—until you told me it didn't mean what it seemed to!
"But I did follow your advice, and it got me out of one' of the worst jams I've ever been in—with a pat on the back from Earth-side to boot! So now let me ask you, Sean, in the name of all that's holy, how did you know so surely which one of the four it was?"
"I didn't know, Jim. It's more accurate to say I guessed."
"You old four-flusher! Do you mean to say you just played a lucky hunch?"
"Not quite, Jim, It was a guess, all right, but an educated guess. It all lay in the numbers, of course, the numbers of gold martians, the numbers of our four beasts. Tlick-Tcha's 666 did strongly indicate that he was in the employ of the League of the Beasts, for I understand they are great ones on symbolic actions and like to ring in the number 666 whenever they can. But that gets us Just nowhere—the League, though highly critical of most Earthmen, has never shown itself desirous of fomenting interstellar war.
"Hrohrakak's 1000 would indicate that he was receiving money from some organization of Earthmen, or from some alien source that happens also to use the decimal system. Anyone operating around Sol would be apt to use the decimal system. Hrohrakak's 1000 points in no one direction.
"Now as to Hlilav's 1024—that number is the tenth power of two. As far as I know, no natural species of being uses the binary system. However, it is the rule with. robots. The indications are that Hlilav is working for the Interstellar Brotherhood of Free Business Machines or some like organization, and, as we both know, the robots are not ones to pound the war drums or touch off the war fuses, for they are always the chief sufferers.
"That leaves Fa's 1728. Jim, the first thing you told me about the Arcturians was that they were hexadactylic bipeds. Six fingers on one hand means 12 on two—and almost a mortal certainty that the beings so equipped by nature will be using the duodecimal system, in many ' ways the most convenient of all. In the duodecimal system, 'one thousand' is not 10 times 10 times 10, but 12 times 12 times 12—which comes out as 1728 exactly in our decimal system.
"As you said, 'one thousand' of the going unit is the price of a being's life. Someone paid 'one thousand' gold martians by an Arcturian would have 1728 in his pocket according to our count.
"The size of Pa's purse seemed to me an odds-on indication that he was in the pay of the Arcturians war party. Incidentally, he must have felt very smart getting that extra 728—a more principled beast-criminal would have scorned to profit from a mere difference in numerical systems."
The Young Captain took some time before he answered. He smiled incredulously more than once, and once he shook his head.
Finally he said, "And you asked me to go ahead, Scan, and make my accusation, with no more indication than that?"
"It worked for you, didn't it?" the Old Lieutenant; countered briskly. "And as soon as Fa started to confess, you must have known I was right beyond any possibility of doubt. Telepaths are always truth-tellers." The Young Captain shot him a very strange look. "It couldn't be, Sean—?" he said softly. "It couldn't be that you're a telepath yourself? That that's the alien thought system you've been studying with your Martian witch doctor?"
"If it were," the Old Lieutenant replied, "I'd tell—" He stopped. He twinkled. "Or would I?"