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All in the Mind
Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?
Painting Cubes
Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?
Tic Tac Toe
In the game of Noughts and Crosses there are 8 distinct winning lines. How many distinct winning lines are there in a game played on a 3 by 3 by 3 board, with 27 cells?
Age 11 to 14
Challenge Level
Can you find a cuboid (with edges of whole number lengths) that has a surface area of exactly $100$ square units?
Can you find them all?
Can you provide a convincing argument that you have found them all?
Click here for a poster of this problem.
NRICH is part of the family of activities in the Millennium Mathematics Project.