“9123468537332006448121021817841607954824103712559441029152917904.”
“Sixty-four in all,” commented Leyland. “It’s obviously impossible that one cipher should stand for one letter, because that means your alphabet is reduced to ten letters. They must be groups of figures, then, that represent letters; and they can’t be groups of three, five, six, or seven, supposing the groups to be uniform, because that wouldn’t divide out right. I take it, then, that they are groups of two, four, or eight. The trouble is, you see, there are no repetitions. That’s to say, if you make the groups eights or fours there are no repetitions at all, and, even if you make the groups twos, the only repetitions you get are 91 and 37, each with a single repetition.”
“And that’s nonsense, isn’t it?” agreed Angela. “Because it would have to mean that the message used all the letters of the alphabet and four nonexistent letters, and only repeated itself twice.”
“I recollect,” said Mr. Quirk, “one of the leading cryptographers in the States telling me that letter-ciphers had been practically abandoned nowadays, and word-ciphers were used instead. Say, isn’t it likely a message of sixteen words, instead of sixteen letters?”
“And if it is, we can take our boots off and go to bed,” replied Leyland. “You can’t solve a word-cipher on a single message, unless you’ve got the key beforehand. Stands to reason they wouldn’t be using any of the recognized codes. Well, here’s for it.”
Their brows were knitted over it three-quarters of an hour later, when Bredon suddenly shouted from the door of the Ingle-room:
“The groups are threes.”
“Go back and count again,” retorted Angela indignantly. “You can’t have even looked at the thing. Three won’t go into 64.”
“You will go the wrong way about these things. You sit over the cipher and try to worry it out, and of course it won’t come out. But if you do as I do, keep taking a look at it and then going away and forgetting about it, you come to it fresh every time. And then, with luck, you see the arrangement of groups which makes the whole thing look natural. It’s the eye does it, not the brain.”
“Well, how do you work out the threes, anyhow?”
“Don’t count up to nine; count up to twelve. You can count tens, elevens, or twelves as if they were single units.”
“Have you read it yet?”
“No, but you ought to be able to do it now. I’m busy.”
They rewrote the cipher accordingly, and it certainly did look more promising. “912/346/853/733/200/644/812/1021/817/841/607/954/824/1037/1255/944/1029/152/917/904.”
Bredon came down to luncheon rubbing his hands, with the intimation that he had “got it out.”
“The cipher?”
“No, the patience. It was a long sight more difficult. Leyland gone back to Oxford?”
“No, he’s scouring round the country investigating another of Mr. Quirk’s great ideas. You do give us all plenty of exercise, I must say. Come on, Mr. Quirk, spill it.”
With some hesitation, Mr. Quirk unfolded his great idea. He argued, in the first place, that it must be a book-cipher of some description; that was the only possible method for a couple of amateur cryptographers. If it was a book, it must be a book which was in the possession of both parties. “Now, we know Nigel Burtell was one of the two parties who’s the other? I put it to you—Derek Burtell!”
“Derek! But you’ve spent a week trying to convince us that they’re both in a watery grave.”
“I must admit that I have been led to revise my conclusions very considerably. One of our greatest American thinkers has said that it’s only a fool who doesn’t acknowledge his mistakes. Now, according to my latest view both those two cousins are alive, and what’s more, they’re in correspondence with one another.”
“This all opens up very wide possibilities. But let us have the great idea.”
Stripped of some circumlocution, the great idea was as follows. The cipher must have been prearranged between the two cousins, possibly just before they parted, but more probably in the course of their tour. It appeared that, for whatever reason, they had separated on the Sunday night, Nigel sleeping at Millington Bridge, as we have seen, and Derek presumably finding a bed somewhere else. It looked, therefore, as if the cousins had meant to part for good on the Sunday night, keeping the cipher as a means of correspondence. Each, then, had already access to the book from which the cipher was taken; Nigel at Millington Bridge, and Derek—where? Derek could not have been far off; they had been on the river till late, and there were no last trains to be caught. Derek, therefore, was somewhere close at hand; Mr. Quirk had been looking at the map, and he suggested White Bracton, a village inland, it was true, but only a mile and a half by road from the bridge. Assuming that Derek spent the night there, the book which gave the clue to the cipher had been, and probably still was, at the White Bracton Inn.
“Isn’t it a brainwave?” said Angela. “Wasn’t it a very remarkable idea?”
“It was,” Bredon admitted, “a very remarkable idea. But it’s rough luck on Leyland to be sent scouting across to White Bracton for the book, when of course, equally, it’s here.”
“What’s that?” asked Mr. Quirk.
“Of course it’s here. Any country hotel keeps a railway timetable. Most country hotels don’t keep Bradshaw, which fortunately narrows the area of our search.”
“Oh, oh, oh, how perfectly beastly of you!” moaned Angela. “You mean the groups were the names of trains?”
“Of course they were. That’s the advantage of playing patience. You come fresh to the puzzle every time; and about the sixteenth time those figures suddenly stand out in your mind as train times—8:24, 10:37, 12:55, and so on. Of course the extra noughts in 200 and 607 are only to make the cipher look uniform. Once you’ve got the idea, you see that it must be so. The cipher runs up to 12 because the clock runs up to
