MathDB

B3

Part of 2022 Putnam

Problems(1)

2022 Putnam B3

Source:

12/4/2022
Assign to each positive real number a color, either red or blue. Let DD be the set of all distances d>0d>0 such that there are two points of the same color at distance dd apart. Recolor the positive reals so that the numbers in DD are red and the numbers not in DD are blue. If we iterate the recoloring process, will we always end up with all the numbers red after a finite number of steps?
PutnamPutnam 2022