CONTINUING last week's discussion of magic squares, Cipher No. 166, by Raymond L. Heitlinger, used the subjoined nine by nine de la Loubère square as key. To decipher this cryptogram, first transcribe it by successive horizontals, left to right, counting spaces in the cryptogram as blanks in the magic square, as shown herewith:
|
47 H |
58 N |
69 S |
80 - |
1 T |
12 H |
23 A |
34 Y |
45 S |
|
57 I |
68 E |
79 - |
9 C |
11 P |
22 W |
33 B |
44 B |
46 T |
|
67 H |
78 - |
8 F |
10 I |
21 G |
32 D |
43 A |
54 D |
56 E |
|
77 - |
7 O |
18 T |
20 N |
31 E |
42 T |
53 O |
55 B |
66 T |
|
6 T |
17 I |
19 I |
30 S |
41 R |
52 H |
63 M |
65 D |
76 - |
|
16 R |
27 E |
29 U |
40 A |
51 T |
62 R |
64 E |
75 E |
5 R |
|
26 V |
28 N |
39 P |
50 E |
61 E |
72 T |
74 L |
4 A |
15 W |
|
36 H |
38 S |
49 M |
60 T |
71 Y |
73 A |
3 E |
14 R |
25 E |
|
37 E |
48 E |
59 G |
70 C |
81 - |
2 H |
13 E |
24 S |
35 T |
Then take the letters in the order indicated by the numbers, and you will get the message: "The art of cipher writing was even used by the Spartans, the method being termed the Scytale." The blank spaces in this square could have been filled with nulls if desired.
The de la Loubère method applies only to odd magic squares, and any such square can easily be constructed by observing the following rule: start with the middle space of the top line as 1, and number the spaces serially along the diagonal sloping upward and to the right; when a number falls outside the square, place it in the corresponding space on the opposite side of the square; when an occupied square is reached, place the number in the space next below instead.
It is thus evident that the de la Loubère formula could easily be used in enciphering or deciphering a message without reference to the magic square itself, by merely memorizing the "path" peculiar to this square. But this very fact also works against the system, since it could also be readily deciphered without the key by merely inspecting the diagonals, once the cryptogram had been arranged in one or more squares of the proper dimensions.
Of course, any other type of magic square of the desired size could be selected as key to a cipher system, and there are plenty of them to choose from. There are only eight different 3 x 3 squares, and seven thousand and forty of the 4 x 4 size, to be sure; but the larger squares more than make up this deficiency. The number of 5 x 5 squares alone is said to be in excess of seven hundred and fifty thousand.
Regardless of the structure or size of the square, however, one or more messages representing several similar applications of the same square are always liable to decipherment by the multiple anagram method. This method was last described in the December 3, 1927, issue of this magazine, and is applicable to many types of transposition ciphers.
Cipher No. 169 in this issue, for example, will afford the reader another opportunity to use it. After translating this, and determining the order of transposition, try to reconstruct the key square. This latter is of a different type than any we have yet described. A constant total exists between certain numbers, but not in the rows, columns, and diagonals, as in the above square. Can you solve the mystery?
Last week's simple substitution cipher. No. 164, conveyed the message: "Time will bring to light whatever is hidden; it will cover up and conceal what is now shining in splendor." This cipher offered a number of clews. Probably the most obvious was in the two-letter words, one of which, PV—IN was repeated in YBPVPVN—SHINING. Once a few letters in this type of cipher are determined, the rest is easy.
In last week's price mark cipher. No. 165, the selling priee was enciphered in a null-transposition system, and the cost price in an arithmetical substitution system. To decipher the selling prices, disregard the first and last figures of each group, and reverse the rest. The group 18923, for example, would thus become $2.98; and so on.
To decipher the cost prices, add the first figure in any group to the remaining figures of that group, disregarding the tens figures resulting from such additions. In this manner 3827 would become $1.50; and so on. Ciphers of this kind can be solved by inspection with little difficulty.
This week's opener. No. 167, by Arthur Bellamy, puts our own twenty-seven-letter "jawbreaker" of March 3 to rout. Somehow Mr. Bellamy has managed to recruit a word of thirty-four-letter dimensions. This is a straight substitution cipher. Try to solve it, and send in your own jawbreaker crypts for the fans to puzzle over. They're great sport!
In No. 168, by Robert Spencer, you have another straight substitution cipher. After you have deciphered the message, try to determine the key and the method of using it. You'll find this a fascinating task, and well worth your while. Answers to this week's ciphers will appear next week.
CIPHER No. 167, by Arthur Bellamy, Boston, Massachusetts.
YIMFUFACAMYDNFARVCIMYOFYI- FAMFLYNNS AWCYXFIE TRYMCK- CO TYA EPPU CIPHER GPO PHO GYMRCOA ARPHNU DC EPPU CI- PHER GPO HA.
CIPHER No. 168, by Robert Spencer. Seattle, Washington
ULT—MCT—MCF—UCS—BRT—BLS— MCT—BRT—BLS—URS—UCS—BRT— MCT—MLT—UCF—BRT—MCF—URT— MLT—MLT—BRT—ULF—BLS—BRT— MCS—URT—MCS—UCS—BRT—BLS— MCT—MCS—URT—URF—URS—BLS— BRT—ULS—URT—MLT—MLT.
CIPHER No. 169.
SMCNU UOQFT ACICS ORHIO TGNTE NUCSH NITMI SEESA NARMA AETNE DDRBA PGIEA INCNE TNVIC ENIEI ESTEA EBRIH TNENF CRVAR EIHOE
Fans who have been asking for solvers' lists will be interested to look over the following list of solutions submitted to Ciphers Nos. 111 to 130, inclusive. Arthur Bellamy heads the list with the largest number of answers, and Cipher No. 122, by L. A. Harper, brought forth the largest number of solutions. No answers were received to Nos. 111, 112, 120, 123, 126, 128, and 130.
A goodly number of solutions have already been received for our next solvers' list to be published in a few weeks. Keep them coming, fans! Let's make it a whopper while we're at it! Send in that new cipher, too! Let the fans have a look at your problem through the pages of this department every week.