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?
A circle is inscribed in an equilateral triangle. Smaller circles
touch it and the sides of the triangle, the process continuing
indefinitely. What is the sum of the areas of all the circles?
P is a point on the circumference of a circle radius r which rolls,
without slipping, inside a circle of radius 2r. What is the locus
The edges in these 4 graphs show the colour pairings of opposite
faces of the cubes.
To solve the problem combine all 4 graphs then look for 2
subgraphs, one representing the colours on the front and back walls
of the tower and the other representing the colours on the left and
right hand walls of the tower, such that each contains all 4
colours and precisely one edge of each numbered cube.