## New Problem: Look Up!

I learned a game today. A group of people sit in a circle, looking down. The game leader counts to three, and on three everyone lifts their head and looks at one other person. If the other person is looking back at you, you’re both out. The game continues until there are one or two people left (depending on if your group has an even or odd number). The wonderful part is that no one feels bad about getting knocked out, because it’s impossible not to laugh when you look up to see the person you chose staring right back at you – the power of human eye contact.

The question is: for a given number of players, $n$, and assuming each person chooses who to look at randomly, how many rounds do you expect the game to take before ending?

### 3 Responses to “New Problem: Look Up!”

1. inf Says:

infinite, first person looks at 2nd, 2nd at 3rd, …, nth at 1st.

2. Mark Eichenlaub Says:

Sorry, I forgot to specify at first that they look at another person at random.

3. michelle selvans Says:

ooh, i’m going to have to try this next time i have a pliant group!