes made from small cubes?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Which of these dice are right-handed and which are left-handed?