December 1–December 7, 2009

Problem

Suppose we have a circle with 2n segments, n of them colored red and n colored black in some random order. Make a smaller concentric circle, also with 2n segments, again with n colored red and n colored black, again in some random order (not necessarily the same order as the larger circle). We can spin the smaller circle relative to the larger circle so that segments line up. Show that there is some way to spin the smaller circle so that at least half (that is, n) of the segments have matching colors.

Solution

here

List of solvers

Mauricio Duarte (graduate); Qiyuan Wei, Lloyd Sakazaki, Dod Moshe, Congpa You, Hardik Bati (outside).

Qiyuan Wei wins the prize!