sábado, 22 de dezembro de 2012

Tic Tac Toe

The game of Tic Tac Toe (TTT) is among humanity's best-known and most ancient games. Although the precise date of TTT with its modern rules may be relatively recent, archeologists can trace what appear to be "three-in-a-row games" to ancient Egypt around 1300 B.C., and I suspect that similar kinds of games originated at the very dawn of human societies. For TTT, two players, O and X, take turns making their symbols in the spaces of a 3x3 grid. The player who first places three of his own marks on a horizontal, diagonal, or vertical row wins. A draw can always be obtained for the 3x3 board.
In ancient Egypt, during the time of the great pharaohs, boar games played an important role in everyday life, and TTT-like games are known to have been played during these ancient days. TTT may be considered an "atom" upon which the molecules of more advanced games of position were built through the centuries. With the slightest variations and extensions, the simple game of TTT becomes a fantastic challenge requiring a significant time to master.
Mathematicians and puzzles aficionados have extended TTT to larger boards, higher dimensions, and strange playing surfaces such as rectangular or square boards that are connected to their edges to form a torus (doughnut shape) or Kline bottle (a surface with just one side).
Consider some TTT curiosities. Players can place their Xs and Os on a TTT board in 9! = 362,880 ways. There are 255,168 possible games in TTT when considering all possible games that end in 5, 6, 7, 8, and 9 moves. In the early 1980s, computer geniuses Danny Hillis, Brian Silverman, and friends built a Tinkertoy computer that played TTT. The device was made of 10,000 Tinkertoy parts. In 1998, researchers and students at the University of Toronto created a robot to play three-dimensional (4 x 4 x4) TTT with a human.

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