I'm trying to do the following 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.
I am totally stuck and have been for some hours (although by the rated difficulty it should not be that hard :( ).
What I've concluded is that there's: 6 hooks, 15 strings and 20 triangles. I, however, can't find any way to prove that at least one triangle should have the same color.
I've tried creating a map of all the strings and triangles but this very quickly becomes really confusing so that's not the way to go.
Hints are very much appreciated.