MathDB

Alice and Bob play a game in which they take turns removing stones from a heap that initially has

n

stones. The number of stones removed at each turn must be one less than a prime number. The winner is the player who takes the last stone. Alice plays first. Prove that there are infinitely many such

n

such that Bob has a winning strategy. (For example, if

n=17,

then Alice might take

6

leaving

11;

then Bob might take

1

leaving

10;

then Alice can take the remaining stones to win.)

Problem Statement