• ▸We believe the solution is present within these families16 blocked, 5 noted, 104 closed

  • ▸Excluded by the known letters alone, before any search4 closed

    • Pure transposition: the known letters need three Es, the copper has twoclosed · exact · 51
    • One substitution alphabet: the same carved letter stands for different known lettersclosed · exact
    • Rotor machines: K encrypts to K, S to Sclosed · exact
    • Systems with 25 or fewer symbols (Playfair, bifid, ADFGVX): K4 uses all 26 lettersclosed · exact · 52
  • ▸1stFamily 1: One keyed stage, no move8 blocked, 2 noted, 30 closed

    • ▸A repeating key on the table1 blocked, 1 noted, 10 closed

      • Standard or KRYPTOS alphabets, key lengths 1-26 and 30-52closed · exact · 5
      • Key lengths 27-29 and 53+ on alphabets from the puzzle's words; the completed key reads as noiseclosed · exact · 34 35 48 53
      • Alphabets from any dictionary word, key lengths 1-26closed · exact · 109
      • Alphabets one swap or move from KRYPTOSclosed · exact · 71
      • ▸F1.1 One alphabet in an unknown order on both sides (Quagmire III), key lengths 3-264 closed

        • Added form (Quagmire III proper, and variant Beaufort), lengths 1-26: S under S and K under K force key 0 in slots another known letter sharesclosed · exact · 119
        • Beaufort form, lengths 1-22, 24, 25: no alphabet fitsclosed · exact · 119
        • Beaufort form, length 23 (7 checks): design 2 (F1.5) puts K4 9th of 13 among copies of itself; planted texts beat all their own copies 6 of 8 (0139)closed · sampled · 119 120 139 140
        • Beaufort form, length 26 (1 check): K4 12th of 13 among copies of itself; power 5 of 6 (0140)closed · sampled · 119 140 142
      • ▸F1.2 Two alphabets in unknown orders (Quagmire IV), key lengths 3-261 blocked, 1 noted, 2 closed

        • Lengths 1-7, 9-12, 14, 15, 17, 18, 21, 22, 25: no pair of alphabets fitsclosed · exact · 123
        • Lengths 8, 13, 16: design 2 on two alphabets puts K4 2nd, 13th and 7th of 13 among kept-place copies; power 4/4, 5/5, 4/5closed · sampled · 143 144 145 146
        • Lengths 20, 23, 24, 26: above 0136's bound, only a better English model could decideblocked · exact · 123 136
        • Length 19: a pair fits, 26 of 1,000 coppers do (R under P at 28 and 66, 38 apart)noted · exact · 123 124
    • A progressive keyclosed · exact · 11 42 155
    • ▸A self-feeding key (autokey)2 blocked, 3 closed

      • Ciphertext autokey, any lag, on 1,092 keyword tablesclosed · exact · 2 25 64 118
      • Plaintext autokey, lags 1-52closed · exact · 3 12
      • ▸Plaintext autokey, lags 53-96: the known letters force too little2 blocked

        • Lags 85-96: open bits above what 73 letters of English carry at Shannon's lowest entropy; no English test can decideblocked · exact · 136
        • Lags 53-84: above the quadgram scorer's 130 bits; only a better English model could decideblocked · exact · 136
      • Autokey plus a repeating keyclosed · exact · 66 67 73
    • ▸A running key from a text3 closed

      • K1-K3, the sculpture's texts, Carter, Sanborn's lettersclosed · exact · 4 17 21 45 47 78 98 117
      • An unknown English text, on standard, KRYPTOS or puzzle-word alphabetsclosed · sampled · 9 10
      • F1.3 An unknown English text, on any dictionary-word alphabetclosed · sampled · 125
    • ▸A key schedule worked by hand2 blocked, 3 closed

      • The Berlin clock, the Carter datesclosed · exact · 79 38
      • ▸F1.4 Other hand schedules (C20(c)-(e))2 blocked, 2 closed

        • The tableau rows as repeating keys ("layer two", C20(d)): 6 of 24 known letters, coppers 5-8closed · exact · 126 128
        • A key word stepped by skip, stutter, back and forth, triangle or square numbers, or restarted at each carved line, on standard or KRYPTOS tables: no setting fitsclosed · exact · 127 128
        • The same rules on free alphabets: consistent at the coppers' rate; a decider exists (F1.5) but about 1,900 settings at 20-30 min each: blocked by costblocked · exact · 127 128
        • K5 as the key (C20(e)): no textblocked
    • ▸F1.5 A decider for cells the known letters cannot decide (the shared blocker of F1.1, F1.2, F1.4's free alphabets, autokey lags 53-96, F6.1, F6.2, F8): bound each cell by key bits against English redundancy, then a climb that passes 0120's power bar on planted texts (P6)3 closed

      • Step 2, design 1 (check-keeping climb, compiled): plants beat K4's copies 10 of 12 but only 6 of 12 their own: power came from letter counts, failsclosed · sampled · 137 138
      • Step 2, design 2 (parallel tempering in the check-keeping set): plants beat their own copies 6 of 8 at 23, 5 of 6 at 26, 4/4-5/5 with two alphabets; decides F1.1 and F1.2's cellsclosed · sampled · 139 140 143 145
      • Step 1, the bound: the quadgram scorer extracts 1.78 bits per letter (130 bits in 73 letters); one free alphabet at every length, two to 16 (14 with a move), Hill with any key decidable in principle; two alphabets from 19 (15 with a move) and autokey 53-84 only with a better model; autokey 85-96 by noneclosed · exact · 136
    • ▸F1.6 One carved letter wrong, missing or extra, through the exact unknown-alphabet tests1 blocked, 3 closed

      • One and two free alphabets, periodic, 604 variants: at the coppers' rateclosed · exact · 147
      • K1/K2's system revived at length 19 by a slip at 33: decider power 3 of 5, too weakblocked · sampled · 148
      • Gromark (all free-alphabet rules and bases), 605 variants: no fitclosed · exact · 150
      • Trifid and Hill, every single-letter error anywhere (5,044): no cube; Hill at the coppers' rateclosed · exact · 151 152
    • ▸F1.7 Autokey on one unknown alphabet, with no move, then after each move1 blocked, 1 closed

      • No move: dead lags closed; fitting lags at the coppers' rateclosed · exact · 149
      • Fitting lags judged by English, and the move-first version: blocked by costblocked
    • ▸F1.8 Carter's book as a running key on an unknown alphabet1 blocked, 1 closed

      • One alphabet, every offset both ways: no fit on K4 or copiesclosed · exact · 154
      • Two alphabets, any running key: almost no checks; undecidable by the known lettersblocked · exact · 154
    • ▸F1.9 The per-letter progressive key; its periods 26-30 against coppers1 noted

      • Period 34 (K4 40 and 20 consistent pairs against copy maxima 10 and 7), inside the fixed statisticnoted · exact · 155
    • F1.10 Friedman's keyword-only key-advance schedulesclosed · exact · 156
    • F1.11 A split key phrase: one part mixes the plain alphabet, the other the cipher alphabetclosed · exact · 157
  • ▸2ndFamily 6: A move, then the table2 blocked, 2 noted, 26 closed

    • ▸One move, then a repeating key on standard, KRYPTOS or word alphabets1 noted, 3 closed

      • Columnar (plain, keyed, double, Myszkowski, AMSCO), rail fenceclosed · exact · 6 26 58 84 85 110 111 112 113 114
      • K3's rule, quarter turns, grid paths, the ? as a 98th symbolclosed · exact · 8 41 82 83 86 99
      • Key on both sides of the move, the same table both sidesclosed · exact · 80
      • AMSCO at key length 23: above the coppers, within the number expected by chancenoted · exact · 114
    • One move with an autokey, running key or clock scheduleclosed · exact · 63 81 90 91
    • One carved letter wrong, missing or extra, through every moveclosed · exact · 93 94
    • ▸Three stages3 closed

      • Three clockwise quarter turns, every widthclosed · exact · 83
      • ▸F6.3 Mixed three-stage routes2 closed

        • Four column readings (turn either way, rows-then-columns-down, its reverse), every pair at widths 2-96 and every triple at 2-24: nothing live below key length 20closed · exact · 134
        • F6.3b Mixed triples at widths 25-96: 105.5 million routes, nothing live below 18, at the coppers' rateclosed · exact · 37 158
    • ▸Alphabets in unknown orders after or before a move2 blocked, 1 noted, 2 closed

      • ▸F6.1 One unknown alphabet (Quagmire III)1 blocked, 1 closed

        • Every type-1 move, either order, added or Beaufort form, key lengths 1-5: no alphabet fitsclosed · exact · 129 130
        • Lengths 6-26: settings fit at the scrambled-copper rate; only an English climb could judge them (0120)blocked · exact · 129 130
      • ▸F6.2 Two unknown alphabets (Quagmire IV)1 blocked, 1 noted, 1 closed

        • Every type-1 move, either order, key lengths 1-2 (and 3 with the table first): no pair fitsclosed · exact · 133
        • The rest: fits at the scrambled-copper rate (exact to 10, per-slot above); only an English climb could judgeblocked · exact · 133
        • Move first, key length 3: K4 at the top of its coppers in 0097, 0100, 0133; p 0.04-0.10 (0102)noted · exact · 100 102 133
    • ▸F6.4 Padding at each grid stage; nulls dropped between grids1 closed

      • Blanks in any of eight places per grid, dropped or kept as dummies, one stage (widths 2-96) or two (2-48), periodic key 1-26 on standard/KRYPTOS tables: nothing live below 21closed · exact · 135
    • F6.5 Direction words as routes through the grid ("east, then northeast"), then the tableclosed · exact · 159
    • F6.6 Move, change, move again (844-move library, all pairs)closed · exact · 160
    • F6.7 Change, move, change on two different tablesclosed · exact · 161
    • F6.8 Three-stage routes with a keyword columnar stageclosed · exact · 162
    • F6.9 Both autokeys with 0084's width-7 double columnar routesclosed · exact · 163
    • F6.10 Blank cells chosen by a key, then the tableclosed · exact · 165
    • F6.11 Keyword-disrupted and triangle columnar transpositions, then the tableclosed · exact · 164
    • F6.12 EVA's double triangle transposition, then the tableclosed · exact · 166
    • F6.13 Chiffre XIII's keyword-shaped five-row mask, then its period-5 table (parametric masks; the documented rule not in hand)closed · exact · 166
    • F6.14 Nihilist transposition on a 10 x 10 square with three blanksclosed · exact · 167
    • F6.15 YAR's "1-2-3" spacing as an ordering, then the tableclosed · exact · 166
    • F6.16 Interrupted-key columnar transposition, then the tableclosed · exact · 164
    • F6.17 Trapezoid transposition, then the tableclosed · exact · 164
    • F6.18 Letters reshuffled inside each row at widths other than 7, then the tableclosed · exact · 165
    • F6.19 The French diagonal method, then the table (key-named diagonals)closed · exact · 165
  • ▸3rdFamily 12: Stein's way: look, quantify, then crib1 blocked, 6 closed

    • F12.1 The 97 letters and the "?" checked against images of the copperblocked
    • F12.2 K4's statistics by segment and width against shufflesclosed · sampled · 168
    • F12.3 Stein's I.C. peak at 13 in K1 and K2: real or chanceclosed · sampled · 169
    • F12.4 A pencil session: every pattern noted before any codeclosed · sampled · 170
    • F12.5 Parts with their own keys, split where the statistics breakclosed · exact · 171
    • F12.6 Probable words through the cells the known letters cannot decideclosed · exact · 172
    • F12.7 Stein's K1-K3 method as such: column shifts scored by log frequencies, then a cribclosed · by subsumption · 5
  • ▸4thFamily 3: A two-part key with a combiner11 closed

    • Two words added: both from the puzzle, or one from the dictionaryclosed · exact · 14 43 59 115
    • A word plus digits from the storyclosed · exact · 24 38
    • A word plus the misspelt or raised lettersclosed · exact · 61
    • A column word plus a row keyclosed · exact · 87 88
    • F3.1 Combiners other than additionclosed · exact · 173 174
    • F3.2 Number keys from the Morse and the plate layoutclosed · exact · 175
    • F3.3 Direction words as numbers: the bearing 67.5, compass points 6 of 32 and 3 of 16closed · exact · 176
    • F3.4 Three or more stacked tables (Scheidt's patent, "triple matrixes")closed · exact · 177
    • F3.5 The misspelt letters' positions as indices, and their orientationclosed · exact · 178
    • F3.6 The Weltzeituhr's rotating ring as an offset over 26 lettersclosed · exact · 179
    • F3.7 "Point" as a decimal point, a place or a punctuation markclosed · exact · 180
  • ▸5thFamily 2: Masked plaintext, then a keyed stage1 blocked, 6 closed

    • Masks that move or pad letters: reversal, nulls, doublets as nullsclosed · exact · 23 57 75
    • Masks that change letters: affine, Atbashclosed · exact · 74
    • The message written along a grid pathclosed · exact · 92
    • F2.1 Fragments from 0057's letter strike-outs at key lengths 24-25 not yet matched against wordsclosed · exact · 181
    • F2.2 Nulls placed by a ruleclosed · exact · 182
    • F2.3 A plain component with repeated letters: homophones that keep the lengthclosed · exact · 183
    • A code layer, phonetic spelling, another language: these change the known letters or need a codebookblocked
  • ▸6thFamily 4: Sanborn's visual systems1 blocked, 7 closed

    • Trifid, any cube, periods 2-15closed · exact · 40
    • The plates as a key by position, straight or foldedclosed · exact · 89
    • K4 read from behind the screenclosed · exact · 108
    • F4.1 A route that follows the plates' physical layoutclosed · exact · 184
    • F4.2 Free trifid cubes at periods above 15closed · exact · 185
    • F4.3 The physical anomalies' positions as a keyclosed · exact · 186
    • F4.4 The extra L and HILL as a marker matching YARclosed · by subsumption · 5 17 89
    • F4.5 Antipodes' plate order and spelling differencesblocked
  • ▸7thFamily 10: Alphabets that change after every letter1 blocked, 2 closed

    • F10.1 Chaocipher: two wheels permuted after every letter (1918, disclosed 2010)closed · exact · 187
    • F10.2 Wheatstone cryptograph or Alberti disk advanced by the plaintextclosed · exact · 188
    • F10.3 A key stream from a deck of cards (Solitaire, Mirdek)blocked
  • ▸8thFamily 11: Agency hand systems, now public4 closed

    • F11.1 Strip ciphers and cylinders with published alphabets (M-94, Jefferson wheel, M-138-A)closed · exact · 189
    • F11.2 Poem code: double transposition keyed by words from a memorized text, then the tableclosed · exact · 190
    • F11.3 The CIA's Polish key box: a key text transposed in a box, then the tableclosed · exact · 191
    • F11.4 Friedman's keyed alphabet box as the key streamclosed · exact · 192
  • ▸9thFamily 8: Hill ciphers1 blocked, 2 closed

    • Hill 2-5, plain and affine, 330 numberings, chained, with a repeating keyclosed · exact · 15 36 44 55 105 116
    • F8.1 Hill with an unknown letter numbering: count the equations firstclosed · exact · 194
    • Settings with too few equations to decide (5x5 affine; long keys with 4x4)blocked · exact · 105 116
  • ▸10thFamily 5: Gromark and number feedback3 closed

    • Two- and three-term rules, bases 2-26 (three-term free alphabet in base 10 only)closed · exact · 13 28 46 54 69 76 107
    • F5.1 Multiplicative feedback; the raised YAR as primerclosed · exact · 196
    • F5.2 Three-term Gromark on a free alphabet in other basesclosed · exact · 195
  • ▸11thFamily 9: Substitution, then a move1 blocked, 2 closed

    • One-to-one substitution, then any of the 1.86M built routesclosed · exact · 19 106
    • Routes outside every built set: unbounded without a list of hand methodsblocked
    • F9.1 A bounded list of hand transpositions outside the built sets, then one-to-one substitutionclosed · exact · 197 198
  • ▸Family 7: Construction simulation (a check on the others, not a cipher)1 noted, 1 closed

    • K4's two patterns, doublets lining up in sevens and repeats 21 apart, are realnoted · sampled · 56
    • No construction tried makes both patternsclosed · sampled · 18 27 62 65 96