## Coloured Strings

#### Problem

In a cuboid shaped room a hook is placed in the centre of each wall, the floor, and the ceiling. Every pair of hooks has either a piece of red or blue string tied between them. As this task is being performed triangles will be formed between sets of three hooks with edges being red or blue.

Prove that it is impossible to complete this task without forming at least one triangle of the same colour.

Problem ID: 259 (09 Jan 2006) Difficulty: 3 Star