Noh’s antennae wavered in agitation. “Nonetheless is this naked mental? How justified computer involvement?”
“These categories are fundamentally arbitrary,” Stile explained. “Too many Games are in fact mixed types. The Game Computer assumes for the sake of convenience that it, itself, has no Game significance. The riddles could come from a book or a third person, but it is most convenient and random to draw on the computer memory banks. There are all kinds of little anomalies like this in the Games; I had to play Football using androids termed animals, with robots for referees.”
“This is delightfully mistrustful. Expedient to avoid?”
“Well, I happen to have the numbered facet, so you cannot control that. Myself, I’d rather avoid the dual response; that’s timed, with the first one to answer being the winner. I’m more of a power thinker; I get there, but not always in a hurry.” This was true, but perhaps misleading;
Stile was stronger as a power thinker in proportion to his other skills, but still by no means a slow thinker. “That is—“
“Can we collude? Choose 2B for mutual accommodationality?”
“We could—but how could we know one of us won’t cheat? Deals are permissible but not legally enforceable in 1 the Game. An expert liar makes an excellent grid-player. The computer accepts nothing but the signal-buttons.”
“Chance it must be risked,” Noh said. “Some trust exists in the galaxy, likewise on little planets.”
“Agreed,” Stile said, smiling at the alien’s phrasing. He touched 2, and sure enough, it came up 2B. They had each kept faith. Game players normally did; it greatly facilitated things on occasion.
Now they adjourned to a bare private chamber. “Select a recipient for the first riddle,” the Game Computer said from a wall speaker. “Recipient must answer within ten minutes, then propose a counter-riddle for the other. In the event of failure to answer, proponent must answer his own riddle, then answer opponent’s riddle within the time limit. The first contestant to achieve such success is the victor.
Computer will arbitrate the technical points.”
“You courtesy explained situation,” Noh said. “Appreciation I yield initial.”
It really did not make any difference who went first, since only an unanswered or misanswered riddle followed by a successful defense counted. But Stile was glad to get into it, for psychological reasons. He had a number of tricky questions stored in the back of his mind. Now he would find out just what the alien was made of, intellectually.
“Picture three equal-length sticks,” Stile said carefully. “Each quite straight, without blemish. Form them into a triangle. This is not difficult. With two additional sticks of the same size and kind a second triangle can be formed against a face of the first. Now can you fashion four congruent triangles from only six such sticks?”
Noh considered. “Enjoyability this example! Permissible to employ one stick to bisect double-triangle figure formed from segments of sticks?”
“No. Each stick must represent exactly one side of each triangle; no projecting points.” But Stile felt a tingle of apprehension; such a device would indeed have formed four congruent triangles, and similar overlapping could make up to six of them. This creature was no patsy. “Permissible to cross sticks to form pattern of star with each point a triangle?”
“No crossing.” So quick to explore the possibilities! The head stalks hobbled thoughtfully for almost a minute. Then: “Permissible to employ a third dimension?”
The alien had it! “Permissible,” Stile agreed gamely.
“Then to elevate one stick from each angle of first triangle, touching at apex to form four-sided pyramid, each side triangle.”
“You’ve got it,” Stile admitted. “Your turn.”
“Agreeable game. Triangles amenable to my pleasure. Agree sum of angles is half-circle?”
“One hundred eighty degrees,” Stile agreed.
“Present triangle totaling three-quarter circle.”
“That’s—“ Stile began, but choked off the word “impossible.” Obviously the alien had something in mind. Yet how could any triangle have a total of 270°? He had understood 180° was part of the definition of any triangle. Each angle could vary, but another angle always varied inversely to compensate. If one angle was 179°, the other two would total 1°. Otherwise there would be no triangle. Unless there could be an overlay of triangles, one angle counting as part of another triangle, adding to the total. That didn’t seem sensible, yet—
“Permissible to overlap triangles?” Stile inquired.
“Never.”
So much for that. Stile paced the floor, visualizing tri-angles of all shapes and sizes. No matter how he made them, none had more than 180°.
Could they have differing definitions of triangles? “Permissible to have more than three angles in the figure?”
“Never.”
