MathDB

Two players play a game on four piles of pebbles labeled with the numbers

1,2,3,4

respectively. The players take turns in an alternating fashion. On his or her turn, a player selects integers

m

and

n

with

1\leq m<n\leq 4

, removes

m

pebbles from pile

n

, and places one pebble in each of the piles

n-1,n-2,\dots,n-m

. A player loses the game if he or she cannot make a legal move. For each starting position, determine the player with a winning strategy.

Problem Statement