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Instant Insanity

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

Is There a Theorem?

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

Chess

What would be the smallest number of moves needed to move a Knight from a chess set from one corner to the opposite corner of a 99 by 99 square board?

All in the Mind

Age 11 to 14
Challenge Level

Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged.

What shape does the surface of the water make around the cube?

bowl of water and cube with string attached to one vertex



This problem has been adapted from the book "Sums for Smart Kids" by Laurie Buxton, published by BEAM Education. This book is out of print but can still be found on Amazon.