MathDB

Alice and Bob play the following game: Alice picks a set

A = \{1, 2, ..., n \}

for some natural number

n \ge 2

. Then, starting from Bob, they alternatively choose one number from the set

A

, according to the following conditions: initially Bob chooses any number he wants, afterwards the number chosen at each step should be distinct from all the already chosen numbers and should differ by

1

from an already chosen number. The game ends when all numbers from the set

A

are chosen. Alice wins if the sum of all the numbers that she has chosen is composite. Otherwise Bob wins. Decide which player has a winning strategy.
Proposed by Demetres Christofides, Cyprus

Problem Statement