MathCastle
Groups and FieldsEasyGroup Actions

Group Actions · Easy problem

Let C9={e,r,r2,…,r8}C_9=\{e,r,r^2,\ldots,r^8\} (rotations only) act on 99 points arranged in a circle, and use k=2k=2 colors. How many colorings of the 99 points are fixed by r3r^3 (rotating by 33 positions)?