The Game of Fif

This is a two person game. You play against your computer. The board consists of a row of nine squares numbered 1 through 9. Players take turns selecting squares. The goal of the game is to select squares such that among those selected by a single player there will be a triplet that sums up to 15 (hence the name Fif.)

If the box "I move first" is checked, you have to click the "Start" button which will cause the computer to make the first move.


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the game of fif


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Acknowledgement

  1. The applet is a modification of the TicTacToe Java sample distributed by Sun Microsystems and written by Arthur van Hoff. The fine graphic files come from the same source.
  2. There is no doubt M.Gardner described the game (the name's mine though) in one of his early books. More importantly, this is where I picked it from.

Theory of the Game

The game is equivalent to playing a regular TicTacToe game on the magic square board. (The square is magic in that the sums of three numbers on any straight line (vertical, horizontal or diagonal) is always 15.) There are eight such lines:

  • Horizontal
    • 4 + 9 + 2 = 15
    • 3 + 5 + 7 = 15
    • 8 + 1 + 6 = 15
  • Vertical
    • 4 + 3 + 8 = 15
    • 9 + 5 + 1 = 15
    • 2 + 7 + 6 = 15
  • Diagonal
    • 4 + 5 + 6 = 15
    • 2 + 5 + 8 = 15

These are all possible representations of 15 with three smaller positive integers.

As is well known, a TicTacToe game ends in a stalemate unless one of the players makes a mistake. In the Fif game, computer has the advantage of knowing the origin of the games and having in front of its Mind's eye the magic square board. To make the game more appealing computer errs with the probability of 1/20.

I must note in passing that my earlier Magic Squares game has no relation to the magic squares as defined here. There is a great many books and Internet sites devoted the theory and construction of magic squares.

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