Puzzle 31: Number Games |

**Its raining outside and Alfonso and Bernadette are bored.**

Alfonso suggests the following games:

**(a)** Two players alternatively erase some 9 numbers from the sequence 1,2,...,101 until only two remain. The player that starts wins *x*−54 dollars from the player that plays second. Here *x* is the difference between the remaining two numbers. Would you rather be the first or the second player?

**(b)** Two players alternatively erase one number from the sequence 1,2,...,27 until only two numbers remain. The first player wins if the sum of these numbers is divisible by 5; otherwise the second player wins. Who has a winning strategy?