Visualising and representing

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
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
Tricky triangles

Age

5 to 7

Challenge level

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
problem
Noughts and crosses

Age

11 to 14

Challenge level

Ever thought of playing three dimensional Noughts and Crosses? This problem might help you visualise what's involved.
problem
Cheese cutting

Age

16 to 18

Challenge level

In this problem we see how many pieces we can cut a cube of cheese into using a limited number of slices. How many pieces will you be able to make?
problem
One out one under

Age

14 to 16

Challenge level

Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?
problem
17s and 23s

Age

11 to 14

Challenge level

Can you form this 2010-digit number...
problem
Crawl around the cube

Age

11 to 14

Challenge level

Weekly Problem 37 - 2010
An ant is crawling around the edges of a cube. From the description of his path, can you predict when he will return to his starting point?
problem
Centre square

Age

14 to 16

Challenge level

What does Pythagoras' Theorem tell you about the radius of these circles?
problem
Kangaroo hops

Age

11 to 14

Challenge level

Weekly Problem 11 - 2011
Kanga hops ten times in one of four directions. At how many different points can he end up?