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“So I am. That’s why I know how tough the job is. There are over a quadrillion possible arrangements to be checked.”

“How do you work that out?” asked Duncan, delighted to discover something that had baffled his friend.

Karl looked at a piece of paper covered with sketches and numbers.

“Well, excluding forbidden positions, and allowing for symmetry and rotation, it comes to factorial twelve times two to the twenty-first-you wouldn’t understand why! That’s quite a number; here it is.”

He held up a sheet on which he had written, in large figures, the imposing array of digits:

1 004 539 160 000000

Duncan looked at the number with satisfaction; he did not doubt Karl’s

arithmetic. “So you’ve given up.”

“NO! I’m just telling you how hard it is.” And Karl, looking grimly determined, switched off.

The next day, Duncan had one of the biggest surprises of his young life. A bleary-eyed Karl, who had obviously not slept since their last conversation, appeared on his screen.

“Here it is,” he said, exhaustion and triumph competing in his voice.

Duncan could hardly believe his eyes; he had been convinced that the odds against success were impossibly great. But there was the narrow rectangular strip, only three squares wide and twenty long, formed from the complete set of twelve pieces…. With fingers that trembled slightly from fatigue, Karl took the two end sections and switched them around, leaving the center portion of the puzzle untouched.

“And here’s the second solution,” he said. “Now I’m going to bed. Good night-or good morning, if that’s what it is.”

For a long time, a very chastened Duncan sat staring at the blank screen.

He did not yet understand what had happened. He only knew that Karl had won against all reasonable expectations.

It was not that Duncan really minded; he loved Karl too much to resent his little victory, and indeed was capable of rejoicing in his friend’s triumphs even when they were at his own expense. But there was something strange here, something almost magical.

It was Duncan’s first glimpse of the power of intuition, and the mind’s mysterious ability to go beyond the available facts and to short-circuit the process of logic. In a few hours, Karl had completed a search that should have required trillions of operations and would have tied up the fastest computer in existence for an appreciable number of seconds.

One day, Duncan would realize that all men had such powers, but might use them only once in a lifetime. In Karl, the gift was exceptionally well developed; from that moment onward, Duncan had learned to take

seriously even his most outrageous speculations. That was twenty years ago; whatever had happened to that little set of plastic figures? He could not remember when he had last seen it.

But here it was again, reincarnated in colored minerals-the peculiar rose-tinted granite from the Galileo Hills, the obsidian of the Huygens

Plateau, the pseudo marble of the Herschel Escarpment. And there—it was unbelievable, but doubt was impossible in such a matter-was the rarest and most mysterious of all the gemstones found on this world. The X of the puzzle was made of Titanite itself; no one could ever mistake that blue-black sheen with its fugitive flecks of gold. It was the largest piece that Duncan had ever seen, and he could not even guess at its value.

“I don’t know what to say,” he stammered. “It’s beautiful-I’ve never seen anything like it.”

He put his arms around Grandma’s thin shoulders -and found, to his distress, that they were quivering uncontrollably. He held her gently until the shaking stopped, knowing that there were no words for such moments, and realizing as never before that he was the last love of her empty life, and he was leaving her to her memories.

CHILDREN OF THE CORRIDORS

There was a sense of sadness and finality about almost everything that he did in these last days. Sometimes it puzzled Duncan; he should be excited, anticipating the great adventure that only a handful of men on his world could ever share. And though he had never before been out of touch with his friends and family for more than a few hours, he was certain that a year’s absence would pass swiftly enough, among the

wonders and distractions of Earth. So why this melancholy? If he was saying farewell to the things of his youth, it was only for a little while, and he would appreciate them all the more when he returned…. When he returned. That, of course, was the heart of the problem. In a real sense, the Duncan Makenzie who was now leaving Titan would never return; indeed, that was the purpose of the exercise. Like Colin thirty years ago, and Malcolm forty years before that, he was heading sunward in search of knowledge, of power, of maturity-and, above all, of the successor which his own world could never give him. For, of course, being Malcolm’s duplicate, he too carried in his loins the fatal Makenzie gene.