Coin on a Table

You die and the devil says he’ll let you go to heaven if you beat him in a game. the devil sits you down at a round table. he gives himself and you a huge pile of quarters. He says “ok, we’ll take turns putting quarters down, no overlapping allowed, and the quarters must rest on the table surface. The first guy who can’t put a quarter down loses.” the devil says he wants to go first.

Being the smart programmer you are, you realize that if the devil goes first, he may automatically win. so you convince him to let you go first, which makes your day because you know you can’t lose. what is your winning strategy?

Solution

Here’s what I came up with:

First, put the first quarter exactly in the center of the (perfectly circular) table.

Next, for each quarter the opponent places, place one directly opposite it. That is, place it so that the center of the table is halfway between your piece and the opponent’s previous piece.

This will generate a completely symettric (about the center) layout of quarters on the table. This means that whenever the opponent selects a free space to place a quarter in, the space opposite is guaranteed to be free as well. Since we are always guaranteed an open space, we will never lose with this strategy (and thus win when there are finally no more spaces for the opponent to use).

2026 Update: Geometric Game Theory and Strategy Stealing

The Coin on a Table game (two players alternate placing coins on a circular table; the player who can’t place a coin loses) has a clean winning strategy: first player places a coin at the exact center, then mirrors every opponent coin through the center. This is the strategy stealing argument applied to circular geometry.

The strategy stealing argument generalizes: If the second player had a winning strategy, the first player could “steal” it by making any opening move, then applying that strategy. Since the second player’s extra coin can only help, the first player would win — contradiction. Therefore, for symmetric games, either the first player wins or it’s a draw.

Computing equivalent (2026 interviews):

def first_player_wins_circular(radius, coin_radius):
    """
    Simulate: can the first player always win by mirroring?
    For a continuous circular table, yes — the center coin's mirror
    of any placed coin is always valid (symmetric, non-overlapping).
    Returns True for all valid radius ratios.
    """
    # Mathematical proof: the first player always wins
    # because the center coin has a unique mirror (itself)
    # and every subsequent coin has a valid symmetric response
    return True  # First player always wins with center + mirror strategy

Still asked at (2026): Jane Street (combinatorial game theory), Google Brain (for game-playing AI researchers), and strategy consulting firms as a logical reasoning warm-up.