Catalog of repeating fragments

=Introduction= Here we attempt to exhaustively list out all repeating fragments of the 340 and 408 cipher texts. A fragment is a repeating sequence of more than one cipher symbol. Non-repeating symbols might be included in the fragment. These non-repeating positions are represented by a question mark wildcard character.

The results are grouped by the number of wildcards that appear in the fragment. In each group, the results are shown in descending order of significance, where significance is considered to be a combination of the number of fragment repetitions, and the "rarity" of the symbols involved.

The sortable tables have the following headings:


 * Pattern: This is the fragment template that repeats in the cipher text.
 * Positions: The list of all positions in which each fragment occurs.  Cipher text positions start at 0.
 * Fragments: The list of all fragment occurrences for this fragment template.
 * Order: The number of non-wildcard symbols in the fragment template.
 * Reps: The number of fragment occurrences
 * Probability: An estimate of probability, used to compare one pattern to another.  A pattern with lower probability implies one or both of the following:
 * The pattern contains symbols that are not used as often.
 * The pattern has more appearances in the cipher text.

Here is an example of the probability calculation for the three occurrences of the fragment "G2" in the 340 cipher:

The symbol G appears six times in the cipher text. The symbol 2 appears nine times in the cipher text.

Consider a six-position string that can hold "G2G2G2". The chance of selecting the first G is 6/340. The chance of selecting the first 2 is 9/339. The chance of selecting the second G is 5/338. The chance of selecting the second 2 is 8/337. The chance of selecting the third G is 4/336. The chance of selecting the third 2 is 7/335. Thus the total probability is 6/340 * 9/339 * 5/338 * 8/337 * 4/336 * 7/335 = 4.09 x 10^-11.

= Repeating fragments of the 408 cipher =

Wildcard length: 12
= Repeating fragments of the 340 cipher =

Wildcard length: 12
= Comments =

Results for wildcard lengths greater than 12 are not included. It is not clear if they would be useful.

Here is the fragment of the 408 that produced the lowest probability:

O??????????????9????????????????????????)?????????????????????Z????p????????+???????????????????????????????????P#B???????????c	

Its probability is: 1.55E-34.

Here is what the fragment looks like along with the cipher text and corresponding segments of the known solution:

Pattern: O?????????????? 9????????????????????????)????????????????????? Z???? p???????? +??????????????????????????????????? P#B??????????? c	 Cipher:  OR=pX=BWV+eGYF6 9HP@K!qYeMJY^UIk7qTtNQYD5)S(/9#BPORAU%fRlqEk^LM ZJdr\ pFHVWe8Y@ +qGD9KI)6qX85zS(RNtIYElO8qGBTQS#BLd/ P#B<font style="color: #aaa">@XqEHMU^RRk c </tt> Solution: N<font style="color: #aaa">GPEOPLEBECAUSE I<font style="color: #aaa">TISSOMUCHFUNITISMOREFUNTHANKILLINGWILDGAMEINTH E<font style="color: #aaa">FORR E<font style="color: #aaa">STBECAUS E<font style="color: #aaa">MANISTHEMOATDANGERTUEANAMALOFALLTOK ILL<font style="color: #aaa">SOMETHINGGI V</tt> Cipher:  O<font style="color: #aaa">VWI5+tL)l^R6HI 9<font style="color: #aaa">DR_TYr\de/@XJQAP5M8RUt%L)NVEKH=GrI!Jk598LMlNA) Z<font style="color: #aaa">(PzU p<font style="color: #aaa">kA9#BVW\ +<font style="color: #aaa">VTtOP^=SrlfUe67DzG%%IMNk)ScE/9%%ZfA P#B<font style="color: #aaa">VpeXqWq_F#8 c</tt> Solution: N<font style="color: #aaa">BETTERTHANGETT I<font style="color: #aaa">NGYOURROCKSOFFWITHAGIRLTHEBESTPARTOFITIATHAEWH E<font style="color: #aaa">NIDI E<font style="color: #aaa">IWILLBER E<font style="color: #aaa">BORNINPARADICESNDALLTHEIHAVEKILLEDW ILL<font style="color: #aaa">BECOMEMYSLA V</tt>

Here is the fragment of the 340 that produced the lowest probability:

R????????????????+????????????????????????(??????????????????+???????+???????P????/????F????????????????????????????|</tt>

Its probability is: 2.85E-29.