$\textbf{Coins on a Table}$
Joe invites you to play a game with him by placing quarters on a rectangular shaped table. Each person places one coin in turn. Coins cannot overlap. The person who cannot find enough space to place the next coin loses the game. Do you want to play first or let Joe play first?$\textbf{Solution}$
You should start first and place your first coin at the center of the table. Then no matter where Joe places his coin, you always put yours at a mirroring spot with respect to the center.
$\textbf{Analysis}$
It is always a good idea to start with a simple case for analysis. Consider an extreme scenario when the table is just big enough to place one coin. Then, it is obvious that the first player will win. Therefore, an educated guess is that the first player is likely to have a winning strategy.
We also note that there is an infinite number of ways to put coins on a table. However, a winning strategy must have a deterministic way to play the game. This means that while we cannot predict where Joe will place his coin, we must have a defined way to put ours after his move. Here is where the principle of symmetry can come to help.