If, after reading Y(S)L – 1, you want more, you’re in luck. Say hi to forced wins again.

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 selected numbers (this may happen after the player has chosen 3, 4 or even 5 numbers) that sum to zero wins the game.

• +Okay, so here's a hint.

  Transform the problem to another very simple two-player game we all know so well. How many numbers do you have to pick from? Arrange them in a square.

• +And here's the solution. Give it a try first!

  Going through all the possible plays by both players might work, but why put in so much effort?

  This ingenious solution combines tic-tac-toe and magic squares.

  You have nine numbers, arrange them in a square such that each row and column sums to zero. It may not seem obvious at first, but a little trial and error will get you there. Zero, as intuition should tell you, is at the center. One such square is the following:

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

  An arrangement of numbers in a square where all the rows, all the columns and the two diagonals add up to the same number, is called a magic square. That sum in question is called the magic sum of the square. Here, it’s zero.

  There are eight ways possible for three numbers from the set to sum in the original question to zero, and all of them have been taken care of in the above square.

  Now, whenever a person picks a number from the set, have them mark an X or an O (as in tic-tac-toe) on the magic square-board we’ve made above. As you can see, the game indeed ends when one person gets three-in-a-row, or equivalently, three numbers that sum to zero.

  Coming to forced winning, you might know that if both players play without making “mistakes,” then any tic-tac-toe game will result in a draw. Which essentially means, the answer to the original question is that: NO, neither player has a forced win in this game.
  

For the previous in this series, go to Y(S)L – 1.