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?
A triangle PQR, right angled at P, slides on a horizontal floor
with Q and R in contact with perpendicular walls. What is the locus
A box of size a cm by b cm by c cm is to be wrapped with a square piece of wrapping paper. Without cutting the paper what is the smallest square this can be?
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.