THE people over at the W. L. Maxson Corporation, which is primarily in the business of developing and manufacturing secret electric, electronic, and electromechanical equipment for the government but also puts out, for commercial users, such things as -Unimax switches, Langevin transformers, and Maxson precision phasemeters; were kind enough a few days back to invite us to come over and have a go at their Nim machine. “A California guided-missiles man built a ticktacktoe machine,” the Maxson gentleman who proffered the invitation said, “so we built a Nim machine. Our machine is a very strong player, so watch out.” In spite of our poor record against machines ofany sort, we marched over to the building housing the firm’s electronic laboratory, at 475 Tenth Avenue, the next day, rode up to the fourteenth floor, and, wondering all the while what Nim might be, stated our business, signed in, had a huge badge pinned on our lapel, and were conducted by three solemn, bespectacled young men into a cubicle with light-green walls. There we were confronted with a walnut box, thirty inches high and eighteen inches deep, whose front was studded with light bulbs and push buttons. The box was sitting inscrutably on a table. In the upper right-hand corner of the front panel was printed the word “Nim.” Below this inscription were two legends that could be illuminated. One was “You Win,” the other “You Lose.” Below them was a button marked “New Game.” The greater part of the panel was taken up by four rows of seven bulbs each. There was a button at the end of each row, and belowthem were, at one side, a button labelled “Machine Play” and, at the other, a bulb labelled “You Play,” which was also lighted. In the upper left-hand corner of the contrivance was a bulb with the word “Tilt” over it. The three young men were labelled Eugene Grant, Herbert Koppel, and Howard Bailer. Grant started off by explaining to us that Nim is an old game for two people, usually played with several rows of counters; the number of rows and the number of counters isimmaterial. Each player takes a turn at removing one or more counters from a single row. The player who removes the last counter of the whole bunch wins. “Other forms of Nim are played with a single row of, say, matchsticks,” Bailer told us. “Then you’re limited to taking one, two, or three matches at a time, and the idea is to make your opponent pick up the last one.” “The origins of the game are shrouded in the mists of antiquity,” Koppel said, “but it seems to come from the Orient. The Anglo-Saxon word for ‘to take’ or ‘to filch’ is‘Inman.’ In ‘The Beggar’s Opera,’ one of the characters says, ‘I expect the Gentleman about this snuffbox that Filch nimm’d two nights ago in the park.’ Charles L. Bouton, the mathematician, called it a game with a complete mathematical theory. On our machine, we use lights instead of counters.”

Grant told us the machine was all set to play and briefed us on procedure: Every time we pressed the button to the right of a row of lights, one of the bulbs in that row would go dark; if we pressed buttons in two rows without allowing the machine a turn, the “Tilt” button would light up and we would lose on a foul. With some trepidation, we pressed the button governing the second row twice. Two lights went off. At Koppel’s nod, we pressed the “Machine Play” button, and with haughty efficiency the machine put out several more lights in the same row. “It’s now impossible for you to Win,” Bailer announced witheringly. Nevertheless, we doggedly kept pressing buttons, and soon there were only two lights left—one in the first row and one in the third. “It’s your turn,” Koppel said. “Press a button.” We did. The light in the first row went out. We pressed the “Machine Play” button, the last light went out, and “You Lose” triumphantly flashed on.

“The way the machine’s arranged now,” said Koppel, “a player can win by pure luck five per cent of the time.” “It ought-to be explained,” said Bailer, “that, mathematically, each play you make produces either a safe or an unsafe condition—that is, relative to your position in regard to the rest of the bulbs. If the condition is safe, and you keep it that way for the rest of the game, you can’t lose. If it’s unsafe just once, you can’t win, no matter what, because the machine never makes a mistake.” “The machine is so keen on winning that sometimes it cheats a little bit,” said Koppel. “It makes the ‘You Play’ bulb light up without taking its turn. Or it puts out lights in two rows at once without flashing the ‘Tilt’ bulb. It also plays a nerve-racking game of attrition when it’s up against an expert, putting out only one bulb at a time. Wears you down.” “The way to maintain the safe condition,” said Grant, “is to see to it that each power of two appears an even number of times in the aggregate of all rows. That is, you are safe when the sums of all individual binary digits are even number s. The formula is—” We urged him to let it go. “When William Maxson, the son of the founder of the firm, played it,” Bailer said, “Koppel, who made the machine from plans by Grant and me, gave him special instructions, and he beat the pants off it. At the end of about the fourth game, the machine started clicking and clacking something terrible.” “Oh, it has a temper,” Koppel said.

The machine weighs fifty pounds, cost two thousand dollars to build, and is loaded with small electronic tubes, germanium crystals, and wires. It was completed, after three months’ work, in time to go on display at the recent National Conference of Airborne Electronics Engineers, in Dayton. “Most of our stuff is so hush-hush we can’t exhibit it,” Grant told us. “So we built this to show people interested in engineering what we could produce in the way of a simple digital computer. Turned out to be the biggest draw in Dayton. It—we call it It—played about fifteen hundred games and only lost a hundred and fifty. That was against some of the best engineering minds in the country. You want a return match ? “ We said no, thanks, walked out, and handed in our badge. ♦