[kurumo]

I have been using this when interviewing people with math degrees:

Two players play a game with a single six-sided die. The player that starts can only win by rolling a 1. If he or she doesn't win, the other player gets to roll; he or she can only win by rolling a 6. The game continues until one player wins. What's the probability the first player wins (eventually)?

[debacle]

Let me see if I can work through this.

Player 1 wins based on the following series:

Chance to get a 1 (turn 1): 1/6 Chance to be allowed to roll: Previous chance to be allowed to roll * 5/6 (Chance player 1 didn't roll a 1) * 5/6 (Chance player 2 didn't roll a 6) Chance to get a 1 (turns 2+): Chance to be allowed to roll * Chance to get a 1

So... summation( 1/6 * (25/36)^(n-1) )

I don't know what that comes out to be.

[kurumo]

It's actually 1/6 * Sum_n (5/6)^2n = 1/6 * 1 / (1 - 25/36) = 6/11. The first move provides a small advantage, as intuition dictates.

[stephencanon]

I like this one. It can be brute-forced easily enough, but there are also a couple much more elegant approaches that I would expect a good mathematician to produce.

[hypeibole]

As a mathematician I'll be interested in knowing why you ask that question to people with math degrees.

What information does that give to you as an interviewer?

[kurumo]

It tells me if they can at least minimally apply their knowledge and reason about a problem. It's a filter question. If a person with a college degree in math cannot solve this, what's the likelihood they will be able to solve an actual real problem I need them to work on?