Z/6Z

A game of dice, speed, and cyclic groups.

Play

Learn

How to Play

Take turns rolling the die, and keep track of the cumulative sum (mod 6).

If the sum becomes a 0 with the current roll, be the first to grab the paper, and you get a point.

But BE CAREFUL grabbing the paper - if the sum is NOT 0, you LOSE a point!

First player to reach 2 points wins.

Background

Define Z/nZ - or Z_n - as the set of nonnegative integers less than n. This forms a cyclic group under addition mod n (so if we keep adding values, we will always get a sum in this set).

For this game, note that every element of Z/6Z has an additive inverse (i.e., for every number a in Z/6Z, there is a b in Z/6Z with a + b = 0).

Note: since 6 ≡ 0 (mod 6), rolling a 6 in this game is essentially the same as if you had rolled a 0.