A painter went to a single mathematical plane, and colored every single point on that plane one of two colors.
Prove that there exist two points on the plane that are exactly one meter apart and have the same color.
Let us choose a line AB with AB = 1m, where A corresponds to red and B corresponds to the color green.
We now choose a point C such that AC =BC = 1m, where C must correspond to one the colors red or green.
We now have an equilateral triangle, two of whose vertices must share the same color.
Edited on September 15, 2023, 5:17 am
Puzzle Solution
