There are two piles of checkers on a table. A takes any number of checkers from one pile, or the same number from both piles. B does the same. The winner is the last one to take the checker. Positions are pairs $[x(i), y(i)]$ of non-negative integers. By starting with small numbers, find the recursive rule for losing positions, as well as a 'closed expression' for positions in L.
x = one pile, y = the other pile.
The first losing position is $[x(0), y(0)]$, which is true because this player with this position is no longer able to take a checker. Likewise, any position with equal amounts of checkers on both tables is a losing position because the opponent is able to take the same number of checkers from both tables, resulting in a loss for his opponent. Positions where one number of checkers is not equal to another is a winning position for the player who moves first.
I'm not sure if that's right or wrong, would appreciate some help w/ this.