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?
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?
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
Design an arrangement of display boards in the school hall which fits the requirements of different people.
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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?
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?
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Can you find ways of joining cubes together so that 28 faces are
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?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
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. . . .
What happens to the area of a square if you double the length of
the sides? Try the same thing with rectangles, diamonds and other
shapes. How do the four smaller ones fit into the larger one?
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?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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?
Can you fit the tangram pieces into the outline of this telephone?
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 the child walking home from school?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of these people?
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 fit the tangram pieces into the outline of Granma T?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
Can you make a 3x3 cube with these shapes made from small cubes?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
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?
Can you visualise what shape this piece of paper will make when it is folded?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Exchange the positions of the two sets of counters in the least possible number of moves
How many different triangles can you make on a circular pegboard that has nine pegs?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Make a flower design using the same shape made out of different sizes of paper.
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Here's a simple way to make a Tangram without any measuring or
Can you fit the tangram pieces into the outline of this goat and giraffe?
Can you fit the tangram pieces into the outline of this sports car?
Can you fit the tangram pieces into the outline of these convex shapes?
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.
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?