CHAPTER V
Geometrical Types — The Turning Grille
The well-known _turning grille_, also known as the _rotating_, or _revolving_ grille, is said to have been originated by an Italian, Girolamo Cardano (or Cardan). Such grilles can be prepared from any substantial material capable of being made into sheets and marked into cells, and may take the form of any geometrical figure which happens to be equilateral. The number of cells to be clipped out, so as to form apertures for the writing of letters, is based on the shape of the grille, as: one-third of the total number for a triangle, one-fourth for a square, and so on; and the writing of the letters is done on a section of paper of the same size and shape as the grille, and preferably ruled off into cells which correspond to those of the grille. After such a grille has been placed on its corresponding section of paper, and a letter has been written through each aperture, the grille is _turned_ a certain number of degrees to a new position on the same section of paper, so as to cover from sight the letters already written, and expose another series of blank cells for the writing of new letters; and this continues until the grille has taken its full number of positions and every cell has been accounted for on the section of paper beneath it. The preferred grille is a square, based on square cells, and takes four positions. Usually it is based on an _even number_ of these cells; otherwise, the full number of cells is not evenly divisible into quarters, leaving an extra central cell which has to be omitted or specially dealt with.
The grille called “Fleissner,” after an Austrian cryptologist, Eduard Fleissner von Wostrowitz, is the perfected Cardan grille as described by Jules Verne in his story, “Mathias Sandorf.” Colonel Fleissner’s grille is a square, taking four positions, and is always based on an even number of cells. In preparing this grille, it is easy enough to select apertures at random in such a way that each one governs its own four cells on the paper beneath, causing each of these to be uncovered exactly once. But concerning the preparation of the grille, there is a phase which affects the value of the cipher itself: unless the grille can be constructed at will, in accordance with a key which is “easily changed, communicated, and remembered,” it requires the keeping on hand of a material apparatus which can be stolen or copied, or which cannot be destroyed in case of emergency.
There are, of course, many ways in which a key could be applied. The method used here is one published several years ago by Ohaver, and can be studied in Fig. 19. First, as shown at (a), we have a quick mechanical method for selecting apertures that cannot conflict. The square is divided into four quarters, and each quarter, treated as if it were the one occupying the upper left-hand corner, receives its consecutive cell numbers, 1 to 9 (or 1 to 4, 1 to 16, 1 to 25, 1 to 36, etc.). If the route of writing-in is made exactly the same for all four of the quarters, it becomes possible to clip _one each_ of the numerals 1, 2, 3, 4, 5 . . . . . . . etc., taken absolutely at pleasure, and each resulting aperture will expose only its particular four cells. This can be seen at (b).
The grille shown at (b), however, was based on the key-phrase FRIENDLY GROUPS, and the method can be studied at (c), following Ohaver’s plan, even to its minute details. The fact that the square is based on 6 is told in the initial letter of the key-word, _F_, 6th letter of the alphabet. This key-word must yield nine letters, one for each proposed aperture in the grille. A short word, such as FRIEND, can be lengthened by a partial repetition, as FRIENDFRI, while a longer word is cut off after its ninth letter, as it was in Fig. 19. This literal key is next converted to a numerical key, as explained in the preceding chapter, and the nine resulting numbers are divided as evenly as possible into four sections. Finally, considering the four quarters of the grille in some definitely agreed rotation, each section of key-numbers will show what numerals are to be clipped from a given quarter. In the figure, the numerals 3 and 8 were clipped from the first quarter, numerals 5 and 2 from the second — proceeding in a clockwise direction, — numerals 7 and 1 from the third quarter, and numerals 6, 9, and 4 from the remaining quarter.
Figure 19 - Preparation of a Grille
(a) (b)
Top 1 2 3 7 4 1 _ _ 3 _ _ _ 4 5 6 8 5 2 _ _ _ _ 5 2 7 8 9 9 6 3 _ 8 _ _ _ _ 3 6 9 9 8 7 _ 6 9 _ _ 7 2 5 8 6 5 4 _ _ _ _ _ _ 1 4 7 3 2 1 _ 4 _ _ _ 1
(c)
F R I E N D L Y G 3 8.5 2.7 1.6 9 4 1st Q: 3,8; 2d: 5,2; 3d: 7,1; 4th: 6,9,4
Another method for selecting cells, proposed by Edward Nickerson, dispenses with numerals, using in their places the letters of a key-word which must be without repetitions, as FRIENDLY G happens to be. If these nine letters, all different, be written into the nine cells of each quarter, following exactly the same route in each case, it becomes possible to clip one each of the letters _F_, _R_, _I_, _E_, _N_, _D_, _L_, _Y_, _G_, taken wherever desired. The choice can be made as follows: Taking the four quarters of the grille in the agreed rotation, follow the normal alphabet, clipping _A_, (when present,) from the first quarter, _B_, (when present,) from the second quarter, _C_, (when present,) from the third quarter, and so on. Or, to insure a more even distribution, rearrange the nine letters in alphabetical sequence: _D E_, _F G_, _I L_, _N R Y_, and divide as in the former plan, clipping _D_ and _E_ from the first quarter, _F_ and _G_ from the second, and so on. While it is possible to provide key-phrases of sixteen letters, without repeating, it is probably more convenient to take whatever number of letters is needed from a key-mixed alphabet of the following type: F R I E N D L Y G O U P S A B C . . . . . . W X Z _f r i e_ . . . . . .
In Fig. 20, at (a), (b), (c), (d), we have a detailed picture of the operation of this grille on the 36-letter plaintext unit: MISFIRE ON VIADUCT JOB X RUSH INSTRUCTIONS. One definite edge of the grille must be designated as the top, and there is a right and a wrong side. Taking precautions in these respects, we place the grille over a sheet of paper and mark its outline with a pencil (or otherwise make sure of maintaining this one location). We write the first nine letters as at (a), and give the grille a quarter-turn to the right. We add the second nine letters as at (b) — where the newly-written letters are the capitals; the others, in lower case, are presumed to be hidden from sight by the solid portion of the grille. Another quarter-turn makes ready for the next nine letters (c), and a remaining quarter-turn completes the revolution (d). The writing-in, at all times, is _straight ahead_: cells taken from left to right, and lines taken from top to bottom.
Figure 20 - Four Stages of Encipherment
(a) (b)
_ _ M _ _ _ _ _ m _ _ _ _ _ _ _ I S V _ I A i s _ F _ _ _ _ _ f D _ _ U _ I R _ _ E _ i r _ _ e _ _ _ _ _ _ _ _ _ _ C _ _ O _ _ _ N T o J _ O n
(c) (d)
B _ m _ X _ b T m R x U v _ i a i s v C i a i s R f d U S u r f d u s u _ i r _ H e T i r I h e I N _ _ c _ i n O N c S t o j S o n t o j s o n
In the Jules Verne story, the three units of his cryptogram were left standing in their blocks. Verne’s heroes were clever enough to unearth a ready-made grille, and, by laying this, in its four successive positions, above each of the three blocks, were able to read the message through the apertures. Today, such blocks would be taken off in five-letter groups, and possibly by a devious route. A little concealment can be afforded, too, by completing the last five-letter group with nulls, or, better, by adding these nulls at the beginning of the cryptogram. It is also possible to make the final 36-letter unit _incomplete_ by blanking out its bottom cells before putting in the letters.
A grille can be used in other ways. Negligible changes can be produced in its cryptograms by altering the customary order of its four positions. A more substantial change is introduced by departures from the straight horizontal direction of the writing-in. It is possible to revolve the paper instead of the grille, setting the letters right-side-up at the time of their taking off. And in all of these cases, the grille is still serving as an instrument for _writing-in_; there would be corresponding cases in which it is used as an instrument for _taking out_ the letters of a prepared block. Each variation, perhaps, would require its own separate analysis before its individual inherent weaknesses could be spotted and used as the basis for a special method. If the student, after observing some special methods applied to ordinary grille encipherment, cares to try his hand at analyzing some one of its variations, we suggest that he take a series of numbers, 1 to 36, 1 to 64, etc., and carry these through a complete encipherment to see what becomes of each one.
* * *
Grille transposition, like the Nihilist, involves a major unit composed of minor units. But here, the four minor units are never left intact, and if the type of encipherment is not known in advance, the decryptment of a single block will give somewhat more trouble than the decryptment of a single Nihilist block, for the reason that the decryptor usually exhausts the simpler possibilities before trying the complex. With grille encipherment known, or suspected, we have a cipher bristling with points of attack.
The strictly horizontal writing-in of each minor unit has had to be done within a fairly short compass, and no two consecutive letters of this unit can have been placed very far apart without causing other letters to draw closer together. Their average distance apart is four cells. For the decryptor, this actual distance apart of letters is made shorter by his knowledge that for each letter considered, there are three others which cannot have been written into the same unit with it, _and that he knows definitely what these three letters are_.
Particularly interesting is the assistance he receives from the symmetrical pattern into which the letters of his four units are written; position 3 is position 1 reversed, and position 4 is position 2 reversed. Thus, having tentatively selected the letters of a probable word, or fairly long sequence, he can check the correctness of his observations by examining another sequence which would automatically build up, traveling in the opposite direction, in the reverse position of the grille.
For a clear understanding of these matters, suppose we consider the decryptment of the block just enciphered, on the assumption that we suspect the presence there of the word VIADUCT. Fig. 21 shows a 6 x 6 block carrying consecutive cell-numbers, which are also the serial numbers of the cryptogram letters, as these appear in a separate block beside the first. It is understood that our first move would be that of ascertaining whether or not the seven letters of this word are all present. It must be remembered, too, that a long word is not necessarily altogether in one unit; the grille might have been turned before the word was completed.
In the present case, however, our first letter, _V_, is found near the top of the square, and only once, so that if the word VIADUCT is present, a substantial portion of it must have been written before the grille was turned. We expect to find letters _I_, _A_, _D_, _U_, and so on, following the letter _V_ in just that order, and without any very great distance between any two of them; and if, approaching the bottom of the square, we find it necessary to proceed backward for _U_, _C_, or _T_, then the grille was surely turned before that _U_, _C_, or _T_, was written.
Now, considering together the two blocks of Fig. 21, we find that our first letter, _V_, occupies cell No. 7. In imagination, we revolve a grille in which the only aperture has been cut in cell 7, and find that this aperture exposes the cells numbered 5, 30, and 32. These three cells, then, were surely covered from sight when the letter _V_ was written into cell 7, and regardless of what the letters are that occupy these three cells, it is definitely impossible that any one of the three could have been used in the same minor unit with the _V_ of cell 7.
Looking for a letter _I_, we find several within a very short range. But the block contains only one _A_, and since we cannot proceed backward after selecting the _I_, the position of _A_ (cell 10) tells us that only the _I_ of cell 9 is possible. We accept, then, the _I_ of cell 9, and, again revolving an imaginary grille with its only aperture cut in cell 9, we eliminate the letters found in cells 17, 28, and 20. Similarly, accepting _A_ of cell 10, we eliminate whatever letters are occupying cells 23, 27, and 14. So far, none of the letters eliminated have been wanted for the development of the word VIADUCT; but notice that the fourth letter, _D_, found only once in the block, occupies cell 15, thus eliminating the letters of cells 16, 22, and 21, one of which is _U_, the next letter needed. Thus, we are not forced to make a decision as between the _U_ of cell 16 and the _U_ of cell 18.
Figure 21
1 2 3 4 5 6 B T M R X5 U
7 8 9 10 11 12 V7 C I9 A10 I S
13 14 15 16 17 18 R F D15 U S U18
19 20 21 22 23 24 T19 I R I22 H E
25 26 27 28 29 30 I N O27 N28 C S30
31 32 33 34 35 36 T O32 J S O N
We have put together, then, the letters _V I A D U_ in the only manner which is possible at all, and their cell-numbers, taken in order, are 7-9-10-15-18. If the grille is reversed, these same openings, named in the same order, will uncover cells 30-28-27-22-19; these new cells, however, will not be seen in reverse order; they will be in straight order like their letters. If, then, our sequence _V I A D U_ is correct, the five letters found in cells 19-22-27-28-30, taken in normal order, should form an acceptable English combination. A glance at the right-hand block of Fig. 21 will show that this check-sequence is _T I O N S_.
When we selected _V_, we automatically selected _S_ of cell 30 as its check-letter. When we added _I_ on the right-hand side of _V_, we obtained with it the _N_ of cell 28 on the _left_ side of _S_, giving the check-digram as _NS_, entirely acceptable. With _A_, we added the _O_ of cell 27, giving the check-trigram as _ONS_, still acceptable; and so on to _IONS_, _TIONS_. Our complete word VIADUCT produces the check-sequence _UCTIONS_. It must not be objected that the fact of having only one each of letters _V_, _A_, _D_, has too greatly facilitated the search. This is an entirely legitimate expectation in a case where we deal with one unit, and the decryptor, when possible, chooses his probable word with this in mind. In the absence of a probable word, we are never without probable sequences: the list of frequent trigrams, and the various common affIxes, such as _-TION_, _-MENT_, _-ENCE_, _-ABLE_, _CON-_, _PRE-_, etc. For the first three or four letters, where decisions are sometimes uncertain, it is more satisfactory to work directly on the square (prepared in ink), so that impossible cells may be canceled in pencil, and the pencil marks erased when wrong; but once well started, a paper or celluloid grille can be prepared to fit the block, and the chosen cells actually cut out as they are selected. Having found seven out of nine apertures, we may, if we like, turn the paper grille and experiment with its other two positions. The letters, in this case, will show gaps in sequence, and may indicate by these gaps just where the new openings ought to be cut. With one full unit determined, we have the grille for reading the others. The only remaining problem would be that of deciding the exact sequence of these four units, with their context as a guide.
For the case in which it is necessary to begin with letter-sequences, particularly if driven back to the digram list, the device shown in Fig. 22 may prove of considerable assistance: The cryptogram is written in both directions, and thus pairs every letter with its check-letter, so that check-sequences here would be written backward. This idea is adapted from General Givierge’s _Cours de cryptographie_.
Figure 22
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 B T M R X U V C I A I S R F D U S U N O S J O T S C N O N I E H I R I T 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 T I R I H E I N O N C S T O J S O N U S U D F R S I A I C V U X R M T B 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
Working with digrams is tedious, but will, in the end, give results. Considering, for instance, Fig. 22, its first letter is _B_. Of letters standing immediately to the right of _B_, the first one which would form a good digram with it is the _R_ of cell 4. But consideration of a possible digram _BR_, cells 1-4, shows the check-digram as _JN_, cells 33-36, and this latter digram is so rare in the language that Meaker did not find it even once in his 10,000-letter text. The next letter known to have an affnity for _B_ is the _U_ of cell 6, but a possible digram _BU_, cells 1-6, cannot be considered, for the reason that cells 1 and 6 are uncovered by the same opening in the grille. The distance away of the next letters to which _B_ is partial proves frightening, and _B_ is abandoned (it is actually followed by the _X_ of cell 5).
Figure 23
R R T H A O U E E O S B A G D E A E A V E B K U N E S F D I A N K S S S T A D P E B R A N S U K O D X F D N C R E A R R N J A T I Y G O A O A R A O I L I D X T U S O B R A A N L E T S G T E P L M A O T V H R A X E X
Beginning over, with _T_ of cell 2: The first frequent digram noticed is _TR_, cells 2-4, and shows the check-digram as _JO_, cells 33-35. We accept this at once, because the letter _J_ must presumably be followed by a vowel, and the only vowel immediately available is this particular _O_. To extend the accepted _TR_, we require a vowel. The first one is U, cell 6, and extends the check-digram to _TJO_, cells 31-33-35, acceptable if _T_ is the final letter of a word. To extend the supposed trigram _TRU_, we experiment with _C_ of cell 8 and obtain a check-sequence _CTJO_, cells 29-31-33-35, which is still encouraging. We must know, of course, that no two of the chosen cells are in conflict with each other. The unit we have partially reconstructed is the second one of Fig. 20, and the check-sequence is the fourth unit.
A method somewhat resembling the foregoing consists in writing another block beside the first, in which the letters of the cryptogram are strictly in reversed order. The pattern of the check-sequence will then follow exactly that of the sequence under examination, merely with its letters in reverse order. Still a further suggestion was made by Herbert Raines: In the preparation of the two blocks, one in straight order and the other in reverse order, the writing should be done vertically, with all columns containing four letters. The symmetry can still be found, and any two consecutive plaintext letters are more nearly at their original distance apart — the average 4.
So far, we have been dealing with an isolated unit. In Fig. 23 we have a longer cryptogram, suspected of being a reply to the first. We have set it up in its three blocks, expecting to decipher it with the same grille, but find that something is wrong. To see quickly how the presence of several units modifies the case, suppose we consider some sequence, right or wrong, which is easily examined, such as the _AVE_ on the second row of the first block. Regardless of what the transposition is, if all three of these units are enciphered alike, each of the additional blocks contains a corresponding trigram in exactly the same location as the one under consideration; here we have _NES_ in the second block and _ANK_ in the third. But if the transposition is specifically that of the grille, each one of the three trigrams _AVE_, _NES_, _ANK_, has a check-trigram in its own block. Thus we have the six trigrams listed with their cell-numbers in Fig. 24. Since all of these are acceptable, we should, in practice, be encouraged to accept them; thus, it may be well to say here that, in dealing with all ciphers these false beginnings will quite frequently pitch the decryptor headlong into a solution, through no act of wisdom on his own part.
Figure 24
Straight Reversed
7 8 9 28 29 30
A V E L I D N E S S O B A N K N L E
Now, in order to arm ourselves against the larger grilles, which are somewhat more troublesome, and for investigation of cryptograms which may or may not have been accomplished with a grille, suppose we take a look at Ohaver’s mechanical method — that is, his use of paper strips. Picturing any block of 36 cells, numbered consecutively as we saw these in Fig. 21, let us imagine that there is a grille placed over this block, and that this grille has only one opening. If the cell that shows is No. 1, then, at the first turn of the grille, we uncover cell No. 6; at the next turn, cell No. 36; and, at the final turn, cell No. 31. We will call this series of cell-numbers an _index_, and say that the index for this particular aperture is 1-6-36-31. In the first block of the new cryptogram, the letters which follow this index are _R O P T_. In the second block, the same index governs the letters _U B V L_, and, in the third block, _A E X H_. But if the single opening in our hypothetical grille has exposed cell No. 2, then its _index_, discovered in the same way, is 2-12-35-25, and the corresponding letters, in the three blocks of this cryptogram are, respectively, _R U E A_, _E I T X_, and _G S E R_. Similarly, each one of the other seven apertures possible in this quarter of the grille has an index, expressible in cell-numbers, and governs a certain series of letters in each cryptogram block. If the grille is the Fleissner, the index for any aperture, in a grille of any size, will always contain four numbers, and will govern four letters per block.
If the grille is a 16-letter one, there will be only four of these indices, beginning in cells 1, 2, 5, 6. If it is a 36-letter grille, there will be nine, beginning in cells 1, 2, 3, 7, 8, 9, 13, 14, 15. A 64-letter grille will have 16, beginning in cells 1, 2, 3, 4, 9, 10, 11, 12, 17, 18, 19, 20, 25, 26, 27, 28; and so on to grilles of 100, 144, etc., letters. After one grows accustomed to the swastika-like route of the open cell, such indices are not at all difficult to prepare at the moment of need; however, many solvers prefer to make them up in sets, once for all, and have them ready as they happen to be wanted. As to the finding of the four letters per block which follow any one index, it is sufficient to remember that the cell numbers, arranged in the manner shown, are also the serial numbers of the letters belonging to any one unit. Thus it is not necessary to write the units into their squares; we need merely number the letters of a unit from 1 to 36, and select those having the desired serial numbers.
Returning, now, to our cryptogram: Our unit appears to be 36, since a division of this kind distributes the vowels uniformly; and a unit of 36 may have been produced with a grille. If so, this grille had 9 apertures, and we need 9 paper strips, one for each aperture. On each strip we are to have: the four index numbers, the four corresponding letters from the first block, the four corresponding letters from the second block, and the four corresponding letters from the third block. But since, in each case, the first three cell-numbers or the first three letters _must be repeated_, our strip will actually contain seven numbers and twenty-one letters. These nine strips are prepared all in one set-up, the details of which can be examined in Fig. 25. In Fig. 26, the strips of Fig. 25 have been cut apart and rearranged in such a way as to bring out plaintext on the top row of every block; this is, of course, the first _full_ row, as pointed out in each case by the four asterisks. It will be noticed that the top row of cell-numbers is arranged in strictly ascending order (our strictly horizontal route of writing-in). If the third row be now examined (as pointed out by two asterisks), it is found that this, too, carries plaintext, merely written backward, and that here the cell-numbers are arranged in strictly descending order.
Figure 25
Preparation of Slips
Index....... 1 2 3 7 8 9 13 14 15 6 12 18 5 11 17 4 10 16 36 35 34 30 29 28 24 23 22 31 25 19 32 26 20 33 27 21 1 2 3 7 8 9 13 14 15 6 12 18 5 11 17 4 10 16 36 35 34 30 29 28 24 23 22
Block 1...... R R T A V E T A D O U B A K E H B P P E T D I L R R A T A C S O R G I E R R T A V E T A D O U B A K E H B P P E T D I L R R A
Block 2...... U E E N E S R A N B I K S D U O F S V T O B O S Y I T L X N M T J A U A U E E N E S R A N B I K S D U O F S V T O B O S Y I T
Block 3...... A G D A N K O D X E S N A S D E S F X E X E L N R A O H R G R A O A A A A G D A N K O D X E S N A S D E S F X E X E L N R A O
Now, to read the cryptogram: Each full row of numbers includes all cell-numbers belonging to some one of the four units, and any one of these four rows of numbers is a key to the grille, since it shows exactly what cells were uncovered when the corresponding unit was written in. To obtain the grille, we have only to select some one row of numbers, as 12-36-10-16-34-9-26-32-13, and clip out these particular cells in a square numbered as we saw it in Fig. 21. The student who cares to know what “instructions” were being sent might also satisfy his curiosity as to whether or not this new cryptogram could have been deciphered rather than decrypted.
Figure 26
One Correct Adjustment of Slips
┌────┐ ┌────┐ │ 9 ├────┬────┤ 13 │ ┌────┐ ┌────┤ 17 │ 8 │ 7 │ 4 │ ┌────┤ 1 ├────┬────┤ 3 │ 28 │ 11 │ 5 │ 24 │ │ 2 │ 6 │ 14 │ 15 │ 18 │ 20 │ 29 │ 30 │ 33 │ **** │ 12 │ 36 │ 10 │ 16 │ 34 │ 9 │ 29 │ 32 │ 13 │ │ 35 │ 31 │ 23 │ 22 │ 19 │ 17 │ 26 │ 7 │ 4 │** │ 25 │ 1 │ 27 │ 21 │ 3 │ 28 │ 8 │ 5 │ 24 │ │ 2 │ 6 │ 14 │ 15 │ 18 │ │ 11 │ 30 │ │ │ 12 │ 36 │ 10 │ 16 │ 34 │ │ 29 │ │ │ │ 35 │ │ 23 │ 22 │ │ E │ │ │ T │ │ │ │ │ │ │ E │ V │ A │ H │ │ │ R │ │ │ T │ L │ K │ A │ R │ │ R │ O │ A │ D │ B │ R │ I │ D │ G │ **** │ U │ P │ B │ P │ T │ E │ O │ S │ T │ │ E │ T │ R │ A │ C │ E │ V │ A │ H │** │ A │ R │ I │ E │ T │ L │ K │ A │ R │ │ R │ O │ A │ D │ B │ │ I │ D │ │ │ U │ P │ B │ P │ T │ │ │ │ │ │ E │ │ R │ A │ │ S │ │ │ R │ │ │ │ │ │ │ U │ E │ N │ O │ │ │ U │ │ │ E │ S │ D │ S │ Y │ │ E │ B │ A │ N │ K │ J │ O │ B │ A │ **** │ I │ V │ F │ S │ O │ S │ T │ M │ R │ │ T │ L │ I │ T │ N │ U │ E │ N │ O │** │ X │ U │ U │ A │ E │ S │ D │ S │ Y │ │ E │ B │ A │ N │ K │ │ O │ B │ │ │ I │ V │ F │ S │ O │ │ │ │ │ │ T │ │ I │ T │ │ K │ │ │ O │ │ │ │ │ │ │ D │ N │ A │ E │ │ │ A │ │ │ D │ N │ S │ A │ R │ │ G │ E │ D │ X │ N │ O │ L │ E │ A │ **** │ S │ X │ S │ F │ X │ K │ A │ R │ O │ │ E │ H │ A │ O │ G │ D │ N │ A │ E │** │ R │ A │ A │ A │ D │ N │ S │ A │ R │ │ G │ E │ D │ X │ N ├────┤ L │ E ├────┘ │ S │ X │ S │ F │ X │ └────┴────┘ │ E ├────┤ A │ O ├────┘ └────┘ └────┴────┘
* * *
Concerning the grille cryptograms which follow, it seems not impossible that the student who has seen his principles applied only to a unit of 36 might find some difficulty in adjusting them to grilles of other sizes. A tip, then, on Example 22: Instead of the regulation nulls, its single unit was completed with a common Spanish phrase beginning with _Q_. And if it still resists: the author’s own name was used as the key for constructing the grille.
In adjusting his paper strips (when this is the method he prefers) it makes no particular difference what plan he follows, so long as it works. Some decryptors prefer to concentrate altogether on the strictly ascending series of cell-numbers, allowing letters to form their own sequences. Others will always have before them the set-up of squares, noting there some possible letter-sequence, finding (by means of their cell-numbers) the strips which contain these letters, and then observing results in other blocks. If the given strip cannot be found, then the cell must be already in use.
The shortest road is that of the probable word. For instance, the set-up shown as Fig. 26 was actually initiated by the solver at the letter _J_ of the second block, this being a rare letter and almost invariably followed by a vowel. Of the several vowels immediately in sight (in the square) the correct one was promptly suggested by the sequence so plainly in sight, _OB_, suggesting the word _JOB_, one already used by these people in discussing their mysterious activities. The corresponding cell-numbers, 20-29-30, were found to be on three separate strips — a necessary condition — and when placed together brought out the straight sequences _RID_ and _OLE_, with reversed sequences _AVE_, _NEU_, and _AND_. Another very probable word was suggested by the check-sequence _AVE_ (_HAVE_), and the necessary _H_ was found with cell-number 33, bringing solution to the point suggested roughly in Fig. 27, where attention was promptly focussed on the tetragram _RIDG_, suggesting _BRIDGE_, another word previously used. There were two strips carrying the desired _E_, but both refused to fit; and here the cell-numbers came into play. The last one found, 33, was large and suggested that its letter, _G_, might be the last letter of a unit; afterward, the building was continued on the left, with _B_.
Figure 27
Straight Reversed
20 29 30 33 17 8 7 4
R I D G E V A H (Have) J O B A U E N O (one u) O L E A D N A E (e and)
22. By PICCOLA. (Probable word: CRYPTOGRAMS).
T S T H E T T U S H O E D G F R D O E O G R I S A A M S N M Q E U G I B R I E L N O S T H S I C L S E T S W A T H A B R Y P A E.
23. By DAMONOMAD and POPPY. (Probable word: RIGHT FLANK).
A E K D S P V T O O N N A A O N R O N P R O C T I E H T R E H N E T I A F G S R H T N I L O V T E F F A L M K I E C L A A S N M.
24. By DAMONOMAD and POPPY. (Probable word: SPECIAL MESSENGER).
E Y U I S S N S F P A O P E R I S C O A M N R A I R G A A T A L I M N E G E E I S O S N O S A D N B E I T N O N G U E P R H T E E W S R U A S S K V Y P I T O N O U E Y S O C M W O T N S T E U O B D G.
25. By SAHIB.
R N I I I N G T F L A I L N N D E E T D R V E U S E S T H R E I G E Y F I A N O U R R D L G Y T N H A E O N R N E K C D E E I S E Y B S E F W Y P G R L O L O E U O F H P A T V E R E H E R A E D G M I T R H N E E I S Y T Q T S I I S A U S G I E A I C A S L L K L L T T X H V H E A R X A X.
26. By NEMO.
I K O T H N N E H N E E I R C R A G E L O R N O H K T W T C H O H E I E S S W W T N E T R H A R E O L S P L A A G E A E R L D B R Y E U I T R T R E N I D T H E I A D E I E N D P D A B R A E C R K E M T A O A U T O T S Y N B P E S N U H E S R A H E S U P D.
27. By DAN SURR.
O L T L A L I G E R T I V H E L L E R K I E A E I J F E I Y Y O O U U S T H E A V A S G Y A S A W C K E P L U E Z T I Z O S I T.
28. By PICCOLA. (This is not a grille. It's a serious matter!)
H S O E S N P T A E T O H I S T W L E D T T F A I B T Y U Y O T C E O I I T R C Y S B T R A H B T E I D O U S C I U O K R O Q N.