# Suggest a strategy such that player A will always win, no matter how player B will play?

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Suppose two player, player A and player B have the infinite number of coins. Now they are sitting near a perfectly round table and going to play a game. The game is, in each turn, a player will put one coin anywhere on the table (not on the top of coin already placed on the table, but on the surface of the table). And the player who places the last coin on the table will win the game. Given player A will always move first. Suggest a strategy such that player A will always win, no matter how player B will play?

posted Jul 31, 2017

Player 'A' place a coin right in the center of the table. After that, whenever the Player 'B' places a coin on the table, mimic his placement on the opposite side of the table. If Player'B' has a place to place a coin, so will Player 'B' . The Player 'B' will run out of places to put a coin before Player'A' do.
so, player A will always win, no matter how player B will play,by following this strategy

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Consider a two player coin game where each player gets turn one by one. There is a row of even number of coins, and a player on his/her turn can pick a coin from any of the two corners of the row. The player that collects coins with more value wins the game. Develop a strategy for the player making the first turn, such he/she never looses the game?

Note that the strategy to pick maximum of two corners may not work. In the following example, first player looses the game when he/she uses strategy to pick maximum of two corners.

``````Example
18 20 15 30 10 14
First Player picks 18, now row of coins is
20 15 30 10 14
Second player picks 20, now row of coins is
15 30 10 14
First Player picks 15, now row of coins is
30 10 14
Second player picks 30, now row of coins is
10 14
First Player picks 14, now row of coins is
10
Second player picks 10, game over.

The total value collected by second player is more (20 +
30 + 10) compared to first player (18 + 15 + 14).
So the second player wins.
``````
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