A 3x3 array of counters is laid out. Players take turns removing counters. The rule for removing counters is to pick a row or column and take any 1,2 or 3 from it. Whoever removes the last counter wins.
Does the first or second player have a winning strategy?
What is this strategy?
I believe that the first player can force a win.
First Player, Move 1: remove just a single counter (any one will do).
First Player, Move 2: No matter what the 2nd player does, make a play which leaves 4 counters in just two rows or columns. There are two basic positions (excluding reflections, rotations, transposition of rows, etc.). They are (a) 4 counters in a 2x2 and (b) 4 counters in a 2x3 or 3x2
a) xx and b) xx
First Player, Move 3: No matter what the 2nd player does, make a play which leaves exactly one stone