Visualising and representing

problem
Move a match

Age

7 to 11

Challenge level

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?
problem
The Cantor set

Age

11 to 14

Challenge level

Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you picture it?
problem
Sea defences

Age

7 to 14

Challenge level

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?
problem
Tessellating capitals

Age

5 to 7

Challenge level

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.
problem
Cubic covering

Age

14 to 16

Challenge level

A blue cube has blue cubes glued on all of its faces. Yellow cubes are then glued onto all the visible blue facces. How many yellow cubes are needed?
problem
Revolutions

Age

11 to 14

Challenge level

Jack and Jill run at different speeds in opposite directions around the maypole. How many times do they pass in the first minute?
problem
Maximum scattering

Age

16 to 18

Challenge level

Your data is a set of positive numbers. What is the maximum value that the standard deviation can take?
problem
Cuboid-in-a-box

Age

7 to 11

Challenge level

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
problem
Jomista mat

Age

7 to 11

Challenge level

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
problem
Areas of parallelograms

Age

14 to 16

Challenge level

Can you find the area of a parallelogram defined by two vectors?