This is a game for two players.
Begin with a pile of counters. (It might be a good idea to start with, for example, 7 counters.)
The first player must separate the pile into two piles each containing a different number of counters.
Player 2 then splits one of these piles into two unequal piles.
Players take it in turns to separate the piles like this.
The winner is the player who makes it impossible for his or her opponent to divide any of the piles into two unequal piles.
When do you know who will win?
Can you devise a strategy that might help you win?
What happens if you change the number of counters you start with?
This game is a version of the old favourite, Nim. If you search on NRICH for Nim you will find some variations.