Banquets Of The Black Widowers - By Isaac Asimov Page 0,3

recently solved the four - color mapping problem that way; a problem as well known and as recalcitrant as Goldbach's conjecture."

"Good," said Trumbull, "then that's what Pochik's been doing. Apparently, he had worked out the solution to a particular lemma. Now what's a lemma?"

Halsted said, "It's a partway solution. If you're climbing a mountain peak and you set up stations at various levels, the lemmas are analogous to those stations and the solution to the mountain peak."

"If he solves the lemma, will he solve the conjecture?"

"Not necessarily," said Halsted, "any more than you'll climb the mountain if you reach a particular station on the slopes. But if you don't solve the lemma, you're not likely to solve the problem, at least not from that direction."

"All right, then," said Trumbull, sitting back. "Well, Sandino came up with the lemma first and sent it in for publication."

Drake was bent over the table, listening closely. He said, "Tough luck for Pochik."

Trumbull said, "Except that Pochik says it wasn't luck. He claims Sandino doesn't have the brains for it and couldn't have taken the steps he did independently; that it is asking too much of coincidence."

Drake said, "That's a serious charge. Has Pochik got any evidence?"

"No, of course not. The only way that Sandino could have stolen it from Pochik would have been to tap the computer for Pochik's data and Pochik himself says Sandino couldn't have done that."

"Why not?" said Avalon.

"Because," said Trumbull, "Pochik used a code word. The code word has to be used to alert the computer to a particular person's questioning. Without that code word, everything that went in with the code word is safely locked away."

Avalon said, "It could be that Sandino learned the code word."

"Pochik says that is impossible," said Trumbull. "He was afraid of theft, particularly with respect to Sandino, and he never wrote down the code word, never used it except when he was alone in the room. What's more, he used one that was fourteen letters long, he says. Millions of trillions of possibilities, he says. No one could have guessed it, he says."

Rubin said, "What does Sandino say?"

"He says he worked it out himself. He rejects the claim of theft as the ravings of a madman. Frankly, one could argue that he's right."

Drake said, "Well, let's consider. Sandino is a good mathematician and he's innocent till proven guilty. Pochik has nothing to support his claim and Pochik actually denies that Sandino could possibly have gotten the code word, which is the only way the theft could possibly have taken place. I think Pochik has to be wrong and Sandino right."

Trumbull said, "I said one could argue that Sandino's right, but the point is that Pochik won't work. He's sulking in his room and reading poetry and he says he will never work again. He says Sandino has robbed him of his immortality and life means nothing to him without it."

Gonzalo said, "If you need this guy so badly can you talk Sandino into letting him have his lemma?"

"Sandino won't make the sacrifice and we can't make him unless we have reason to think that fraud was involved. If we get any evidence to that effect we can lean on him hard enough to squash him flat. - But now listen, I think it's possible Sandino did steal it."

Avalon said, "How?"

"By getting the code word. If I knew what the code word was, I'm sure I could figure out a logical way in which Sandino could have found it out or guessed it. Pochik, however simply won't let me have the code word. He shrieked at me when I asked. I explained why, but he said it was impossible. He said Sandino did it some other way - but there is no other way."

Avalon said, "Pochik wants an interpretation but he won't tell you the dream, and you have to figure out the dream first and then get the interpretation."

"Exactly! Like the Chaldean wise men."

"What are you going to do?"

"I'm going to try to do what Sandino must have done. I'm going to try to figure out what the fourteen - letter code word was and present it to Pochik. If I'm right, then it will be clear that what I could do, Sandino could do, and that the lemma was very likely stolen."

There was a silence around the table and then Gonzalo said, "Do you think you can do it, Tom?"

"I don't think so. That's why I've brought the problem here. I want us