Puzzle #159:Winning Strategy with Coins

This is a beautiful puzzle contributed by an ex-entrepreneur, Prateek Agarwal, who I met a few weeks back – thanks Prateek.

You and your friend are playing a turn based game. There is a circular table of diameter 10cm and unlimited coins of diameter 1cm. Each player needs to keep the coins on the table such that they don’t overlap. No player can move an already placed coin from its place. If any player is not able to keep the coin on the table in his turn, he loses. Also, players can’t pass their turn. Each of you are playing to win obviously.

Now your friend, being generous, has offered you to play the first turn. Should you play first? If yes, then what should be the strategy? If no, then what should you do. If you choose to not play first, this won’t be considered as passing the turn as the game hasn’t started yet.

Happy Diwali to all readers!

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3 Responses to Puzzle #159:Winning Strategy with Coins

  1. I play first. I place my first coin at the centre of the table. Then the other guy places somewhere. My response is always to place a coin at the exact diamaterical opposite point. Hence I always have a way to put the coin if he has. I win.

  2. Vishal Poddar says:

    Extension of the problem – If there is an hole at the centre of the table, what should be your strategy?

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