How can i show and prove rigorously that for all integers, i can paint all these segments red?
Three counters, A, B, C are placed at the corners of an equilateral triangle of side n. The triangle is divided into triangles of side length 1. Initially all lines of the figure are painted blue. The counters move along the lines, painting their paths red , according to the following rules:
- First A moves, then B, then C, then A, and so on in succession.
- On each turn, each counter moves the full length of a side of one of the short triangles.
- No counter may retrace a segment already painted red, though it can stop on a red vertex, even if another counter is already there.
Show that for all integers n >0 it is possible to paint all of the segments red in this fashion.