R
If you’re coding the pair of letters DE, then, by taking the letters to the right of them (by the horizontal rule) you get DÉER; the letter B appears both in code and clear. And the same for letters that immediately follow one another in a vertical line. Now, in our first pair EX= JU, this doesn’t
The hypothesis that RBEXMG represented a date written entirely in numerals proved to be untenable, and for brevity’s sake, the calculations relating to this supposition are omitted.
happen, some may provisionally write them down in diagonal form
J
E
X
U
Taking these letters as forming the corners of a parallelogram, we can tell ourselves that JX must come on the same line in the diagram either vertically or horizontally; the same with JE, the same with EU, and the same with UX.’
‘But suppose JN follows the horizontal rule or the vertical rule without the two letters actually coming together?’
‘It doesn’t matter; ‘it’ would only mean then that all four of them come on the same line like this;? J E U X, or X U E? J or some arrangement of that kind, So taking all the letters we have got and writing them in diagonals we get this:
J
E
X
U
N
M
G
E
A
R
B
?
Unfortunately there are no side-by-side letters at all. It would be very helpful if there were, but we can’t have everything.
‘Now the first striking thing is this that U and X have to come on the same line. That very strongly suggests that they both come in the bottom line. There are five letters that follow U in the alphabet, and only four spaces in which to put them. One of them, therefore, must be in the key-word. We’ll take a risk with it and assume that it isn’t Z. If it is, we’ll have to start all over again, but one must make a start somewhere. We’ll risk Z. That gives us three possibilities for our last line: UVXYZ with W in the key-word, or UWXYZ with V in the key-word, or UVWXZ with Y in the key-word. But in any case, U must be in the bottom left-hand corner. Now, looking again at our diagonals, we find that E and U must come in the same line. We can’t suppose that E comes immediately above U, because it would be a frightful great key-word that only left us with four spaces between E and U, so we must put E in one of the top three spaces of the left-hand column, like this:
e
e
e
U
Z
‘That’s not much, but it’s a beginning. Now let’s tackle X. There’s one square in which we know it can’t be: It can’t come next to U, or there would be two spaces between X and Z with only one letter to fill them, so X must come in either the third or the fourth square of the bottom line. So now we have two possible diagrams.
e
e
e
U
X
Z
e
e
e
U
X
Z
‘Looking at our diagonal pairs again, we find that J and X come in the same line and so do J and E. That means that J can’t come immediately above X, so we will again enter it on both our diagrams in the top three squares in
the X line. Now we come to an interesting point. M and N have got to come in the same line. In Diagram 1 it looks fearfully tempting’ to put them into the two empty spaces on the right of J, leaving K and L for the key-word; but you can’t do that in Diagram 2, because there’s not room in the line. If Diagram 2 is the right; one, then M or N or both of them must come in the key-word. M and E,come in the same line, but N can’t come next-door to E. That warns us against a few arrangements, but still leaves a devil of a lot of scope. Our key-word can’t begin with EN, that’s a certainty. But now, wait! If E is rightly, placed in the third square down, then N can’t come at the right-hand extremity of the same line, for that would bring it next to E by the horizontal rule; so in Diagram, I that washes out the possibility of JMN or JLN for that line. It would give us JLM, which is impossible unless N is the key-word, because N can’t come next to E and yet must be in the same line with it and also with. M.’
Wimsey clawed a little at his hair and sat muttering.
‘It looks as though we’d sucked our five letter rather dry,’ said Harriet. ‘How about trying the rest of the message? I’ve got it all ready sorted out into pairs., Hullo! Here’s our old friend EXMG appearing again in the body of it.’
‘Is there?’ Wimsey sat up. ‘Then, if we’re right, that will be another, date in June. I can’t believe it’s part of two words, one of which ends in J, or I, or JU or IU or IUN or JUN. If the letter was making an appointment for June 18th, why shouldn’t the two letters before it be the letters for 18, that is AH? We’ll try it, anyway; what are they?’
‘O B’
‘OB=AH. That’s a fat lot of use. Well, we’ll stick em down.
O
A
H
B
O and A in the same line, 0 and H in the same line, and A and B we knew about before. That looks as though we might be on the right track, but it doesn’t help us much, because none of the letters we’ve; already placed comes into it.
‘Just a moment,’ put in Harriet. “I’ve got a brainwave. That town in the heading it’s supposed to be something in Central Europe. It’s got six letters, and the last two are the first two reversed. How about Warsaw?’
‘By jove! that’s bright! We can but try it. Let’s see — that gives us this He wrote down the new pairs of diagonals.
W
X
N
A
R
A
T
S
“W and X come in the same line,’ he observed, ‘and it’s terribly tempting to imagine that W comes in-’the last line, next door to X. Otherwise, of course, it must be in the keyword. Just for fun, let’s enter it in the last line in both our diagrams. Now, this becomes interesting. W and N are also in the same line. We can’t place N in the fourth line down, because it’s got to be in line with E. Nor can we put it in the third line down, because there are only six letters that come between N and U, and we should have eight spaces left to put them in. Therefore, if W is rightly placed, N has got to go in the top two lines, which means that it definitely does belong to the key-word.
Harriet filled the letters in tentatively.
1
e
n
i
e
n
i
e
U
W
X
Y
Z
2
e
n
i
e
n
i
e
i
U
W
X
Z
‘That makes Diagram 1 look wrong,’ she said. ‘Why? What have we done? Oh, I know. E and N can’t come together, so if that’s the right diagram, E must come in the third line. I say! That would mean a key-word of eleven letters!’
‘Not necessarily. E may be in its proper alphabetical place. But if Diagram 1 is right, then the beginning of Line 3 is the only place for it. Let’s get on. S and T come in one line, and so do R and T, but RST don’t follow one another, or RS would become ST, which it doesn’t. I should like ST to go in the two places next before U, but we can’t be sure that that is the right place for them. Well, dash, it! stick ’em down — if we’re wrong we must do it again, that’s all. There! Now in that case, R must be in the key-word and therefore in one of the top two spaces on the right of the diagram. That means that RS will be something — T.’
But we know RS! If AT=RS, then RS=AT.”
‘Good lord! so it does! That’s fine? That practically proves that our S and T are correct. And now we know that
AR must come next to one another in the key-word.’
Harriet pored over the diagrams again.
‘Can’t we do something now with NX=AW? Yes — look! If we put A into either of the squares in Diagram 1, so as to make NX=AW, then A won’t come next to R! So either we’re all wrong, or we can wash our Diagram 1 altogether.’
‘Hurray! — Brilliant woman! I always hated Diagram 1, so we’ll stash it. That leaves us with a very hopeful-looking Diagram 2.’
e
N
ia
r
e
N
ia
r
e
S
T
U
V
W
X
Z
‘I’m glad you think it’s hopeful! How about this, of M and N coming in the same line? Can we do anything with that now?’
‘Why not? Let’s try. Put M immediately, below the N spaces. That leaves five spaces, between it and S and only three letters to fill them, because we know that N and R are in the key-word. So that M must come in one of the four spaces in the top left-hand corner: Now we do know that NÉMG. Obviously G can’t come immediately between E and N anywhere, because that would give us a key-word with MNG in it, which sounds almost incredible. But that still leaves us with several possible arrangements. Is there anything else we can do?’
‘We can fill in Q in the space before S. It isn’t likely to be in the key-word without its U, and we know roughly what has become of R.
‘Yes. All right. There it is. Do any of these pairs of letters make sense in the letter itself, by the way?’
‘No. I’ve been trying to fit them in, but they’re remarkably unhelpful. There’s a group ATGM which works out as RSEN, but that might be anything. And quite near the beginning there’s TS followed by QJ. TS=SQ, and you’d expect the next group to be U — something, but it isn’t. QJ must be S — something-?
‘So it is; that shows we’re on the right track. Q is an arbitrary letter stuck in to separate the two S’s it’s curious how little one can get out of the actual text at this stage. Shows what an ingenious beast of a code it is, doesn’t it? Wait a jiff the group before that is MG=NE — that gives us NESS. Perfectly possible and even probable, but it might be anything. Here it comes again! Whatever it is, it appears to be important — its the same word, BFFY followed by NESS, but BFFY is simply baffling, I can see nothing for it but to go on struggling with the top left-hand corner. Let’s write out all the possible positions for NE =MG.
E
G
M
N
E
G
M
N
M
N
E
G
‘I cam see one thing,’ said Harriet, ‘and that is that we have got to have a vowel of some kind between M and N, and that vowel can’t be A, E, I, or U, because we’ve placed those elsewhere. Therefore it’s got to be either 0 or Y.’
‘O for preference. The number of words with MYN in them must be limited: But Y has got to be in the key-word somewhere: The end would be the likeliest place for it. perhaps it ends in MONY. That gives us MONY in Diagram (1), and a word of nine letters. That’s quite plausible. And it’s got to begin with E — G. That’s less pleasant. EBG, ECG; let’s run through the alphabet. EHG — I think not. EIG pronounceable, but we got I elsewhere. ELG — where’s the dictionary? Nothing there. ENG is impossible, we know where N is — same with ERG. My child, you can wash out all words ending in MONY — they won’t work on Diagram, (1) or on Diagram (3), and as for Diagram (2), I refuse to believe in a fourteen-letter word until I’m absolutely forced to.’
‘In that case, you can wash out Diagram (2) altogether.’
‘Right-ho! I don’t mind, though a thirteen-letter word ending in MON is not absolutely; inconceivable. In that case, either our word begins with Mon, or it doesn’t.’
‘But it does! We couldn’t find any words beginning E — G’
‘Nor we could. — Now then! We’ve got our E and our G fixed as well as our MON. Now we shan’t be long! Fill them in! Oh! and look here! I’m sure the F must go between the E and the G — it’s so obviously the place for it.’
Harriet filled the diagram in with a quivering pencil.
M
O
N
ia
r
ia
r
E
F
G
i
Q
S
T
U
V
W
X
Z
That does look better,’ she admitted. Now, let’s see if it helps to get any sense out of the letter. Bother! What a lot of groups that we still haven’t got! Still no sense for BFFY. Oh! wait! Here’s something! MZ TS XS RS. Now, MZ is something — U, and quite possibly RU; it’s a 50–50 chance, anyway. TS is SQ and XS is S — something, which means that the Q is just a fill-in letter. Now suppose XS = SI — there’s no reason why it shouldn’t. Then RS might, quite likely be AT there’s nothing against it: And suppose — suppose all these supposes are right, then MZTSXSRS is RUSQSIAT. Knock out the Q and we’ve got RUSSIAT. Why couldn’t that be RUSSIA?’
‘Why, not, indeed? Let’s make it so. Write the, letters down. M O N A R-oh, Harriet!’
‘Don’t joggle!’
‘I must joggle! We’ve got the key-word. MONARCH. Wait a jiff. That leaves three spaces before E, and we’ve only got B and D to put in. Oh, no, I forgot! Y — dear old Y! MONARCHY! Three loud cheers! There you are’ All done by kindness! There! There’s your square complete.. And jolly pretty it looks, I must say.’
M
O
N
A
R
C
H
Y
B
D
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