Tom Tiddler's Island, стр. 36

Some of these must have occurred in the original message. Since TH occurs fairly often in English—in words like THE, THEM, THEIR, THIS, THAT which turn up again and again in the simplest sentences—I started on that pair of letters. Some of the T’s in the cipher had no H’s as companions: they may have occurred in words like TEST or TEN or PUT. But some T’s must have had H’s as neighbours in the original message. If we can identify these T’s and their mates among the H’s, we’ll have a clue to how the transposition was done.”

Colin rubbed his ear with a whimsical air to suggest that he was getting out of his depth at this stage.

“Going’s a bit rocky, now,” he confessed.

“You’ll see it clearly enough soon,” Northfleet assured him. “Struggle on, for a moment or two. What I did to start with was this. I wrote out the message and numbered each letter in succession, like this:

T e i i l l f i l h. . .

1 2 3 4 5 6 7 8 9 10. . .

so that the last Z was No. 336, since there are 336 letters in the message.”

“I see that all right.”

“When I’d done that, I found that the H’s were numbered 10, 18, 31, 43, 53, 75, 81, and so forth, while the T’s were numbered 1, 11, 14, 39, 49, 55, 65, and so on. The next thing I did was this: I wrote down in a horizontal line all the numbers of the H’s, and in a vertical line all the numbers of the T’s. Then by subtracting each T number from the H numbers in turn, I got a series of differences. When the H number is smaller than the T number, I added 336—the total number of letters in the message—to the H number before doing the subtraction. Here’s part of the table—enough to illustrate the results.”

Northfleet spread another sheet of paper on the table, and Colin stared at it rather uncomprehendingly.

“You don’t see it?” said Northfleet, after glance at Colin’s puzzled face. “Well, isn’t clear enough that there’s a repetition of 42 as a difference in six lines out of the seven, and that no other number turns up so often? I’ve underlined the 42’s so that they’ll catch your eye.”

“Plain enough, that.” Colin admitted. “But I don’t see what it means.”

“Think again. Take the first letter in the cipher. It was T. If an H was next to it as part of TH, then that H would have been No. 2. But during the enciphering this H No. 2 has got shifted along until it is now No. 43, so that between it and its original companion there’s an interval of 42. Similarly, the T numbered 11 was followed by an H in the original. That H has got shifted forty-two places farther on; so that instead of being No. 12 it is now No. 53. On the other hand, the T numbered 14 doesn’t yield the common difference 42 with any of the H’s. Evidently it wasn’t part of a TH digraph at all, but belonged to some word like 4 true’ or ‘two 5 or 4 turn’ where no H follows the T. Do you follow me, Watson?”

“I get a glimmering,” Colin asserted. “But I’d like it put in words of one syllable, just to make sure I do understand it.”

“Very well,” Northfleet agreed. “Take a simple example. Suppose I want to encipher the words: ‘This is my message.’ I write them down in groups of three letters, like this :

Then I rewrite the letters as they occur in downward order, column after column, and I get

Now your H, which was the second letter in the original, has got shifted to place No. 6; and the I which was the third letter in the original has dropped into the eleventh place. Subtract 1 from 6 and you get the difference 5. Subtract 6 from 11 and again you get 5 as the difference. Now do you see what the 5 corresponds to?”

Colin studied the paper for a moment or two.

“It’s the number of letters in each vertical column, isn’t it?” he said as he looked up again.

“Yes. And in the Morse cipher we got a common difference of 42, didn’t we?”

“Jove, yes! I see now,” Colin exclaimed excitedly. “The original message must have been arranged in vertical columns, like yours, only with forty-two letters per column instead of your five. Is that it?”

“And since the message contained 336 letters, there must have been eight columns,” Northfleet suggested. “Unfortunately, it’s not quite so simple as that. There’s a second regular series of differences in addition to the 42 set. When I went over the whole of the H’s and T’s, I found that the H’s numbered 18, 31, 177, 184, and 199 were linked up with the T’s numbered 142, 155, 301, 308, and 323, with a common difference of 212, instead of the 42. Here you have the thing without any extraneous figures to confuse your eye.”

He laid another sheet of paper before Colin.

Colin gazed at the figures disconsolately.

“Frank and honest’s my motto,” he declared at length. “I do not follow you this time. In fact, if you gave me a month of Sundays in the next blue moon I doubt if I’d get much further forward on my own wheels. I give it up. How d’you set about it?”

“We’ll leave it aside for a moment,” Northfleet said. “Go back to your own suggestion and arrange the letters in vertical columns with forty-two letters in each column. Here’s how it works out when you do that.”

He produced yet another sheet of paper and confronted Colin with the following arrangement:

“I’ve underlined the TH digraphs which have been brought together again by this arrangement,” Northfleet pointed out. “You can see from