MathDB

Alice and Bob play the following game: They start with non-empty piles of coins. Taking turns, with Alice playing first, each player choose a pile with an even number of coins and moves half of the coins of this pile to the other pile. The game ends if a player cannot move, in which case the other player wins.
Determine all pairs

(a,b)

of positive integers such that if initially the two piles have

a

and

b

coins respectively, then Bob has a winning strategy.
Proposed by Dimitris Christophides, Cyprus

Problem Statement