but of course, it could have been something unnoticeable and for that matter she didn't watch him closely. It wouldn't occur to her that she'd have to know someday.”
Halsted said, “Let me look at that again.” He stared at the combination solemnly. “This is only a copy. Dr. Puntsch. This can't be exactly the way it looked. It seems clear here but you might be copying it just as you thought it was. Isn't it possible that some of the numbers in the original might be equivocal so that you might mistake a seven for a one, for instance?”
“No, no,” said Puntsch, shaking his head vigorously. “There's no chance of a mistake there, I assure you.” '
“What about the spaces?” said Halsted. “Was it spaced exactly like that?”
Puntsch reached for the paper and looked at it again. “Oh, I see what you mean. No, as a matter of fact, there were no spaces. I put them in because that was how I thought of it. Actually the original is a solid line of symbols with no particular spacing. It doesn't matter, though, does it? You can't divide it any other way. I'll write it down for you without spaces.” He wrote a second time under the first and shoved it across the table to Halsted.
I2R27I5
He said, “You can't divide it any other way. You can't have a 271 or a 715. The numbers don't go higher than thirty.”
“Well now,” muttered Halsted, “never mind the numbers. What about the letter R?” He licked his lips, obviously enjoying the clear atmosphere of suspense that had now centered upon him. “Suppose we divide the combination this way”:
12 R27 15
He held it up for Puntsch to see, and. then for the others. “In this division, it's the twenty-seven which would have the sign for 'right' so it's the other two numbers that turn left. In other words, the numbers are twelve, twenty-seven, and fifteen all right, but you turn left, right, left, instead of right, left, right.”
Gonzalo protested. “Why put the R there?”
Halsted said, “All he needs is the minimum reminder. He knows what the combination is. If he reminds himself the middle number is right, he knows the other two are left.”
Gonzalo said, “But that's no big deal. If he just puts down the three numbers, it's either left, right, left, or else it's right, left, right. If one doesn't work, he tries the other. Maybe the R stands for something else.”
“I can't think what,” said Puntsch gloomily.
Halsted said, “The symbol couldn't be something other than an R, could it, Dr. Puntsch?”
“Absolutely not,” said Puntsch. “I'll admit I didn't think of associating the R with the second number, but that doesn't matter anyway. When the combination wouldn't work right, left, right, I was desperate enough not only to try it left, right, left; but right, right, right and left, left, left. In every case I tried it with and without complete turns in between. Nothing worked.”
Gonzalo said, “Why not try all the combinations? There can only be so many.”
Rubin said, “Figure out how many, Mario. The first number can be anything from one to thirty in either direction; so can the second; so can the third. The total number of possible combinations, if any direction is allowed for any number, is sixty times sixty times sixty, or over two hundred thousand.”
“I think I'll blow it open before it comes to trying them all,” said Puntsch in clear disgust.
Trumbull turned to Henry, who had been standing at the sideboard, an intent expression on his face. “Have you been following all this, Henry?”
Henry said, “Yes, sir, but I haven't actually seen the figures.”
Trumbull said, “Do you mind, Dr. Puntsch? He's the best man here, actually.” He handed over the slip with the three numbers written in three different ways.
Henry studied them gravely and shook his head. “I'm sorry. I had had a thought, but I see I'm wrong.”
“What was the thought?” asked Trumbull.
“It had occurred to me that the letter R might have
Halsted said, “Let me look at that again.” He stared at the combination solemnly. “This is only a copy. Dr. Puntsch. This can't be exactly the way it looked. It seems clear here but you might be copying it just as you thought it was. Isn't it possible that some of the numbers in the original might be equivocal so that you might mistake a seven for a one, for instance?”
“No, no,” said Puntsch, shaking his head vigorously. “There's no chance of a mistake there, I assure you.” '
“What about the spaces?” said Halsted. “Was it spaced exactly like that?”
Puntsch reached for the paper and looked at it again. “Oh, I see what you mean. No, as a matter of fact, there were no spaces. I put them in because that was how I thought of it. Actually the original is a solid line of symbols with no particular spacing. It doesn't matter, though, does it? You can't divide it any other way. I'll write it down for you without spaces.” He wrote a second time under the first and shoved it across the table to Halsted.
I2R27I5
He said, “You can't divide it any other way. You can't have a 271 or a 715. The numbers don't go higher than thirty.”
“Well now,” muttered Halsted, “never mind the numbers. What about the letter R?” He licked his lips, obviously enjoying the clear atmosphere of suspense that had now centered upon him. “Suppose we divide the combination this way”:
12 R27 15
He held it up for Puntsch to see, and. then for the others. “In this division, it's the twenty-seven which would have the sign for 'right' so it's the other two numbers that turn left. In other words, the numbers are twelve, twenty-seven, and fifteen all right, but you turn left, right, left, instead of right, left, right.”
Gonzalo protested. “Why put the R there?”
Halsted said, “All he needs is the minimum reminder. He knows what the combination is. If he reminds himself the middle number is right, he knows the other two are left.”
Gonzalo said, “But that's no big deal. If he just puts down the three numbers, it's either left, right, left, or else it's right, left, right. If one doesn't work, he tries the other. Maybe the R stands for something else.”
“I can't think what,” said Puntsch gloomily.
Halsted said, “The symbol couldn't be something other than an R, could it, Dr. Puntsch?”
“Absolutely not,” said Puntsch. “I'll admit I didn't think of associating the R with the second number, but that doesn't matter anyway. When the combination wouldn't work right, left, right, I was desperate enough not only to try it left, right, left; but right, right, right and left, left, left. In every case I tried it with and without complete turns in between. Nothing worked.”
Gonzalo said, “Why not try all the combinations? There can only be so many.”
Rubin said, “Figure out how many, Mario. The first number can be anything from one to thirty in either direction; so can the second; so can the third. The total number of possible combinations, if any direction is allowed for any number, is sixty times sixty times sixty, or over two hundred thousand.”
“I think I'll blow it open before it comes to trying them all,” said Puntsch in clear disgust.
Trumbull turned to Henry, who had been standing at the sideboard, an intent expression on his face. “Have you been following all this, Henry?”
Henry said, “Yes, sir, but I haven't actually seen the figures.”
Trumbull said, “Do you mind, Dr. Puntsch? He's the best man here, actually.” He handed over the slip with the three numbers written in three different ways.
Henry studied them gravely and shook his head. “I'm sorry. I had had a thought, but I see I'm wrong.”
“What was the thought?” asked Trumbull.
“It had occurred to me that the letter R might have
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