Experiment 52

“Ciphers that cannot write all 26 letters, or cannot write an odd number of them”

Experiments 15, 36 and 44 tested Hill ciphers. The other classic polygraphic systems, Playfair, two-square, four-square and bifid, work on a 5 by 5 square of 25 letters, and the Berlin World Clock reading of the clock clue suggests a 24-letter ring. Such systems leave a fingerprint in the ciphertext itself: a letter that never appears, or an even length. This checks the fingerprint before any key search.

revertedstatus
experiment 15parents
0 stime, all phases
0candidates
0/24known letters
unclocked
1

The experiment method

What the method does with the 24 known letters.

Some famous ciphers use a five-by-five squarea five-by-five square A 5 by 5 grid holding 25 of the 26 letters, used by Playfair, bifid and their relatives; one letter is always left out or merged. of letters, which has room for only 25 of the 26, so one letter can never come out of them. Others swap letters two at a time, so the messagethe message The 97 letters of English that Jim Sanborn wrote and enciphered. they make always has an even number of letters. The copper has 97 letters, an odd number, and we check whether every letter of the alphabet appears on it. Either fact rules out a whole group of ciphers at once, without trying a single secret word.

Words in the margin are defined on the glossary page.

1.1

The method at work

The carved letters go in at the top; the reading comes out at the bottom.

OBKRUOXOGHULBSOLIFBBWEASTNORTHEASTOTWTQSJQSSEKZZWATJKLUDIAWINFBBERLINCLOCKWGDKZXTJCDIGKUHUAUEKCARIN: THE COPPER, ALL 97 LETTERS, THE 24 KNOWN PLACES IN ACCENThow often each of the 26 letters is carved on K44A5B2C3D2E4F4G2H4I3J8K4L1M3N5O3P4Q4R6S6T6U2V5W2X1Y4ZI and J both appear (I at 17, 57, 60, 85; J at 41, 52, 82): no square merges themQ appears four times: no square drops it97 letters, an odd count: nothing that works in pairs fits without a padding letterOUT: NO READING; EVERY 25-LETTER AND PAIRWISE SYSTEM IS EXCLUDEDEASTNORTHEASTBERLINCLOCK
26 letters

K4 uses every letter of the alphabet. Playfair, two-square, four-square, bifid and ADFGX all work from a 5 x 5 square of 25 letters, so they cannot have produced it.

97 letters

Playfair and the square ciphers also encipher two letters at a time, which needs an even length; K4 has 97.

the escape

A padding letter, a 6 x 6 square with digits spelled out, or a 26-letter rectangle would get round these counts; none is a standard system.

2

Best candidate against the known letters

This experiment produced no candidate: the search ruled everything out before a full text was built. Its product is the bounded negative in section 7.

3

Walkthrough, by hand

Redo the method on a few letters with pencil and paper.

  1. Write the 26 letters A to Z in a row.
  2. Read the copper's 97 letters and tick each letter as it appears.
  3. J appears at place 41 and I at place 16, so a square that merges I and J cannot have made this text.
  4. Q appears at places 26 and 27, so a square that drops Q cannot either.
  5. Every one of the 26 ticks gets ticked, so no 25-letter square made it.
  6. Count the letters: 97, an odd number, so no cipher that works two letters at a time made it without an extra letter.
the worksheet: the first steps by hand, on squared paper
TICK EACH LETTER AS IT APPEARS ON THE COPPERABCDEFGHIJKLMNOPQRSTUVWXYZfirst seen at place502835645189101741312703012826414365252176547All 26 ticked: no 25-letter square made this text. Count the letters:97, odd, so no cipher that works two at a time made it without apadding letter.
4

Worked example, generated

The same steps run by the code on the real letters.

letter counts on the copper:
A4  B5  C2  D3  E2  F4  G4  H2  I4  J3  K8  L4  M1  N3  O5  P3  Q4  R4  S6  T6  U6  V2  W5  X2  Y1  Z4
length 97
5

Hypothesis, for a cryptanalyst

Family, key space, the constraint under test, and the clues it reads.

Playfair, two-square and four-square encipher digraphs on 5x5 squares (25 symbols, I/J or Q dropped) and need an even-length text; bifid on a 5x5 square emits only the square's 25 letters; ADFGX and ADFGVX emit 5 or 6 letters; a cipher on the Weltzeituhr's 24-zone ring (C12b) emits at most 24 letters. Count the distinct letters of K4 and its length. If all 26 letters occur, every system whose ciphertext alphabet has at most 25 symbols is excluded, whatever the key; if the length is odd, every digraphic system without a null is excluded. Ten shuffles of K4 are not needed: the test is structural and exact.

6

Prediction

Written before the run; the result decides it.

All 26 letters occur in K4 and its length is odd, so Playfair, two-square, four-square, bifid on 5x5, ADFGX, ADFGVX and any 24-letter ring cipher are excluded. Zero candidates.

7

Method

  1. List the distinct letters of K4 and the count of each.
  2. Note the length.
  3. For each system, state its output alphabet size and length rule.
  4. Mark each system excluded or open.
  5. Say which escape routes remain: a null letter appended, a 6x6 square with digits spelled out, a 26-symbol variant.
8

Result and bounds

The harness's record: candidates, gates, loss, and the negative result this experiment leaves behind.

0candidates returned
0passed every gate
0/24known letters, best
–lowest loss
34champion before

K4 uses all 26 letters and has 97 letters; every listed system is excluded: Playfair; two-square; four-square; bifid 5x5; ADFGX; ADFGVX; Weltzeituhr 24-letter ring; Polybius 5x5 to letters.

What was searched, as the harness recorded it.

family
ciphers with fewer than 26 output symbols or an even-length rule
distinct letters
26
length
97
rarest letters
Y
1
M
1
X
2
H
2
V
2
E
2
verdicts
Playfair
excluded: emits at most 25 letters; K4 has 26; needs an even length; K4 has 97
two-square
excluded: emits at most 25 letters; K4 has 26; needs an even length; K4 has 97
four-square
excluded: emits at most 25 letters; K4 has 26; needs an even length; K4 has 97
bifid 5x5
excluded: emits at most 25 letters; K4 has 26
ADFGX
excluded: emits at most 5 letters; K4 has 26; needs an even length; K4 has 97
ADFGVX
excluded: emits at most 6 letters; K4 has 26; needs an even length; K4 has 97
Weltzeituhr 24-letter ring
excluded: emits at most 24 letters; K4 has 26
Polybius 5x5 to letters
excluded: emits at most 25 letters; K4 has 26
escape routes
a null letter appended to make the length even (then the 25-letter rule still applies), a 6x6 square with digits written out as words, a variant on a 26-letter rectangle

How this experiment sits among the others is on the lineage page; its family's open hypotheses are on the families page.

Rendered from the record on 2026-10-18 12:26 UTC; updated after every experiment.
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