**The Best of Creative Computing Volume 2 (published 1977)**

castle is placed in any of the 36 remaining squares it appears to control 14 squares 4 of which must be excluded. Thus the revised computation power of a castle is 412241136101 6463646364636 and so forth. The remaining computations and further modifications of definition of checking power are left to you. An article discussing chess related recreations would be incomplete without considering some of the many "tour" problems, particularly since they offer interesting programming challenges as well. There are many different types of tour questions the fewest number of moves to accomplish a task, covering all squares once and only once, the minimum distance traveled, ... Here we'll consider just three different questions. First, can you determine a path traveled by a king such that each square is occupied once and only once? No, it's not that easy. There's one additional catch. As the king moves, number each square consecutively starting with 1. When you've finished, the squares will each contain one of the integers 1 thru 64. What's the catch? The resulting board with numbered squares must be an 8X8 magic square. A solution will be published in a future issue. As a second problem, try moving the castle from one corner of the board to the diagonally opposite corner, again passing through each square once and only once. This one isn't quite as easy as a quick reading suggests, but you should be able to solve it in a reasonable period of time. Finally, consider the standard "Knight's Tour" problem that is considered in so many articles on recreational chess. A knight must cover the entire board occupying each square once and only once. Don't, however attack this one with a knight and a chessboard-try something different. Write a problem that will find a solution for you. Kemeny (2) offers a BASIC program that attempts to find a solution by making random moves. The small sample of runs he published doesn't include a complete solution, in fact not one of 25 runs exceeded 50 squares before no moves were possible. Perhaps surprisingly, however, in 15 of the 25 runs the tour did pass thru over half the squares before terminating. Actually, when a knight's tour is attempted using only random moves, long tours are quite common but a complete tour ls very unlikely indeed. How then can a program help? By adding a little bit more to the move selection than simply the choosing of a random number. When selecting a move, add one additional criteria. Always move to a square from which the knight will command the fewest squares that have not been occupied. Fewest is not a misprint, even if it does contradict your intuition. If several squares fit this criteria equally well, then select one of them at random. This additional criteria ls reasonably implemented in a program, and although it doesn't guarantee a successful tour, you are apt to be surprised by the results! Bibliography 1) Ball, W.W. Rouse, Mathematical Recreations and Essays, Macmillan and Co., London 1940 2) Kemeny, J.G. and Kurtz, T.E., BASK Programming Second Edition, John Wiley and Sons, New York, 1971 *** Big Surprise From Small Computers in Chess Matches Good things come in small packages-especially when computers compete in chess matches. In two matches here and abroad, small computers performed surprisingly well against giant competitors. David actually conquered Goliath in an intramural chess match at Columbia University when a small Data General Supernova-about the size of an attache case-checkmated an IBM System 360/91-one of the largest in the world-in just 25 moves. The Supernova, owned by Columbia's Department of Electrical Engineering and Computer Science, had a memory capacity of 32,768 bytes; the IBM system, part of the university's computer center, had a capacity of over 2 million bytes. The Supernova's chess program was written by Professor Monroe Newborn of the Electrical Engineering and Computer Science Department and by student George Arnold. It is written in assembly language and uses a technique that determines the best move by searching between four and eight half-moves ahead, selectively analyzing about 1,000 terminal positions. A move is determined in about one minute-well within chess tournament rules. The game lasted more than 90 minutes, but the Supernova gained a decided advantage on the sixth move: the System 360/91, playing white, blundered, and traded a knight for a pawn. One of the program authors noted that the computer saw the correct move (bishop takes bishop) but didn't realize that exchanging bishops would save the knight. Once the big computer decided it could not save the knight, it decided to pick up a pawn. "Having exclusive use of the smaller computer, along with running the program on-line, helps offset the greater speed and capacity of the larger machines," Professor Newborn said. In another surprising match, a Computer Automation Naked Mini computer using only 16,000 words of 16-bit memory came in 12th in stiff competition in the World Computer Chess Championships held in Stockholm, Sweden. "I'm no expert at chess; in fact, I'm just an average amateur, but I love to play with computers. Even so, I was surprised, indeed," said Bob Prisen, Interscan Data Systems, Ltd., United Kingdom, who programmed the Naked Mini. He spent approximately 300 hours in an eight-month period and used BASIC assembler language. The first-place winner, by contrast, was a large-scale English-built ICL 4/70 computer entered by the Moscow Institute of Control Science. The machine and its programming had been prepared by a team of 10 fulltime staffers for more than two years. The computer used a program called KAISSA. During the Swedish match, the Naked Mini stayed in England. Communications between Prisen and the computer were established using international telephone lines and an acoustic coupler with a Teletype and an on-line visual display unit. Prisen said he hopes that a European or British Chess Computer Championship can be arranged in the future. "If it occurs, I'm confident the Naked Mini computer will greatly improve its position in the Chess Computer League with a bit more core memory and programming effort," he said. 35