An Advantage!!!
A two player game consists of 50 random numbers written side by side. The players can see all numbers but can select a number from either end.After each player has chosen 25 numbers, the player with greater sum wins.Player 1 chooses first and player 2 chooses second.
If the sum of all 50 numbers is odd, find who has the advantage?
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1 solution
Let's denote the first number as 1, second number as 2,... 50th number as 50. now the first player adds the odd-placed numbers(1,3,5,...) and even-placed numbers(2,4,6,...)If the sum of odd-placed numbers is less,he chooses 50 to force the second player to choose an odd number(1 or 49)Thus, he can force the second player to have only odd placed numbers and hence lesser sum.
Thus player 1 has the advantage