Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
What happens when you try and fit the triomino pieces into these
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?
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 cover the camel with these pieces?
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?
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?
Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
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
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
Move just three of the circles so that the triangle faces in the
What does the overlap of these two shapes look like? Try picturing
it in your head and then use the interactivity to test your
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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?
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 game for two players. You'll need some counters.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
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?
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?
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Which of these dice are right-handed and which are left-handed?
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
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.
Here are shadows of some 3D shapes. What shapes could have made
Can you fit the tangram pieces into the outlines of the candle and sundial?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
I've made some cubes and some cubes with holes in. This challenge
invites you to explore the difference in the number of small cubes
I've used. Can you see any patterns?
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.
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outline of the child walking home from school?
How many balls of modelling clay and how many straws does it take
to make these skeleton shapes?
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!
Can you find ways of joining cubes together so that 28 faces are
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?