[math-fun] 3-coloring the rationals

There's a unique way to 3-color the rationals in [0,1] using the colors red, blue, and green so that 0 is red, 1 is blue, and the fractions a/b, c/d, and (a+c)/(b+d) all have distinct colors whenever ad-bc=1. Puzzle (no spoilers till Sunday please!): What color is 355/113? Jim Propp