50 Coins
On a table is a row of fifty coins, of rupees 1,2,3,4,...,49,50 in an arbitrary order. Alice picks a coin from one of the ends and puts it in her pocket; then Bob chooses a coin from one of the (remaining) ends, and the alternation continues until Bob pockets the last coin. Now, who can earn more money, that person will be the winner. Who has winning strategy?
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1 solution
Number the coins from 1 to 50 and observe that no matter how Bob plays, Alice can capture all the even-numbered coins, or, if she prefers, all the odd-numbered coins. One of these choices must contain greater amount of money than the other choice. Hence, Alice has the winning strategy.