The Heckler

“That’s simply the mathematical way of writing the permutations of 52. We callall the arrangements we can make by selecting all the numbers of a group ‘simple permutations.’ The equation becomes…” And he wrote: 52p52=52!

“That tells us how many possible ways there are of arranging a deck of 52 cards.”

“What’s the exclamation point for?” Rafe asked.

“It’s not an exclamation point. There are no interjections in mathematics. It simply indicates that the number must be multiplied by every whole number below it until we get to 1. For example, the number four followed by that symbol simply means 4 times 3 times 2 times 1.”

“So how many wayscan you arrange a deck of cards?”

“52! ways—or 52 times 51 times 50 times 49 times—well, all the way down until you reach the figure 1. It would take all day to multiply it out. But at the risk of making you nervous again, let’s get back to something of more concern to us, policemen. And, specifically, the detectives of the Eighty-seventh Squad. There are normally sixteen men on the squad. But when we pull our job, two will be on vacation and two will be in Washington taking an FBI course.”

“That leaves twelve,” Rafe said.

“Right. Let’s try to figure how many possible combinations those twelve men can arrange themselves into, shall we? The equation would be this.” He wrote: 12p12=12!

“Which means,” he went on, “12 times 11 times 10, and so on. Let’s see what that comes to.” Quickly, he began multiplying figures on his sheet of paper. “Well, here you are,” he said. “All the possible combinations for twelve men, 12 times 11 times 10 down through 1, is 479,001,600. It sounds staggering, doesn’t it?”

“It sure does. Evenone cop sounds staggering to me,” Rafe said.

“Of course, detectives usually work in pairs, and not in teams of twelve or eight or six or what have you. And this would automatically limit the number of possible combinations. Besides, we need not concern ourselves with the permutations of those twelve men. We need only to abstract a theory about law enforcement and crime prevention. It seems to me, Rafe, that the police operate on their own limited theory of probability. Obviously, with their inadequate force of thirty thousand, they cannot possibly hope to be everywhere at once. This is a damned big city and a great many people in it are practicing criminals. So the police operate against percentages. They figure in this fashion, more or less: A certain number of criminals must escape detectionfor the moment because we can’t possibly hope to be where they are when a crime is being committed or because we can’t successfully investigate every crime even after it’s been committed; however,in the long run, we will one day catch a previously undetected criminal because we will be in the right place at the right time or because the situation for a successful investigation will present itself.‘In the long run’ —those are the key words in probability.”

“I think I’d better go make my phone calls,” Rafe said. “Besides, your ferry’s coming in.”

“Just a moment, Rafe.‘In the long run.’ Remember those words. If you flipped a penny five times in succession, the first five flips might come up tails. If you stopped flipping right there, you might come to the conclusion that a penny will come up tails one hundred per cent of the times it is flipped. Deviation, remember? The difference between observation and reality. Actually, the longer you kept flipping that penny, the closer you would come to the truth. Which is, of course, that it will turn up heads fifty per cent of the time and tails the remaining fifty per cent. So the cops are playing the long run. They’ve got this rather cute, quaint, antiquated, friendly, bumbling law enforcement machine andin the long run, through a combination of choice and chance, they will make their arrests and maintain order—primarily because the percentages are on their side. Most citizens, you see, are law-abiding. But tell me something, Rafe.”

“What?” Rafe asked.

“What happens when someone comes along and screws up the percentages? What happens when the police are forced to cope with something the likes of which they’ve never encountered before? What happens when they’re pushed into dealing with theshort run?”

“I don’t know,” Rafe said. “What happens?”

“We’ll walk off with two and a half million bucks,” the deaf man said. “That’s what.”

THE REAL ESTATE AGENTin Majesta was quite taken with his caller. The man was tall and good-looking, with pleasant blue eyes and a manner reminiscent of the Old South. At the same time, the man knew what he wanted and he wasted no time in stating his needs.

“A small house with a garage,” the deaf man said. “It needn’t be close to the ferry, and I shall only need it for a few weeks. The garage must be large enough to hold two cars; a sedan and a small truck.”