[ Symmetric Strategy ]

On the table, there are two stacks of coins: one has 30 coins, and the other has 20. On a turn, a player is allowed to take any number of coins from one stack. The player who cannot make a move loses. Who wins with correct play?
Reduce to the possibility of making symmetric moves.

## Solution

The first player wins. The first move he makes the piles equal, with 20 coins each, and then no matter what the second player does, the first player has the option to take the same number of coins from the other pile (there is the possibility of making symmetric moves)

## Answer

With correct play, the first player wins.