HORTLY after the middle of the nineteenth century the peculiar behavior of a class of students of a certain European nation's higher educational institutions began to excite general curiosity and attention.
These young men and women made no attempt to disguise their contempt for the existing order of things. They became their own criterion, and shaking off the shackles of public opinion, took pleasure in shocking those who still felt the influence of what they termed antiquated prejudices.
Claiming that virtue was found in utility, these young people placed the work of a good carpenter or shoemaker above that of a Rembrandt or Shakespeare, holding that humanity had a greater need for houses and shoes than for art or literature.
As an emblem of their utter disregard for the traditional, these young men and women refused to be governed by custom even in their external appearance.
The male students allowed their hair to grow long, while the females trimmed theirs short. They preferred to wear slovenly attire, sometimes rounding out their queer guise with a pair of blue spectacles.
If questioned about these things they would reply that they were fully occupied with the theory of reorganizing society on a scientific basis, and that being thus absorbed in affairs of genuine importance they had no time to waste on trivialities.
Denied the possibility of spreading their revolutionary doctrines in the open, this organization cleverly disseminated them disguised as fiction through the press. The public soon learned to read between the lines, and its teachings spread like wildfire.
One of the greatest instruments in popularizing the movement was a book written in this manner in prison by an academical leader of the movement, and published with the government's sanction.
In one of his novels Turgueniev applied the term Nihilism—from the Latin nihil, nothing—to the tenets of this society. And from this, much 'to their displeasure, its members came to be known as Nihilists.
By the winter of 1861-1862 this movement, in which the Nihilists of Russia have probably been recognized by now, had spread to people of all ages, classes, and professions. And its revolutionary ideas came to be openly expressed in the streets.
Originally Nihilism was a philosophical or literary movement, rather than revolutionary. But now its former academical nature gradually took on the aspect of terrorism, aiming at the assassination of prominent officials, and even at that of Alexander 11, the Czar himself, in the effort to force concessions from the government.
A number of attempts were actually made to kill the Czar, but somehow he seemed to bear a charmed life, escaping unharmed time and again.
In April, 1879, five shots were fired at him while walking round the crescent-shaped space facing the Winter Palace. The would-be assassin in this instance had become skillful by practice in the use of his own weapon, but through accident at the last moment had to use one with which he was not familiar. All of the shots went wild. And the terrorist was apprehended later and hanged in St. Petersburg, now Leningrad.
In the summer of this same year a number of mines were laid in anticipation of the Czar's return from the Crimea, one being on a railway embankment near Alexandrovsk, where an ordinary shock would have sent the train into a deep ravine. The mine failed to explode at the critical moment, and the Czar only learned of his danger long afterward.
A few months later an attempt to blow up the imperial yacht with the Czar on board was frustrated by an unexpected visit of the police to the house where the battery and wire leading to the mine were located. The plotters were arrested and hanged.
In February of the following year dynamite was placed beneath the dining hall at the Winter Palace. The explosion was terrific, occurring as scheduled, and killing ten men and wounding over fifty others. The Czar had delayed his entrance to the hall, escaping without a scratch.
In the meantime a new and formidable organization, the People's Will , had come into existence, worked by conspirators unknown to each other, directed by leaders having the power to punish disobedience with death, and determined to carry out the sentence previously passed on the Czar by the executive committee.
Preparations to this end were completed early in 1881. and this time, thanks to their thoroughness, the terrorists were successful. Alexander II was assassinated on March 13, 1881. Some of the details of this plot are given further on, and the assassination itself has been made the subject of one of the accompanying ciphers.
The government now took rigorous measures to suppress the movement. In a period of several years thousands of Nihilists were apprehended and tried. Many of these were meted out minor punishments. Some were sentenced to penal servitude. A number were put to death, and many were exiled.
In a movement of this kind, where it would often be necessary for conspirators to communicate secretly with each other, it would be very strange if no need had been felt for ciphers.
And in this connection a number of ciphers are attributed to the Nihilists. Several methods of using the checkerboard key have already been described in FLYNN'S for March 28, 1925. And a method of solving the numerical cipher with keyword has been given in the June 27 issue.
Another of these Nihilist ciphers is a transposition cipher described below, together with a method of solving it, and used for enciphering the first two ciphers in this issue.
The cipher in question is one in which the letters of the message are written into squares, the location of any letter in its square being determined by key numbers, derived from a key word agreed upon by the corresponding parties.
To explain the cipher, the message— POLICE HAVE LEARNED OF THE PLOT TO BLOW UP THE IMPERIAL YACHT—will now be enciphered with the key word ONEGA.
The word key must first be transformed into a numerical key, done by numbering its letters serially from 1 up, according to their alphabetical order, repeated letters, if any, being numbered from left to right.
The key may be a word or phrase of any length, take ST. PETERSBURG for example, which will also illustrate the method of numbering repeated letters:
S T P E T E R S B U R G 8-10-5-2-11-3-6-9-1-12-7-4
In this way ONEGA provides the numerical key 5-4-2-3-1.
This numerical key is now written across the top and down the side of the intended square or squares, which may for convenience be ruled into the requisite number of smaller squares.
In placing the letters in the squares, the horizontal rows are completed in the order indicated by the key numbers at the side, the order of the letters in each row being similarly determined by the key numbers at the top.
Thus P, the first letter of the message, will be placed at the intersection of row 1, and column 1. The second letter of the message, O, is placed at the intersection of row 1 and column 2. This is continued until row number 1 is completed, when row number 2 is similarly dealt with, and after it the other rows of the square, likewise in numerical order as indicated by the key, until the whole square has been completed.
Additional squares, as required by the length of the message, are filled in exactly the same way. In case there are not enough letters in a message to complete the last square, all unoccupied spaces must be filled with non-significant letters.
From this it will be observed that the letters in every row of each square are transposed in the same way, which fact is used later in effecting the solution of the cipher without the key.
The present message requires two squares of the size indicated by the key:
5 4 2 3 1 5 4 2 3 1 5 O L E P H 5 T H A C Y 4 T F D O E 4 L A R I E 2 E V H A E 2 T P W U O 3 N R E A L 3 P M E I H 1 C I O L P 1 L B T O T
The letters are next taken out of the squares, ordinarily by straight horizontals, and preferably in groups of five, completing the encipherment:
OLEPH TFDOE EVHAE NREAL CIOLP THACY LARIE TPWUO PMEIH LBTOT
At this last step, a variation may be introduced if desired. Thus , the letters can be taken out by verticals—OTENC LFVRI et cetera, by diagonals—OTLEF ENVDP et cetera, or in any other way agreed upon.
When deciphering with the key, the letters of the cryptogram are written back into squares of the size indicated by the key, in the same order—by horizontals or otherwise—as they were taken out. The rows and columns are next assigned their key numbers, and the letters are read individually out of the squares in the same order as they were originally placed in them, being thus restored to the normal order as they occurred in the message.
Decipherment without the key may be effected by considering (1) the size of the squares necessitated by the length of the cryptogram, (2) proportions of vowels and consonants, and (3) letter sequences. For example, the above illustrative cryptogram of fifty letters has evidently been enciphered in a 5 x 5 square used twice.
In other cases there might often be more than a single such possibility. A cryptogram of one hundred letters, for instance, could have been enciphered with a 5 x 5 square used four times, or a 10 x 10 square used once. And a one-hundred-and-forty-four-letter cryptogram could have been done in a 12 X 12 square used once, a 6 x 6 four times, a 4 x 4 nine times, not to mention a 2 X 2.
Where there is thus more than a single possibility, the square actually used may be often learned by making a count of the vowels in the various sections of the cryptogram as divided by the different squares.
The following vowel frequencies per ten thousand letters, taken from the table in FLYNN'S for January 23, show that the vowels comprise approximately forty per cent of all letters in straight English text.
A 806 E 1231 I 683 O 800 U 277 ——— 3810=38.2%
Consequently, in a transposition cipher, where the letters retain their original powers, by actual count the vowels should approximate forty per cent of the whole number of letters. And in the present kind of transposition, cipher, about forty per cent of the letters in each of the several squares should be vowels.
The vowel counts in this case are 11 and 9 vowels respectively in the two squares, or very nearly forty per cent of 25, the total number of letters in each square. In those cases where more than one square is possible by factoring, that square showing by the above test the least deviation from the forty per cent average is the most probable.
Having decided on the size of the square, if the plan followed in taking out the letters is known, the letters of the cryptogram may be written back into the squares in that order at once.
But if this is unknown, the letters may be filled in by horizontals, verticals, diagonals, et cetera, until that arrangement is found where the number of vowels in every row of each square equals approximately forty per cent of all the letters per row.
In this instance, when the squares are formed by straight horizontals, as shown below, every row will contain one, two, or three vowels, there being no excess of vowels or consonants in any row.
1 2 3 4 3 vowels O L E P H 2 T F D O E 2 E V H A E 3 N R E A L 3 C I O L P 3 T H A C Y 1 L A R I E 3 T P W U O 2 P M E I H 2 L B T O T 1
Assuming now that the correct arrangement has been reached in the squares, since the letters in each row are similarly transposed it is now only necessary to rearrange the columns to develop the words in each row.
This is most readily accomplished by carefully copying the letters in the several columns upon as many slips of paper, five in this instance. These slips can now be tried in various combinations, to secure probable sequences of letters in every row.
To start, some of the most frequently used digraphs—TH, HE, ER, IN, AN, ON, et cetera—may be tried.
Slips 1-2 give TH in the first row of the second square. But most of the other sequences thus formed are unfavorable, consonant-consonant sequences predominating.
Slips 5-3, as shown below, give HE in both square 7 row 7, and square 2, row 4. And, besides, all of the other digraphs so formed are very probable, vowel-consonant and consonant-vowel sequences predominating.
Other slips may now be tried before or after the 5-3 combination to form probable sequences of three letters. One by one these various three slip combinations may be eliminated, either because they refuse to be developed into longer sequences, words, or parts of words, by means of additional slips, or because some of the three letter sequences themselves are improbable or impossible.
This process is continued until all of the slips have been used. The several combinations, showing how the present message would be gradually developed, are subjoined.
5-3 5-3-4 5-3-4-2 5-3-4-2-1 H E H E P H E P L H E P L O 1 E D E D O E D Q F E D O F T 2 E H E H A E H A V E H A V E 3 L E L E A L E A R L E A R N 4 P O P O L P 0 L I F O L I C 5 Y A Y A C Y A C H Y A C H T 1 E R E R I E R I A E R I A L 2 O W O W U 0 W U P O W U P T 3 H E H E I H E I M H E I M P 4 T T T T O T T O B T T O B L 5
The arrangement 5-3-4-2-1 has restored the letters in each row to their original order. And the message can now be read from the slips if the rows of each square are also taken in this same order.
It will be noted that the order of the slips, 5-3-4-2-1, is not identical with the numerical key, 5-4-2-3-1. But the original key can ordinarily be found, if desired, by examining the order of the letters in any row of the squares from which the slips were prepared.
However, even with the original numerical key, it will not always be possible to determine the word key, for the reason that the same numerical key can often be had from different words. Thus SMILE, TREND, and WRING, are three other words that will give the same numerical key as ONEGA.
To afford the reader an opportunity to try his hand at this transposition cipher of the Nihilists, two cryptograms are offered.
The first of these tells briefly how Alexander II was assassinated.
The Czar was to attend a review dinner on March 13, 1881. On his return to the palace he had choice of three routes. One of these was over the Stone Bridge, another by way of Little Garden Street, and the third along the Catherine Canal.
The bridge and the street had been mined. And six conspirators with bombs were in waiting by the canal.
The route by which the Czar returned, and some of the details of the assassination are told in the first cipher. Incidentally, the key word used for this cryptogram is a proper name you will find in the message.
The second cipher is a portion of a letter written by a Nihilist exiled to the mines at Karà.
This excerpt, brief as it is, may serve to give some idea of the terrible sufferings endured by those in exile; a fate comparable to a living death, than which, indeed, many would have chosen death itself!
CIPHER No. 1 (Nihilist transposition).
NWEYR ODYAB FLVBA AGYNI WAHHE TTICR EANAE VHGGE ISTNH REATT TERSU BGDAM TADEM HCWAL ERNEH AETRH IFBET SFOAR NEHID HCKEY WOGAA UMONN CAAIE KREGR IDNIA NBNMU GENOA DTNMI REEOS FSRKC CAOGN TBSWE YDUAN LNIAE ONWDG UAENH RSDSA TAAHR TUEDS ESCBH OTDST TEHAI KTYWL SLIKE NBDMO RBHTO OSMII SLNES HF.
CIPHER No. 2 (Nihilist transposition).
PMATS OGMDO LADCB ABLKC NADEA NIRNA OCITF FDANU SPOIE LEVWN TBUET ETDNE IWELU INLAT TRTHA EYHNS ATDTE YBANO HNEER OCHGE FBNIO BIALE VTDSE TNAKP YNLEK OEHLF POGNE THISY SFSOU MDSTA RUOEE TRESO OORTU HNEMN EOECM DAARD NENOT HESER EBLOT A.
Of the many ciphers discussed in this department, probably none has aroused any greater enthusiasm than the Nihilist numerical cipher in FLYNN'S for March 28, 1925.
Fans from everywhere took great pleasure in submitting Nihilist ciphers for solution, using their own keys, and in many instances adding interesting and original variations of their own. And now that the Nihilist transposition cipher has been treated in this issue, there could hardly be a time more appropriate than this to place some of these interesting ciphers before our readers.
For the benefit of those who have not the original article on this cipher at hand, a brief example, enciphering the message— LEAVE NOW--with the key—TRY—is subjoined.
1 2 3 4 5
1 A B C D E
2 F G H IJ K
3 L M N O P
4 Q R S T U
5 V W X Y Z
Message: L E A V E N O W
31 15 11 51 15 33 34 52
Key: T r y T r y T r
44 42 54 44 42 54 44 42
—— —— —— —— —— —— —— ——
Cipher: 73——57——65——95——57——87——78——04
The first of these ciphers, which has traveled across the Pacific to reach these pages, combines a rearrangement of the Nihilist checkerboard with the use of private code syllables.
DEAR SIRS :
I recently came across a copy of FLYNN'S containing an Interesting article entitled "Solving Cipher Secrets."
In an idle moment I put together the following code words, made up from the alphabet in squares, and using our own private code letters to express the numbers.
Of course there is nothing about the production, particularly, but it might amuse some one to find the solution.
T. E. CLAYTON ,
T. E. Clayton & Co.
Christchurch, New Zealand.
CIPHER No. 3 (T. E. Clayton).
NIDOJELELI MIHETELITA VEBOBINIBO TEBIBOFONI
Mr. Clayton's message is short, yet ample to afford the solution to properly applied effort. Can you get it?
The next cipher is straight Nihilist, but so written as to circumvent solution by the special method given in the June 27, 1925, issue of FLYNN'S.
Let Mr. Cain himself tell you about it.
DEAR SIR:
The Nihilist code can be used to advantage if the proper key word is used. I have interested several of my friends in FLYNN'S , and taught them the method of solving this cipher.
This bit of a teaser—Cipher No. 4—has them puzzled, and they, as well as myself, would like to have you try your hand at it.
If you have space in your department I would like to have it submitted to the multitude of cipher sharks to lose some sleep over.
Syracuse, N. Y.
JAMES R. CAIN.
CIPHER No. 4 (James R. Cain).
58-57-60-29-28-38-49-38-30-56-27-50-36-38- 29-48-48-48-58-26-29-46-39-58-28-30-36-29- 26-58-26-60-59-58-57-68-59-48-59-38-46-58- 37-30-69-57-60-27-27-30-30-28-58-38-46-50- 46-29-28-48-28-30-58-27-26-59-57-30-47-48- 57-29-26-46-60-47-29-20-56-58-59-37-26-47- 27-49-47-49-46-38-27-26-59-29-29-48-47-30- 58.
In No. 5, Frank Spalding, of far-off Wrangell, Alaska, offers a slogan for Solving Cipher Secrets department. Mr. Spalding owns two of the best bear dogs in all Alaska, and takes great delight in making life a burden to the great North American grizzly.
Here is his cipher, the shortest of its kind submitted to this department. What is the slogan?
CIPHER No, 5 (Frank Spalding).
85-60-67-54-84-60-59-75
J. Levine, of Los Angeles, California, writes this about No. 6: "Here is a Nihilist cipher that will tax your skill to the utmost."
The difficulty here is in the length of the key. How long this is you can find by solving the cipher. Or, failing in this, look for the solution in the next cipher article.
CIPHER No. 6 (J. Levine).
55-66-26-35-46-57-47-53-64-65-85-87-46-26- 24-66-59-37-67-54-30-66-66-67-38-59-36-98- 47-58-43-58-74-77-44-44-26-57-49-55-57-66- 26-76-46-77-67-64-59-65-55-67-45-54-88-46- 30-57-30-97-67-45-35-57-39-55-86-30-74-65
One step in enciphering with the Nihilist numerical cipher is the addition of the numerical substitutes for the letters of the message and of the key word.
In the following cipher, submitted jointly by Benjamin Miller and Samuel M. Kurtz, New York City, a mathematical process other than addition has been employed.
Just what principle has been used is left for you to discover. For the present it must suffice to say that very likely it is something you have never thought of, and, further, that it is distinctly different from anything that has yet appeared in these pages.
The original of this cipher was continuously written. The grouping by sixes here is for convenience.
CIPHER No. 7 (Benjamin Miller—Samuel M. Kurtz),
126413 085015 019062 011333 114740 149065 083725 169194 088789 085442 113462 169194 148614 029267 144220 085015 074669 117557 125846 114740 143984 148840 148614 114740 146326 146326 126130 013976 146787 163315 146787 144456 149065 169378 0S8789 146557 027763 147018 083725 169010 0887S9 125846 084157 141828 08501S 120597 116627 167523 148614 114740 143746 117248 013103 074669 027267 142311 143984 148840 151293 114740 036464 146787 143746 167710 113462 012222 041211 163120 027763 119695 043178 149065 043178 085015 074669 027763 04317S 123256 011333 076547
All right, fans, there's the lot! Give them a thoughtful trial, and send in your solutions!
The answers to all seven will be given in next Solving Cipher Secrets in FLYNN'S for April 24.
Probably the shortest route to the solution of the first of the Confederacy ciphers in FLYNN'S for February 20 would be to assume the value WHICH for the cipher group KTMTL, thus discovering five letters —OMERE— of the key. You will note that WHICH is on the word frequency table in FLYNN'S for May 16 , 1925.
The application of this much of the key to other parts of the cryptogram would unlock generous chunks of the message, capable of further development by the method described for this cipher.
The second of the Confederacy ciphers, with its many short words, should have fallen an easy victim to your wiles. Here follows the keys and solutions to these two.
CIPHER No 1. Key: COME RETRIBUTION. Message: I recommend that the REMOVAL OF PUBLIC PROPERTY, MACHINERY, STORES and ARCHIVES WHICH are not of immediate necessity BE COMMENCED. ALL POWDER should be SECURED.
CIPHER No. 2. Key: COMPLETE VICTORY. Message: THE PRESIDENT DEEMS IT ADVISABLE THAT YOU SHOULD BE CHARGED WITH THE MILITARY OPERATIONS ON BOTH BANKS OF THE MISS. AND THAT YOU SHOULD ENDEAVOR AS PROMPTLY AS POSSIBLE TO CROSS THAT RIVER WITH AS LARGE A FORCE AS MAY BE PRUDENTLY WITHDRAWN FROM YOUR PRESENT DEPT. YOU WILL ACCORDINGLY EXTEND YOUR COMMAND TO THE EAST BANK OF THE MISS. AND MAKE ARRANGEMENTS TO BRING TO THIS SIDE SUCH OF YOUR PRESENT FORCES AS YOU MAY DEEM BEST
Of the four three-letter groups in cipher No. 3, two represent words given in the word frequency table just mentioned:
Message: has and Cipher: MLQ NFI Key: FLY NSF
The key word FLYNN'S is plainly suggested here, and being tried, it works!
CIPHER No 3 (F. B. Willits-Arthur J. Lindsay). Key: FLYNN'S. Message; FLYNN'S HAS BEEN STOWED IN OUR PACKS AS RELIGIOUSLY AS OUR PIPES AND TOBACCO.
Cipher No. 4, modified Vigenère, when solved by the usual methods gives the keyword POF. Of course, this might be FOP written backward. But you will note that by substituting for each of these letters that next before it in the alphabet POF is transformed into ONE. And ONE as a key will give the cipher only when the bottom alphabet of the square is used as a message alphabet, instead of that at the top.
The first cipher group UZDCB'X (=FLYNN'S) IS the logical starting point in this instance.
CIPHER No. 4 (A. J. Simon). Key. ONE. Message: FLYNN'S IS ONE OF THE BEST WEEKLY MAGAZINES IN NEW YORK CITY.
No. 5 was a straight Vigenère using a key phrase. In solving any Vigenère cipher by the method described, especially one using a key phrase, it must be kept in mind that any short words found by applying other short words to the cipher, might belong either to the key or message.
For instance, AND tried with YBX near the middle of this cryptogram gives YOU as a result. Here both AND and YOU must be tried as parts of the key. To try AND alone would be to fail in the solution, since it is a part of the message and not the key.
CIPHER No. 5 (Ralph Raphael). Key: CAN YOU SOLVE ME? Message: When you have solved this secretive way of conveying a message, et cetera
In No. 6 (W. W. Reeves, F. P. E.) the Vigenère table was numbered from 1 to 26 across the top and bottom, and similarly down both sides, any letter being expressed as a fraction, the numerator of which indicated the column, and the denominator the row, occupied by that letter.
Thus
means the letter found in the intersection of the thirteenth column and the
eighth row, or T, and so on. Mr. Reeves's message being: " This is a code
designed on the Henry file."13 8
The curious part of this cipher, due to the peculiar construction of the Vigenère table and to the way Mr. Reeves has numbered it, is that the sum of the numerator and denominator of any fraction, less 26 if in excess of that number, will indicate the proper letter in the alphabet: Z-1 , A-2, B-3 . . . Y-26. The cipher is thus reducible to a simple substitution cipher, which can be used without the table.
The feature of Mr. Walker' s cipher (No. 7) aside from the fact that he used the bottom row for his message alphabet, also done in No. 4 above, is that his key was continuous and nonrepeating, the twenty-third Psalm having been used for this purpose.
Key: THELO RDISM YSHEP HERDI etc. Cipher: CPTBT LLNYN MLENB TJFNX etc. Message: IHOPE THEFA NSWIL LENJO etc.
Here is the whole message: " I hope the fans will enjoy this one. It is just difficult enough, without being a discouragement."
Cipher No. 5 (William E. Bowns) in the October 31 issue was done in Vigenère cipher, with the key word EVOLUTION. This cipher was published without any suggestion as to its type. The first solution was submitted by A. P. Schmutz, Philadelphia. G. A. Ferrell, Bessemer, Alabama, and Charles P. Winsor, Boston, Massachusetts, also submitted correct solutions.
Mr. Winsor discovered the key by trying THE, AND, and ARE with three-letter groups, finding the key thus:
Message: the the are the and Cipher: GLZ OVP UKM MPS NRY Key: NEV VOL UTI TIO NEV
Last, but by no means least, here is the explanation to cipher No. 3 (Hobart Hollis) of the January 23 issue. This cipher, to the first solver of which, as you may remember, Mr. Hollis offered ten dollars, may be deciphered as follows:
First, write out the cryptogram in lines of fifteen numbers each, forming fifteen columns of numbers. Then transpose these columns according to the numerical key:
1-2-15-3-4-14-5-6-13-7-8-12-9-10-11.
Now write the numbers 1, 2, 3 , 4, et cetera, under the groups, as shown below, continuing this as long as these numbers divide evenly without remainder into the cipher groups with which they are thus placed in conjunction, and as long as the quotients resulting from such divisions continue to represent letters from the subjoined alphabetical key which develop the message being deciphered.
A B C D E F G H I J K L M 13 12 11 10 9 8 7 6 5 4 3 2 1 N O P Q R S T U V W X Y Z 26 25 24 23 22 21 20 19 18 17 16 15 14
When this is no longer the case, begin again with 1, and continue as before, and as many times as may be necessary to decipher the. whole message.
Here is a part of the message so deciphered:
Cipher: 5 2 39 20 130 120 13 10 78 80 30 78 140 etc. Key: 1 2 3 4 5 6 1 2 3 4 5 6 7 etc. Quotients: 5 1 13 5 26 20 13 5 26 20 6 13 20 etc. Message: I M A I N T A I N T H A T etc.
The whole message is: "I MAINTAIN THAT YOU CANNOT SOLVE THIS CIPHER. IF YOU DO YOU WIN TEN DOLLARS AND PROVE ME WRONG!"
The list of any who may have been successful in solving this cipher will be published in the next issue of this department.
In the list of successful solvers of January 2 ciphers, Mr. Winsor rings the bell with correct solutions to all seven, including the troublesome but simple No. 5.
This list, while not large, is nevertheless gratifying in that it dearly demonstrates that we are not expecting the fans to do the impossible.
Send in your solutions, fans, any time before the answers have been published, and swell the list of solvers!