Here's a small puzzle with an ingenious solution:

Consider the set of numbers {-4, -3, -2, -1, 0, 1, 2, 3, 4}. Two players alternately choose one number at a time from the set (without replacement).

The first player who obtains any three out of his or her selected numbers (this may happen after (s)he has chosen 3, 4 or even 5 numbers) that sum to zero wins the game.

Now, the question is that, does either player have a forced win? That is to say, can either player always choose in a way such that a win is guaranteed?

note: this problem is not original. I found the game on this blog .
http://recreational-math.blogspot.in

3 years ago

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Your game is analogous to Tic Tac Toe. So no, there is no forced win.

 +3 -4 +1 -2 0 +2 -1 +4 - 3