MathDB

Antonio and Bernardo play the following game. They are given two piles of chips, one with

m

and the other with

n

chips. Antonio starts, and thereafter they make in turn one of the following moves: (i) take a chip from one pile; (ii) take a chip from each of the piles; (ii) remove a chip from one of the piles and put it onto the other. Who cannot make any more moves, loses. Decide, as a function of

m

and

n

if one of the players has a winning strategy, and in the case of the affirmative answer describe that strategy.

Problem Statement