## Tuesday, September 6, 2011

### Coins on a table

This is a game for two players.  We take turns placing quarters on a round table.  The round table has five times the diameter as the quarters.  When a player cannot place their quarter fully flat on the table (not on top of any other quarters) without disturbing any of the other quarters, that player loses.

Which player has the winning strategy?  What is the winning strategy?

(This is not an original puzzle.)

See solution

drransom said...

May we assume that the quarters are perfect circles without reeded edges? (I doubt the reeding makes a difference to the answer, but in principle it might.)

miller said...

You may assume that they're perfect circles. :)

Secret Squïrrel said...

Intuition says that the first to play can always win, and that the first play must be to the exact centre.

Not sure what the strategy should be after that. It's late here - will sleep on it and have another think tomorrow.

Secret Squïrrel said...

Ok, it became obvious once I considered the simplest case - placing coins on a ruler.

The player who goes first should place their first coin in the exact centre of the table. The second player then has a turn. Wherever they play a coin, the first player should place one diametrically opposite, and the same distance from the centre. This will guarantee that if the second player can legally play, so can the first.

Interestingly, if you were to drill a hole in the centre of the table such that this would form an inner border that coins were not allowed to overhang, the second player could then ensure that they always won.