There is a strange circular disk on a table. It has twelve congruent sectors, each of which is either opaque or transparent.

An identical disk is placed on top of it, and spun around. The table underneath the disks is brightly colored, so that every 30 degrees of rotation, you can count the number of regions out of 12 that are transparent. Those numbers are 2, 3, 4, 4, 0, and 4 for the first half of a revolution. Without any more information, can you figure out exactly what a single disk looks like?

(In reply to Solution by Sir Percivale)

Perhaps you could explain how this works, as the sequence of rotations of this disk with itself seems to produce the following sequence of numbers of clear segments:

6, 2, 2, 3, 4, 3, 2, 3, 4, 3, 2, 2, 6, 2, 2, 3, 4, 3, 2, 3, 4, 3, 2, 2

(repeated so that sequences wrapping around show up directly).

Posted by Charlie on 2005-12-04 11:12:01