MathDB
2 player game with stones, 1 bowl of p stones and one bowl of q stones

Source: 1992 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p1

November 20, 2022
combinatoricsgamegame strategy

Problem Statement

There are two bowls on the table, in one there are pp, in the other qq stones (p,qNp, q \in N* ). Two players AA and BB take turns playing, starting with AA. Who's turn: \bullet takes a stone from one of the bowls \bulletor removes one stone from each bowl \bullet or puts a stone from one of the bowls into the other. Whoever takes the last stone wins. Under what conditions can AA and under what conditions can BB force the win? The answer must be justified.