Your friend pulls out a perfectly circular table and a sack of quarters, and proposes a game.
“We’ll take turns putting a quarter on the table,” he says. “Each quarter must lay flat on the table, and cannot sit on top of any other quarters. The last person to successfully put a quarter on the table wins.”
He gives you the choice to go first or second. What should you do, and what should your strategy be to win?
Answer
You should go first, and put a quarter at the exact center of the table.
Then, each time your friend places a quarter down, you should place your next quarter in the symmetric position on the opposite side of the table.
This will ensure that you always have a place to put the coin, and eventually your friend will run out of space.