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Who becomes richer?



I saw this puzzle a while ago.. not sure where. Not too difficult to solve, so give it a go!


There are 50 coins of various denominations kept in a single line. Two players (A and B) take alternate turns in removing one coin at a time and adding it to their purse. At any point in time, they are allowed to remove only the coin from the extremities (i,e, either the extreme right coin or the extreme left). Coins in between the line can't be removed. At the end of the game, each player will have 25 coins. Whoever has more net value of coins is the winner.


Is this a fair game? If not, who has an advantage? What is their strategy?

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Paint the coins alternately red and blue. First player can capture all the coins of either group. One will likely have a greater total value. If not, first player picks the higher-valued end coin. On his next turn the red-blue totals will no longer be equal and he can choose the color with the higher total. The worst outcome for first player is a draw.
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