Visualising and representing

problem
Map folding

Age

7 to 11

Challenge level

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?
problem
Green cube, yellow cube

Age

7 to 11

Challenge level

How can you paint the faces of these eight cubes so they can be put together to make a 2 x 2 x 2 cube that is green all over AND a 2 x 2 x 2 cube that is yellow all over?
problem
Christmas boxes

Age

11 to 14

Challenge level

Find all the ways to cut out a 'net' of six squares that can be folded into a cube.
problem
Single track

Age

7 to 11

Challenge level

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

Age

7 to 11

Challenge level

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?
problem
Square to L

Age

7 to 11

Challenge level

Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.
problem
In a box

Age

14 to 16

Challenge level

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?
problem
Flight of the Flibbins

Age

11 to 14

Challenge level

Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to the new planet?
problem
The root of the problem

Age

14 to 18

Challenge level

Find the sum of this series of surds.
problem
Cubic conundrum

Age

7 to 16

Challenge level

Which of the following cubes can be made from these nets?