**Screaming Toes**: More than an

ice breaker, it's

probability in practice!

How to play:

Get your group together in a big

circle, then everyone looks at someone else's toes, and then everyone looks up, if the person you're looking at is looking at you, you both have to

scream. Naturally, two person screaming toes has the highest probability of a scream, whereas one person screaming toes has the lowest

probability. One person screaming toes with a

mirror might be interesting, though I will not

speculate further.

Now to the more interesting issue, given a set of N people who

randomly look at other people's toes (no person's toes are more attractive than another's), on

average, how many screams should occur per

turn? Here is my solution, though it's probably wrong:

The

event space, E = nCr(N,2)

The

sample space, S = N!

Thus, the probability is

^{nCr(N,2)}/

_{N!} that a given

*pair* will scream and, on average,

^{nCr(N,2)}/

_{N!} * N people will scream per game.

As it turns out, both 2 and 3 person games have the same probability, .5, (which, remember, is the probability two people will scream) and thus more screams will happen in the 3 person

game.

Don't ask me how this is a

game.