Analysis of zz-www.sudokuoftheday.co.uk-20060701-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006
level: medium
position: 17.59.2.8...3..5..59...8.........8..8....6.75...4.....6..........9..572...2.6..84 initial
Autosolve
position: 17.5942.82..3..5.959.628..7....5.8..82.9.6.75..548.6..6......5...9..5726.52.6..84 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H3: 3,4 => CTR => H3: 1 * DIS # E7: 1,7 => CTR => E7: 3,4 * DIS # F4: 1,7 => CTR => F4: 2,3 * DIS # F7: 1,7 => CTR => F7: 2,3,9 * PRF # F9: 1,7 => SOL * DIS # C2: 4,6 => CTR => C2: 8 * DIS # B4: 1,4 => CTR => B4: 3,6 * PRF # C4: 1,4 => SOL * DIS # G5: 1,4 => CTR => G5: 3 * PRF # G5: 3 => SOL * DIS # C7: 1,4 => CTR => C7: 7,8 * DIS # B4: 1,3 => CTR => B4: 4,6 * DIS # F6: 1,3 => CTR => F6: 2,7 * DIS # H6: 1,3 => CTR => H6: 9 * PRF # I6: 1,3 => SOL * DIS # B7: 1,3 => CTR => B7: 4,8 * DIS # F6: 1,3 => CTR => F6: 2,7 * DIS # G5: 4 => CTR => G5: 1,3 * DIS # E7: 1,3 => CTR => E7: 4,7 * DIS # B7: 3,4 => CTR => B7: 1,8 * DIS # B8: 3,4 => CTR => B8: 1,8 * DIS # E8: 1 => CTR => E8: 3,4 * DIS # A4: 3,4 => CTR => A4: 7,9 * PRF # F9: 3,7 => SOL * DIS # A4: 3,7 => CTR => A4: 4,9 * DIS # D7: 1,8 => CTR => D7: 2,7 * DIS # B8: 3,4 => CTR => B8: 1,8 * DIS # D7: 1,7 => CTR => D7: 2,8 * DIS # E7: 1,7 => CTR => E7: 3,4 * DIS # F7: 1,7 => CTR => F7: 2,3,9 * PRF # F9: 1,7 => SOL * DIS # D4: 2 => CTR => D4: 1,7 * DIS # B7: 1,3 => CTR => B7: 4,8 * DIS # E7: 1,3 => CTR => E7: 4,7 * PRF # I6: 1,3 => SOL * CNT 35 HDP CHAINS / 79 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H3: 3,4 => CTR => H3: 1 * DIS H3: 1 # E7: 1,7 => CTR => E7: 3,4 * DIS H3: 1 + E7: 3,4 # C2: 4,6 => CTR => C2: 8 * DIS H3: 1 + E7: 3,4 + C2: 8 # B4: 1,4 => CTR => B4: 3,6 * PRF H3: 1 + E7: 3,4 + C2: 8 + B4: 3,6 # C4: 1,4 => SOL * STA H3: 1 + E7: 3,4 + C2: 8 + B4: 3,6 + C4: 1,4 * CNT 5 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 17.59.2.8...3..5..59...8.........8..8....6.75...4.....6..........9..572...2.6..84 | initial |
| 17.5942.82..3..5.959.628..7....5.8..82.9.6.75..548.6..6......5...9..5726.52.6..84 | autosolve |
| 176594238248371569593628417961753842824916375735482691687249153419835726352167984 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) C1: 3,6 C3: 3,4 E2: 1,7 F2: 1,7 H1: 3,6 H2: 4,6 C5: 1,4 B6: 1,3 E5: 1,3 A8: 3,4 A9: 3,7 D8: 1,8 D9: 1,7 I7: 1,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,F2: 1.. / E2 = 1 => 0 pairs (X) / F2 = 1 => 12 pairs (_) G3,H3: 1.. / G3 = 1 => 0 pairs (X) / H3 = 1 => 16 pairs (_) I4,I6: 2.. / I4 = 2 => 0 pairs (*) / I6 = 2 => 0 pairs (X) D7,F7: 2.. / D7 = 2 => 14 pairs (_) / F7 = 2 => 0 pairs (X) F6,I6: 2.. / F6 = 2 => 0 pairs (*) / I6 = 2 => 0 pairs (X) D4,D7: 2.. / D4 = 2 => 0 pairs (X) / D7 = 2 => 14 pairs (_) C1,C3: 3.. / C1 = 3 => 0 pairs (X) / C3 = 3 => 15 pairs (_) C1,H1: 3.. / C1 = 3 => 0 pairs (X) / H1 = 3 => 15 pairs (_) E5,G5: 3.. / E5 = 3 => 0 pairs (X) / G5 = 3 => 0 pairs (_) H4,G5: 4.. / H4 = 4 => 13 pairs (_) / G5 = 4 => 0 pairs (X) E7,E8: 4.. / E7 = 4 => 13 pairs (_) / E8 = 4 => 0 pairs (X) C5,G5: 4.. / C5 = 4 => 13 pairs (_) / G5 = 4 => 0 pairs (X) A4,A8: 4.. / A4 = 4 => 0 pairs (X) / A8 = 4 => 15 pairs (_) G3,G5: 4.. / G3 = 4 => 13 pairs (_) / G5 = 4 => 0 pairs (X) H1,H2: 6.. / H1 = 6 => 0 pairs (X) / H2 = 6 => 15 pairs (_) B4,C4: 6.. / B4 = 6 => 15 pairs (_) / C4 = 6 => 0 pairs (X) C1,H1: 6.. / C1 = 6 => 15 pairs (_) / H1 = 6 => 0 pairs (X) B2,B4: 6.. / B2 = 6 => 0 pairs (X) / B4 = 6 => 15 pairs (_) E2,F2: 7.. / E2 = 7 => 12 pairs (_) / F2 = 7 => 0 pairs (X) C7,A9: 7.. / C7 = 7 => 0 pairs (*) / A9 = 7 => 0 pairs (X) A6,F6: 7.. / A6 = 7 => 0 pairs (*) / F6 = 7 => 0 pairs (X) C4,C7: 7.. / C4 = 7 => 0 pairs (X) / C7 = 7 => 0 pairs (_) E2,E7: 7.. / E2 = 7 => 12 pairs (_) / E7 = 7 => 0 pairs (X) B2,C2: 8.. / B2 = 8 => 0 pairs (X) / C2 = 8 => 15 pairs (_) D7,D8: 8.. / D7 = 8 => 0 pairs (X) / D8 = 8 => 13 pairs (_) B8,D8: 8.. / B8 = 8 => 0 pairs (X) / D8 = 8 => 13 pairs (_) C2,C7: 8.. / C2 = 8 => 15 pairs (_) / C7 = 8 => 0 pairs (X) A4,A6: 9.. / A4 = 9 => 18 pairs (_) / A6 = 9 => 0 pairs (X) H4,H6: 9.. / H4 = 9 => 0 pairs (X) / H6 = 9 => 18 pairs (_) F7,F9: 9.. / F7 = 9 => 21 pairs (_) / F9 = 9 => 15 pairs (_) G7,G9: 9.. / G7 = 9 => 15 pairs (_) / G9 = 9 => 21 pairs (_) A4,H4: 9.. / A4 = 9 => 18 pairs (_) / H4 = 9 => 0 pairs (X) A6,H6: 9.. / A6 = 9 => 0 pairs (X) / H6 = 9 => 18 pairs (_) F7,G7: 9.. / F7 = 9 => 21 pairs (_) / G7 = 9 => 15 pairs (_) F9,G9: 9.. / F9 = 9 => 15 pairs (_) / G9 = 9 => 21 pairs (_) * DURATION: 0:00:40.907059 START: 00:14:26.479064 END: 00:15:07.386123 2019-05-01 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,B6,C1,C3,C5,D8,D9,E2,E5,F2,H1,H2,I7) * 17.5942.82..3..5.959.628..7....5.8..82.9.6.75..548.6..6......5...9..5726.52.6..84 * PAIR C3: 3,4 ROW 3 G3: 3,4,1 # reduction candidate for 3,4 G3: 3,4 # 16 pairs H3: 3,4,1 # reduction candidate for 3,4 H3: 3,4 => CTR * 17.5942.82..3175.959.6281.74672518..821936475.3548.6.26......5131984572675216..84 H3: 1 # 16 pairs * PAIR E2: 1,7 COL E E7: 1,7,3,4 # reduction candidate for 1,7 E7: 1,7 => CTR * 17.5942.82..3..5.959.628..74...5.89.8219364759354876126......5131984572675216..84 E7: 3,4 # 13 pairs * PAIR F2: 1,7 COL F F4: 1,7,2,3 # reduction candidate for 1,7 F4: 1,7 => CTR * 17.5942382.83715695936284179...578..82.9163757.54836926.7.429534.9.35726352769184 F4: 2,3 # 15 pairs F6: 1,7,2,3 # reduction candidate for 1,7 F6: 1,7 # 18 pairs F7: 1,7,2,3,9 # reduction candidate for 1,7 F7: 1,7 => CTR * 17.5942.82..3..5.959.628..7....5.8..82.916375..548.6..6..2..953.19835726352.69.84 F7: 2,3,9 # 14 pairs F9: 1,7,3,9 # reduction candidate for 1,7 F9: 1,7 => SOLVED * 176594238248371569593628417961753842824916375735482691687249153419835726352167984 F9: 3,9 # 15 pairs * PAIR H2: 4,6 ROW 2 B2: 4,6,8 # reduction candidate for 4,6 B2: 4,6 # 15 pairs C2: 4,6,8 # reduction candidate for 4,6 C2: 4,6 => CTR * 17.5942.828.3..5.959.628..7.6725.8..821936475.354876.26.874..5...98.572675216..84 C2: 8 # 15 pairs * PAIR C5: 1,4 BLK 4 B4: 1,4,3,6 # reduction candidate for 1,4 B4: 1,4 => CTR * 17.5942.82683..549594628..7..6.5.8..821936475.3548.6..6.7....5.3.9..5726.52.6..84 B4: 3,6 # 15 pairs C4: 1,4,6,7 # reduction candidate for 1,4 C4: 1,4 => SOLVED * 176594238248371569593628417961753842824916375735482691687249153419835726352167984 C4: 6,7 # 15 pairs * PAIR C5: 1,4 ROW 5 G5: 1,4,3 # reduction candidate for 1,4 G5: 1,4 => CTR * 17.5942.82..3175.959.628..7..72518..82.936.75..548.6..6......5...9..572675216..84 G5: 3 => SOLVED * 176594238248371569593628417961753842824916375735482691687249153419835726352167984 * PAIR C5: 1,4 COL C C7: 1,4,7,8 # reduction candidate for 1,4 C7: 1,4 => CTR * 176594238248371569593628..7.672538.182.916375.154876926.174295...9..572675216..84 C7: 7,8 # 18 pairs * PAIR B6: 1,3 BLK 4 B4: 1,3,4,6 # reduction candidate for 1,3 B4: 1,3 => CTR * 17.5942.82683..549594628..74.6.5.89.8219.6.75..548.6..6......5...9..5726.52.6..84 B4: 4,6 # 15 pairs * PAIR B6: 1,3 ROW 6 F6: 1,3,2,7 # reduction candidate for 1,3 F6: 1,3 => CTR * 17.5942.82.83715.959.628..79...5.8..82.9.6.757154836926.7....5.489..5726352.6..84 F6: 2,7 # 15 pairs H6: 1,3,9 # reduction candidate for 1,3 H6: 1,3 => CTR * 17.5942.82..3715.959.628..7....5.89.8219364759354876126......51319845726.52.6..84 H6: 9 # 18 pairs I6: 1,3,2 # reduction candidate for 1,3 I6: 1,3 => SOLVED * 176594238248371569593628417961753842824916375735482691687249153419835726352167984 I6: 2 # 15 pairs * PAIR B6: 1,3 COL B B7: 1,3,4,8 # reduction candidate for 1,3 B7: 1,3 => CTR * 17.5942.82..3715.959.628.179...5384.82491637573548.69.61....953..9.35726352769184 B7: 4,8 # 15 pairs B8: 1,3,4,8 # reduction candidate for 1,3 B8: 1,3 # 16 pairs * PAIR E5: 1,3 BLK 5 F4: 1,3,2,7 # reduction candidate for 1,3 F4: 1,3 # 19 pairs F6: 1,3,2,7 # reduction candidate for 1,3 F6: 1,3 => CTR * 17.5942.82.83715.959.628..79...5.8..82.9.6.757154836926.7....5.489..5726352.6..84 F6: 2,7 # 15 pairs * PAIR E5: 1,3 ROW 5 G5: 1,3,4 # reduction candidate for 1,3 G5: 4 => CTR * 17.5942.82..3175.959.628..74672518..821936475.3548.6..6......5.3.9..572675216..84 G5: 1,3 # 13 pairs * PAIR E5: 1,3 COL E E7: 1,3,4,7 # reduction candidate for 1,3 E7: 1,3 => CTR * 17.5942.82..3715.959.628..74...5.89.8219364759354876126...1..53..9.45726.52.6..84 E7: 4,7 # 15 pairs E8: 1,3,4 # reduction candidate for 1,3 E8: 1,3 # 13 pairs * PAIR A8: 3,4 BLK 7 B7: 3,4,1,8 # reduction candidate for 3,4 B7: 3,4 => CTR * 17.5942.82..3715.959.628..7.672538.182.916375.1548769263.....5...9..572675216..84 B7: 1,8 # 15 pairs B8: 3,4,1,8 # reduction candidate for 3,4 B8: 3,4 => CTR * 17.5942.82..3715.959.628.17...15.8..821936475.3548.69161.....5...9815726.5276.184 B8: 1,8 # 16 pairs * PAIR A8: 3,4 ROW 8 E8: 3,4,1 # reduction candidate for 3,4 E8: 1 => CTR * 17.5942.82..3715.959.628.17...15.8..821936475.3548.691617.4..5...9.15726.5276.184 E8: 3,4 # 16 pairs * PAIR A8: 3,4 COL A A4: 3,4,7,9 # reduction candidate for 3,4 A4: 3,4 => CTR * 17.5942.82..3715.959.628..7..725.89.82.9.64759.54876.26......5...9..572675216..84 A4: 7,9 # 19 pairs * PAIR A9: 3,7 ROW 9 F9: 3,7,1,9 # reduction candidate for 3,7 F9: 3,7 => SOLVED * 176594238248371569593628417961753842824916375735482691687249153419835726352167984 F9: 1,9 # 15 pairs * PAIR A9: 3,7 COL A A4: 3,7,4,9 # reduction candidate for 3,7 A4: 3,7 => CTR * 17.5942.82..3715.959.628..7....5.89.8219364759354876126...4..51419..5726.52.6..84 A4: 4,9 # 15 pairs A6: 3,7,9 # reduction candidate for 3,7 A6: 3,7 # 18 pairs * PAIR D8: 1,8 BLK 8 D7: 1,8,2,7 # reduction candidate for 1,8 D7: 1,8 => CTR * 17.5942.82..3715.959.628.17...25.8.182.916375.1548.6926....295...9..5726.52769184 D7: 2,7 # 14 pairs * PAIR D8: 1,8 ROW 8 B8: 1,8,3,4 # reduction candidate for 1,8 B8: 3,4 => CTR * 17.5942.82..3715.959.628.17...15.8..821936475.3548.69161.....5...9815726.5276.184 B8: 1,8 # 16 pairs * PAIR D9: 1,7 BLK 8 D7: 1,7,2,8 # reduction candidate for 1,7 D7: 1,7 => CTR * 17.5942.82..3715.959.628417..125.8..82.916375..548.6.26....2953.19835726352769184 D7: 2,8 # 15 pairs E7: 1,7,3,4 # reduction candidate for 1,7 E7: 1,7 => CTR * 17.5942.82..3..5.959.628..74...5.89.8219364759354876126......5131984572675216..84 E7: 3,4 # 13 pairs F7: 1,7,2,3,9 # reduction candidate for 1,7 F7: 1,7 => CTR * 17.5942.82..3..5.959.628..7....5.8..82.916375..548.6..6..2..953.19835726352.69.84 F7: 2,3,9 # 14 pairs F9: 1,7,3,9 # reduction candidate for 1,7 F9: 1,7 => SOLVED * 176594238248371569593628417961753842824916375735482691687249153419835726352167984 F9: 3,9 # 15 pairs * PAIR D9: 1,7 COL D D4: 1,7,2 # reduction candidate for 1,7 D4: 2 => CTR * 17.5942.82..3715.959.628417...25.841824916375..548.6.26....2953..9.35726352769184 D4: 1,7 # 14 pairs * PAIR I7: 1,3 BLK 9 G7: 1,3,9 # reduction candidate for 1,3 G7: 1,3 # 21 pairs G9: 1,3,9 # reduction candidate for 1,3 G9: 1,3 # 15 pairs * PAIR I7: 1,3 ROW 7 B7: 1,3,4,8 # reduction candidate for 1,3 B7: 1,3 => CTR * 17.5942.82..3715.959.628.179...5384.82491637573548.69.61....953..9.35726352769184 B7: 4,8 # 15 pairs E7: 1,3,4,7 # reduction candidate for 1,3 E7: 1,3 => CTR * 17.5942.82..3715.959.628..74...5.89.8219364759354876126...1..53..9.45726.52.6..84 E7: 4,7 # 15 pairs F7: 1,3,2,7,9 # reduction candidate for 1,3 F7: 1,3 # 22 pairs * PAIR I7: 1,3 COL I I4: 1,3,2 # reduction candidate for 1,3 I4: 1,3 # 15 pairs I6: 1,3,2 # reduction candidate for 1,3 I6: 1,3 => SOLVED * 176594238248371569593628417961753842824916375735482691687249153419835726352167984 I6: 2 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060701-absurd-base-pr-000.dot * REASONING * DIS # H3: 3,4 => CTR => H3: 1 * DIS # E7: 1,7 => CTR => E7: 3,4 * DIS # F4: 1,7 => CTR => F4: 2,3 * DIS # F7: 1,7 => CTR => F7: 2,3,9 * PRF # F9: 1,7 => SOL * DIS # C2: 4,6 => CTR => C2: 8 * DIS # B4: 1,4 => CTR => B4: 3,6 * PRF # C4: 1,4 => SOL * DIS # G5: 1,4 => CTR => G5: 3 * PRF # G5: 3 => SOL * DIS # C7: 1,4 => CTR => C7: 7,8 * DIS # B4: 1,3 => CTR => B4: 4,6 * DIS # F6: 1,3 => CTR => F6: 2,7 * DIS # H6: 1,3 => CTR => H6: 9 * PRF # I6: 1,3 => SOL * DIS # B7: 1,3 => CTR => B7: 4,8 * DIS # F6: 1,3 => CTR => F6: 2,7 * DIS # G5: 4 => CTR => G5: 1,3 * DIS # E7: 1,3 => CTR => E7: 4,7 * DIS # B7: 3,4 => CTR => B7: 1,8 * DIS # B8: 3,4 => CTR => B8: 1,8 * DIS # E8: 1 => CTR => E8: 3,4 * DIS # A4: 3,4 => CTR => A4: 7,9 * PRF # F9: 3,7 => SOL * DIS # A4: 3,7 => CTR => A4: 4,9 * DIS # D7: 1,8 => CTR => D7: 2,7 * DIS # B8: 3,4 => CTR => B8: 1,8 * DIS # D7: 1,7 => CTR => D7: 2,8 * DIS # E7: 1,7 => CTR => E7: 3,4 * DIS # F7: 1,7 => CTR => F7: 2,3,9 * PRF # F9: 1,7 => SOL * DIS # D4: 2 => CTR => D4: 1,7 * DIS # B7: 1,3 => CTR => B7: 4,8 * DIS # E7: 1,3 => CTR => E7: 4,7 * PRF # I6: 1,3 => SOL * CNT 35 HDP CHAINS / 79 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,B6,C1,C3,C5,D8,D9,E2,E5,F2,H1,H2,I7) * 17.5942.82..3..5.959.628..7....5.8..82.9.6.75..548.6..6......5...9..5726.52.6..84 * PAIR C3: 3,4 ROW 3 G3: 3,4,1 # reduction candidate for 3,4 G3: 3,4 # 16 pairs H3: 3,4,1 # reduction candidate for 3,4 H3: 3,4 => CTR * 17.5942.82..3175.959.6281.74672518..821936475.3548.6.26......5131984572675216..84 * RESTART * PAIR RESTART * PAIR E2: 1,7 COL E E7: 1,7,3,4 # reduction candidate for 1,7 E7: 1,7 => CTR * 17.5942.82..3..5.959.628.174...5.89.82193647593548.6..6......5...9.45726.52.6..84 * PAIR RESTART * PAIR H2: 4,6 ROW 2 B2: 4,6,8 # reduction candidate for 4,6 B2: 4,6 # 16 pairs C2: 4,6,8 # reduction candidate for 4,6 C2: 4,6 => CTR * 17.5942.828.3715.959.628.17.672538.18219.6.75..548.6..6.8....5...98.572675216..84 * RESTART * PAIR RESTART * PAIR C5: 1,4 BLK 4 B4: 1,4,3,6 # reduction candidate for 1,4 B4: 1,4 => CTR * 17.5942.8268371549594628317..6.5.8..821936475.3548.6916.7.4..533.9..5726.52.6..84 C4: 1,4,6,7 # reduction candidate for 1,4 C4: 1,4 => SOLVED * 176594238248371569593628417961753842824916375735482691687249153419835726352167984 * DURATION: 0:00:06.436911 START: 00:15:58.117396 END: 00:16:04.554307 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060701-absurd-base-pr-001.dot * REASONING * DIS # H3: 3,4 => CTR => H3: 1 * DIS H3: 1 # E7: 1,7 => CTR => E7: 3,4 * DIS H3: 1 + E7: 3,4 # C2: 4,6 => CTR => C2: 8 * DIS H3: 1 + E7: 3,4 + C2: 8 # B4: 1,4 => CTR => B4: 3,6 * PRF H3: 1 + E7: 3,4 + C2: 8 + B4: 3,6 # C4: 1,4 => SOL * STA H3: 1 + E7: 3,4 + C2: 8 + B4: 3,6 + C4: 1,4 * CNT 5 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060701, absurd
Solution
position: 176594238248371569593628417961753842824916375735482691687249153419835726352167984 solved
See section Pair Reduction for the HDP chains leading to this result.
Appendix: Full HDP Chains
A1. Pair Reduction Analysis
Full list of HDP chains traversed:
* INC # G3: 3,4 => UNS * DIS # H3: 3,4 => CTR => H3: 1 * INC # H3: 1 => UNS * DIS # E7: 1,7 => CTR => E7: 3,4 * INC # E7: 3,4 => UNS * DIS # F4: 1,7 => CTR => F4: 2,3 * INC # F4: 2,3 => UNS * INC # F6: 1,7 => UNS * DIS # F7: 1,7 => CTR => F7: 2,3,9 * INC # F7: 2,3,9 => UNS * PRF # F9: 1,7 => SOL * INC # F9: 3,9 => UNS * INC # B2: 4,6 => UNS * DIS # C2: 4,6 => CTR => C2: 8 * INC # C2: 8 => UNS * DIS # B4: 1,4 => CTR => B4: 3,6 * INC # B4: 3,6 => UNS * PRF # C4: 1,4 => SOL * INC # C4: 6,7 => UNS * DIS # G5: 1,4 => CTR => G5: 3 * PRF # G5: 3 => SOL * DIS # C7: 1,4 => CTR => C7: 7,8 * INC # C7: 7,8 => UNS * DIS # B4: 1,3 => CTR => B4: 4,6 * INC # B4: 4,6 => UNS * DIS # F6: 1,3 => CTR => F6: 2,7 * INC # F6: 2,7 => UNS * DIS # H6: 1,3 => CTR => H6: 9 * INC # H6: 9 => UNS * PRF # I6: 1,3 => SOL * INC # I6: 2 => UNS * DIS # B7: 1,3 => CTR => B7: 4,8 * INC # B7: 4,8 => UNS * INC # B8: 1,3 => UNS * INC # F4: 1,3 => UNS * DIS # F6: 1,3 => CTR => F6: 2,7 * INC # F6: 2,7 => UNS * INC # G5: 1,3 => UNS * DIS # G5: 4 => CTR => G5: 1,3 * DIS # E7: 1,3 => CTR => E7: 4,7 * INC # E7: 4,7 => UNS * INC # E8: 1,3 => UNS * DIS # B7: 3,4 => CTR => B7: 1,8 * INC # B7: 1,8 => UNS * DIS # B8: 3,4 => CTR => B8: 1,8 * INC # B8: 1,8 => UNS * INC # E8: 3,4 => UNS * DIS # E8: 1 => CTR => E8: 3,4 * DIS # A4: 3,4 => CTR => A4: 7,9 * INC # A4: 7,9 => UNS * PRF # F9: 3,7 => SOL * INC # F9: 1,9 => UNS * DIS # A4: 3,7 => CTR => A4: 4,9 * INC # A4: 4,9 => UNS * INC # A6: 3,7 => UNS * DIS # D7: 1,8 => CTR => D7: 2,7 * INC # D7: 2,7 => UNS * INC # B8: 1,8 => UNS * DIS # B8: 3,4 => CTR => B8: 1,8 * DIS # D7: 1,7 => CTR => D7: 2,8 * INC # D7: 2,8 => UNS * DIS # E7: 1,7 => CTR => E7: 3,4 * INC # E7: 3,4 => UNS * DIS # F7: 1,7 => CTR => F7: 2,3,9 * INC # F7: 2,3,9 => UNS * PRF # F9: 1,7 => SOL * INC # F9: 3,9 => UNS * INC # D4: 1,7 => UNS * DIS # D4: 2 => CTR => D4: 1,7 * INC # G7: 1,3 => UNS * INC # G9: 1,3 => UNS * DIS # B7: 1,3 => CTR => B7: 4,8 * INC # B7: 4,8 => UNS * DIS # E7: 1,3 => CTR => E7: 4,7 * INC # E7: 4,7 => UNS * INC # F7: 1,3 => UNS * INC # I4: 1,3 => UNS * PRF # I6: 1,3 => SOL * INC # I6: 2 => UNS * CNT 79 HDP CHAINS / 79 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G3: 3,4 => UNS * DIS # H3: 3,4 => CTR => H3: 1 * DIS H3: 1 # E7: 1,7 => CTR => E7: 3,4 * INC H3: 1 + E7: 3,4 # B2: 4,6 => UNS * DIS H3: 1 + E7: 3,4 # C2: 4,6 => CTR => C2: 8 * DIS H3: 1 + E7: 3,4 + C2: 8 # B4: 1,4 => CTR => B4: 3,6 * PRF H3: 1 + E7: 3,4 + C2: 8 + B4: 3,6 # C4: 1,4 => SOL * STA H3: 1 + E7: 3,4 + C2: 8 + B4: 3,6 + C4: 1,4 * CNT 7 HDP CHAINS / 7 HYP OPENED