Circles in a circle

[Susam Pal]

Alan and Bryan meet one Sunday morning to play a game. They sit
together at a perfectly circular table with a bag full of perfectly
circular coins. All coins are identical. They have enough coins to
cover the entire table. Each player takes turns placing one coin on
the table such that no coin touches any other coin or the edge of
the table. The game ends when nobody can place a coin. The last one
to place a coin wins.

If Alan takes the first turn, who can definitely win the game?

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Originally posted at: http://cotpi.com/p/25/
Correct solutions will be archived at the cotpi link mentioned above.
Solutions to 'Thief-turned-teacher': http://cotpi.com/p/24/#responses

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[Vikram Agrawal (विक्रम अग्रवाल)]

If Alan is taking first turn then he can win definetely.

He has to put first coin exactly at center. After that just put coin exactly diameterically opposite (e.g. on a diameter passing through center of Brayn's coin but to opposite side and with same distance from center). Since table is circular and so are coins is gauranteed that whenever Brayn put a coin there will be a space available on diameterically opposite side due to symmetry.

So, as long as Brayn can put a coin Alan can also put one. Hence, this way Alan will put the last coin if follows above strategy.

 

-Vikram

 

-vicky
विक्रम अग्रवाल

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