Petar Maymounkov

Winning a coin play on a symmetric table

Wed, Oct 30, 2013

Two players take turn placing coins on a circular table. Initially the table is empty. On a turn, a player has to put a coin on the table such that the placed coin does not overlap or displace any other coin. Both players have an unlimited supply of identical coins. The loser is the one who is unable to place a coin on his turn due to lack of space.

The question.

If your goal is to win the game, would you rather start first or second? Why?

Here are some questions that come up, whose answers are not necessary to solve the game:

Q1.

What is the relative size of the table in comparison to the coin?

A1.

It should be immaterial to your solution. The latter should work for every case.

Q2.

How close to the edge or over the edge of the table can I place a coin before it falls?

A2.

Any choice of rule is fine, as long as it applies to all coins.

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