2022 Putnam B3
Source:
December 4, 2022
PutnamPutnam 2022
Problem Statement
Assign to each positive real number a color, either red or blue. Let be the set of all distances such that there are two points of the same color at distance apart. Recolor the positive reals so that the numbers in are red and the numbers not in are blue. If we iterate the recoloring process, will we always end up with all the numbers red after a finite number of steps?