**The Best of Creative Computing Volume 1 (published 1976)**

ln general, the second player should attempt to play so that for every missing marker the symmetrically opposite marker is also missing. The center marker must also be missing. lf the second player succeeds in obtaining this board configuration at the end of any turn, he has successfully taken advantage of the first player's error and has a winning strategy. On all subsequent turns he should remove only those markers symmetrically opposite those removed by his opponent. Following this strategy, if the first player's opening play is 3, 8, 13 the second player's play should be 18, 23. But what should the second player do if the opening play is 16- 18? That's part of the chalIenge of the problem! Perhaps play 9 - 10, but that seems to increase the first player's chances of making a winning move next time. We do assume the first player is smart even if he does err on his first play. Perhaps play at random, but that seems to decrease the second player's chance of obtaining a winning board configuration. The complexity of the problem is indeed increased by letting the first player be human. The problem is very good because it is a mini-version of what one often faces in much larger problems: the solution is not trivial; although each step of a solution can be well defined, some definitions will reflect the problem solver's best judgment rather than an absolute truth; once a solution is well defined, a program can be written that plods through many cases while another can be written that uses reflections and rotations of the board to reduce the number of cases. The challenge of writing a program that plays Tac Tix with a smart but fallible user who is given the first move properly belongs under the title "Creative Computing." And those who write such a program are likely to have done some "creative analysis" before they finish. A modified version of Tac Tix that looks easier but is actually much more complex is played on a 4 x 4 board rather than a 5 x 5 board. The only other change is that the player who removes the last marker is the loser. ls there a winning strategy for either player? After trying to define a winning strategy for one of the players, one may well become interested in writing a program that develops its strategy by learning as it plays. By repeating successful plays and avoiding the repetition of unsuccessful plays, the computer can improve its strategy with each successive game. The writing of such cybernetic programs will be the subject of a future column. Related References Gardner, Martin; Mathematical Puzzles and Diversions; New York: Simon and Schuster; 1959; Chapter 15. Spaulding, R. E.; "Recreation: Tac Tix"; The Mathematics Teacher; Reston, Virginia: National Council of Teachers of Mathematics; November 1973; pages 605-606. *********************************************** Puzzles and Problems for Fun [Image] This puzzle is calculated to test your ability in calculus: A watchdog is tied to the outside wall of a round building 20 feet in diameter. If the dog's chain is long enough to wind halfway around the building, how large an area can the watchdog patrol? A. G. Canne Pittsburgh, Pa. [Image] The Sheik of Abba Dabba Dhu wears this medallion, on which each equilateral triangle represents a wife in his harem.How many wives does the sheik have? David Lydy Cincinnati, Ohio 167