# Math drinking games?

Saw this on Terry Tao’s blog, it’s a drinking game suggested by Mark Schnitzius that can promote mathematical thinking. Mark says:

“I was watching a travel show a while back — they were in Korea, and a group of people were playing a drinking game. The way it worked was, one person was “it”. This person says something like, “ready, set…” then points at one other player and calls out a number (call it x) between 2 and n (where n is the number of people playing). At the same time, everyone else also points at one other player. Then, for whatever number got call out, you jump that many steps from the “it” person, and that person has to drink. So if I call out “two” and point at Joe, and Joe points at Bob, then Bob has to drink.

I think the game is pretty interesting, mathematically, and could easily be adapted to be a game for kids. It’s especially interesting when you relax the x<=n rule. One interesting thing I found: with n=3, if you call x=7, you are guaranteed to stick the player you initially point at, no matter who points to whom.

Some interesting questions to ponder about it:

1. Without the x<=n rule, what is the smallest number the ‘it’ person can call that guarantees he will not stick himself?
2. With the x<=n rule in place, what is the safest number to call for any given n, if the other players choose randomly?
3. If you’re TRYING to lose, what number should you call, both with and without the x<=n rule?
4. What are the odds of winning or losing, for all the answers above?

Hint for questions 1 and 2: prime numbers come in to play!”

Another silly drinking game is below: