QUITE a lot more might be said about magic squares as adapted to ciphers in addition to the observations already made in the preceding issues. And several very interesting letters on the subject have been received from the fans.
We shall close the present discussion of them, however, with a few words about the "knight's tour," last week's Cipher No. 169 and this week's cipher by E. J. Frankenfield having made use of this principle.
The knight's tour is a diversion known to most chess players, and, no doubt, to many cipher fans also. The problem is based on the move of the knight in the game of chess, being any series of proper moves of this piece by which it can be made to occupy successively all sixty-four squares of the chessboard, without touching any square more than once.
The knight's move may be described as being from any corner square in any rectangle of two by three squares on the chessboard, to the square in the diagonally opposite corner of that rectangle. A large number of different "tours" are possible, and the principle may also be applied to squares of other sizes than the regulation chessboard.
Thus, Cipher No. 169 used the subjoined square of twenty-five numbers, the message being: "The construction of magic squares is an ancient amusement, having been practiced in India even before the Christian era."
To decipher this message, arrange the cipher in squares of twenty-five letters each, and trace the path of the knight in each square from one letter to another in the order indicated by the numbers 1 to 25 in the key square. The first of these squares for the above message is given herewith:
23 18 11 6 25 S M C N U 10 5 24 17 12 U O Q F T 19 22 13 4 7 A C I C S 14 9 2 21 16 O R H I O 1 20 15 8 3 T G N T E
To solve this cipher by the method suggested last week, transcribe the cryptogram in four lines of twenty-five letters each, forming twenty-five columns, and transpose the columns so as to develop the message in all four lines simultaneously. Once the order of transposition is known, the numerical key can be easily reconstructed.
The above magic square, aside from illustrating the knight's tour, is also numerically magic in that the sum of any pair of numbers opposite to and at the same distance from the central number is equal to twenty-six, or twice the central number.
Any magic square can, of course, be varied by rotation or reversal. And many combinations are thus possible in a given message, even with only a single key square. Lack of space forbids going into details of all these variations, but the reader can easily figure them out for himself.
Turning now to Mr. Frankenfield's cipher, you will find your magic square already set up for you. To decipher the message, begin at any desired point and follow the trail of the knight.
Bear in mind that as many as eight different moves from a given letter are possible, and that a false turn will throw you off the scent! Once you get started, however, the going should be easy. It would be difficult to imagine a more delightful transposition puzzle than this. And you are bound to be the loser if you don't try to solve it!
Here is the answer to Arthur Bellamy's crypt No. 167, of last week: "Antidisestablishmentarianistically speaking, whatever was good enough for our fathers should be good enough for us."
We have a hunch that Mr. Bellamy smuggled in a few extra prefixes and suffixes in his long work. Which gives us no particular ground for objection, however, seeing that these very same appendages offer such ready clews to solution.
In fact, just about the first thing the solver would notice in this crypt would be the termination -YNNS ALLY. After this, GOOD. FOR and OUR, US SHOULD, and so on. would follow in kaleidoscopic rapidity. Which is to say that solving time would be about ten to fifteen minutes. How long did it take you?
Last week's No. 168, by Robert Spencer, was a simple substitution cipher with a word spacer, using threeletter symbols to represent characters in the subjoined key. The letters U— upper, M—middle, and B—bottom, were used to indicate the rows of the key. Similarly, L—left, C—center, and R—right, were used for the columns ; and F—first, S—second, and T—third, for the place of the letter in the group.
ABC DEF GHI JKL MNO PQR STU VWX YZ-
In this system the cipher group ULT, for example, signifies upper row, left column, third letter, or C; and so on. Message in full: "Come to the old mill at nine to-night. Bill." Upon determining from frequency that BRT— used eight times—was probably a word spacer, the cipher would, of course, yield to simple substitution methods.
In this week's No. 170 you are offered another crypt, or simple substitution cipher. In this type of cipher a given letter of the alphabet is fixedly represented in cipher by the same letter; and vice versa.
We'll leave you to discover for yourself the secret of No. 171, by Edward Peatross. Suffice it to say that the cipher is neat. And that we think it will give you a busy fifteen minutes or so. The answers to all of these, including No. 172, will be published next week.
CIPHER No. 170.
KLNRCENT CVVY XGMCCWIR. NEI- TEDP WDM KVB, SEPM RMYEGEZ. GAWCM GEYDAXVR TIVVUMT FMEDMJLCCZ.
CIPHER No. 171, by Edward Peatross, Cincinnati, Ohio.
63, 11. 31, 53, 11. 34, 11, 22, 43, 24. 71, 53, 31, 22, 41, 11, 12. 42, 11, 11, 71. 42, 11. 31, 71. 13, 54, 72, 53, 71. 31, 43, 12. 51, 41, 72, 42. 74, 71, S3, 11, 11, 71. 71, 63, 54. 71, 21, 22, 53, 71, 61. 51, 11, 71, 11.
CIPHER No. 172, by E. J. Frankenfield, Fosteria, Ohio.
H S V A L I T T K T O N O N D M N E U E L H E E M S O B E H E T O S M R N I I S E I F I A S O R I D F S W H C S A R S I K M A T