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?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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?
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
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 cover the camel with these pieces?
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?
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 quadrilaterals can be made by joining the dots
on the 8-point circle?
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?
Move just three of the circles so that the triangle faces in the
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Exchange the positions of the two sets of counters in the least possible number of moves
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
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?
A variant on the game Alquerque
How many different triangles can you make on a circular pegboard
that has nine pegs?
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
A game for two players. You'll need some counters.
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
What does the overlap of these two shapes look like? Try picturing
it in your head and then use the interactivity to test your
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?
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?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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?
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?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
This 100 square jigsaw is written in code. It starts with 1 and
ends with 100. Can you build it up?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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 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!
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?
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.
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
A game for two players on a large squared space.
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?
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?
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 outlines of the workmen?
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 outline of Little Ming and Little Fung dancing?
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 outlines of Mai Ling and Chi Wing?
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.
Here are shadows of some 3D shapes. What shapes could have made
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.