Analysis of zz-www.sudokuoftheday.co.uk-20190429-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019
level: medium
position: .....9..76....4.9...9..52...2.13..............3.9.7..5.9......3..2.7..8.1.6....7. initial
Autosolve
position: 2....9..76....4.9...9..52...2.13.....6........3.9.7..5.9......33.2.7..8.1.6.93.7. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E2: 1,8 => CTR => E2: 2 * DIS # D5: 2,8 => CTR => D5: 4,5 * DIS # E5: 2,8 => CTR => E5: 4,5 * DIS # F7: 1,6 => CTR => F7: 2,8 * DIS # G4: 4,6 => CTR => G4: 7,8,9 * DIS # I4: 4,6 => CTR => I4: 8,9 * DIS # H6: 4,6 => CTR => H6: 1,2 * DIS # G8: 4,5 => CTR => G8: 1,6,9 * DIS # F7: 1,6 => CTR => F7: 2,8 * DIS # G8: 1,6 => CTR => G8: 4,5,9 * DIS # G7: 4,5 => CTR => G7: 1,6 * DIS # G8: 4,5 => CTR => G8: 1,6,9 * DIS # I5: 2,4 => CTR => I5: 1,8,9 * CNT 13 HDP CHAINS / 78 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E2: 1,8 => CTR => E2: 2 * DIS E2: 2 # I3: 1,8 => CTR => I3: 4,6 * DIS E2: 2 + I3: 4,6 # C6: 4,8 => CTR => C6: 1 * DIS E2: 2 + I3: 4,6 + C6: 1 # G6: 4,8 => CTR => G6: 6 * PRF E2: 2 + I3: 4,6 + C6: 1 + G6: 6 # C5: 7 => SOL * STA E2: 2 + I3: 4,6 + C6: 1 + G6: 6 + C5: 7 * CNT 5 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....9..76....4.9...9..52...2.13..............3.9.7..5.9......3..2.7..8.1.6....7. | initial |
| 2....9..76....4.9...9..52...2.13.....6........3.9.7..5.9......33.2.7..8.1.6.93.7. | autosolve |
| 213869457675324891849715236528136749967542318431987625794258163352671984186493572 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) A3: 4,8 I2: 1,8 A5: 7,9 A6: 4,8 F4: 6,8 F5: 2,8 H4: 4,6 A7: 5,7 B8: 4,5 F8: 1,6 G9: 4,5 I9: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C5,C6: 1.. / C5 = 1 => 21 pairs (_) / C6 = 1 => 12 pairs (_) F7,F8: 1.. / F7 = 1 => 0 pairs (X) / F8 = 1 => 11 pairs (_) D2,E2: 2.. / D2 = 2 => 0 pairs (X) / E2 = 2 => 11 pairs (_) H7,I9: 2.. / H7 = 2 => 0 pairs (X) / I9 = 2 => 11 pairs (_) E6,H6: 2.. / E6 = 2 => 0 pairs (X) / H6 = 2 => 11 pairs (_) D9,I9: 2.. / D9 = 2 => 0 pairs (X) / I9 = 2 => 11 pairs (_) F5,F7: 2.. / F5 = 2 => 10 pairs (_) / F7 = 2 => 13 pairs (_) I5,I9: 2.. / I5 = 2 => 0 pairs (X) / I9 = 2 => 11 pairs (_) C1,C2: 3.. / C1 = 3 => 15 pairs (_) / C2 = 3 => 12 pairs (_) G5,H5: 3.. / G5 = 3 => 13 pairs (_) / H5 = 3 => 12 pairs (_) D3,H3: 3.. / D3 = 3 => 12 pairs (_) / H3 = 3 => 13 pairs (_) A3,A6: 4.. / A3 = 4 => 11 pairs (_) / A6 = 4 => 19 pairs (_) A4,C4: 5.. / A4 = 5 => 10 pairs (_) / C4 = 5 => 15 pairs (_) D5,E5: 5.. / D5 = 5 => 15 pairs (_) / E5 = 5 => 12 pairs (_) A4,A7: 5.. / A4 = 5 => 10 pairs (_) / A7 = 5 => 15 pairs (_) E5,E7: 5.. / E5 = 5 => 12 pairs (_) / E7 = 5 => 15 pairs (_) H1,H7: 5.. / H1 = 5 => 12 pairs (_) / H7 = 5 => 15 pairs (_) F4,E6: 6.. / F4 = 6 => 11 pairs (_) / E6 = 6 => 0 pairs (X) B2,B3: 7.. / B2 = 7 => 13 pairs (_) / B3 = 7 => 11 pairs (_) D2,D3: 7.. / D2 = 7 => 11 pairs (_) / D3 = 7 => 13 pairs (_) G4,G5: 7.. / G4 = 7 => 13 pairs (_) / G5 = 7 => 15 pairs (_) A7,C7: 7.. / A7 = 7 => 10 pairs (_) / C7 = 7 => 15 pairs (_) B2,D2: 7.. / B2 = 7 => 13 pairs (_) / D2 = 7 => 11 pairs (_) B3,D3: 7.. / B3 = 7 => 11 pairs (_) / D3 = 7 => 13 pairs (_) C7,B9: 8.. / C7 = 8 => 14 pairs (_) / B9 = 8 => 12 pairs (_) B9,D9: 8.. / B9 = 8 => 12 pairs (_) / D9 = 8 => 14 pairs (_) A3,A6: 8.. / A3 = 8 => 19 pairs (_) / A6 = 8 => 11 pairs (_) A4,A5: 9.. / A4 = 9 => 13 pairs (_) / A5 = 9 => 12 pairs (_) G8,I8: 9.. / G8 = 9 => 12 pairs (_) / I8 = 9 => 0 pairs (X) * DURATION: 0:00:27.621031 START: 05:40:58.095054 END: 05:41:25.716085 2019-05-01 * CP COUNT: (29) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,A6,A7,B8,F4,F5,F8,G9,H4,I2,I9) * 2....9..76....4.9...9..52...2.13.....6........3.9.7..5.9......33.2.7..8.1.6.93.7. * PAIR A3: 4,8 BLK 1 B1: 4,8,1,5 # reduction candidate for 4,8 B1: 4,8 # 16 pairs C1: 4,8,3,5 # reduction candidate for 4,8 C1: 4,8 # 17 pairs B3: 4,8,1,7 # reduction candidate for 4,8 B3: 4,8 # 18 pairs * PAIR A3: 4,8 ROW 3 I3: 4,8,1,6 # reduction candidate for 4,8 I3: 4,8 # 15 pairs I3: 1,6 # 13 pairs * PAIR I2: 1,8 BLK 3 G1: 1,8,3,4,5,6 # reduction candidate for 1,8 G1: 1,8 # 15 pairs G2: 1,8,3,5 # reduction candidate for 1,8 G2: 1,8 # 16 pairs I3: 1,8,4,6 # reduction candidate for 1,8 I3: 1,8 # 14 pairs * PAIR I2: 1,8 ROW 2 B2: 1,8,5,7 # reduction candidate for 1,8 B2: 1,8 # 14 pairs E2: 1,8,2 # reduction candidate for 1,8 E2: 1,8 => CTR * 2.53.9..76732.459...97.523.52.136749967458321431927865794....533.2.7.98.1.6.93472 E2: 2 # 11 pairs * PAIR I2: 1,8 COL I I5: 1,8,2,4,9 # reduction candidate for 1,8 I5: 1,8 # 13 pairs I5: 2,4,9 # 12 pairs * PAIR A5: 7,9 BLK 4 A4: 7,9,5 # reduction candidate for 7,9 A4: 7,9 # 15 pairs A4: 5 # 10 pairs * PAIR A5: 7,9 ROW 5 G5: 7,9,1,3,4,8 # reduction candidate for 7,9 G5: 7,9 # 16 pairs G5: 1,3,4,8 # 13 pairs * PAIR A6: 4,8 BLK 4 C4: 4,8,5,7 # reduction candidate for 4,8 C4: 4,8 # 11 pairs C5: 4,8,1,7 # reduction candidate for 4,8 C5: 4,8 # 16 pairs C6: 4,8,1 # reduction candidate for 4,8 C6: 4,8 # 21 pairs * PAIR A6: 4,8 ROW 6 E6: 4,8,2,6 # reduction candidate for 4,8 E6: 4,8 # 15 pairs G6: 4,8,1,6 # reduction candidate for 4,8 G6: 4,8 # 20 pairs * PAIR F4: 6,8 BLK 5 E6: 6,8,2,4 # reduction candidate for 6,8 E6: 6,8 # 15 pairs E6: 2,4 # 12 pairs * PAIR F4: 6,8 ROW 4 G4: 6,8,4,7,9 # reduction candidate for 6,8 G4: 6,8 # 16 pairs I4: 6,8,4,9 # reduction candidate for 6,8 I4: 6,8 # 14 pairs * PAIR F4: 6,8 COL F F7: 6,8,1,2 # reduction candidate for 6,8 F7: 1,2 # 13 pairs F7: 6,8 # 10 pairs * PAIR F5: 2,8 BLK 5 D5: 2,8,4,5 # reduction candidate for 2,8 D5: 2,8 => CTR * 2....94576....4.9.4.9..52.6.2.136.4..64258...831947625.984.2..33.2.71.84146893572 D5: 4,5 # 13 pairs E5: 2,8,4,5 # reduction candidate for 2,8 E5: 2,8 => CTR * 2.36.9.576....4.9.4.9..52..52.136.4.9645..731831947625798.5...33.2.71.84146893572 E5: 4,5 # 13 pairs E6: 2,8,4,6 # reduction candidate for 2,8 E6: 2,8 # 16 pairs * PAIR F5: 2,8 ROW 5 I5: 2,8,1,4,9 # reduction candidate for 2,8 I5: 2,8 # 18 pairs I5: 1,4,9 # 11 pairs * PAIR F5: 2,8 COL F F7: 2,8,1,6 # reduction candidate for 2,8 F7: 1,6 => CTR * 2....9..76...24.9.4.9..52.6527138964961..27388349671257982...133.2.7..891.6893.72 F7: 2,8 # 11 pairs * PAIR H4: 4,6 BLK 6 G4: 4,6,7,8,9 # reduction candidate for 4,6 G4: 4,6 => CTR * 2..6.9..76..724.9..793.5264.2.13864996...273.43.967.25.982.6..33.2.719861.6893.72 G4: 7,8,9 # 12 pairs I4: 4,6,8,9 # reduction candidate for 4,6 I4: 4,6 => CTR * 2....9..76...24.914.93.526..271389..961..27388349671257982....33.2.7.6891.6893.72 I4: 8,9 # 13 pairs G6: 4,6,1,8 # reduction candidate for 4,6 G6: 4,6 # 15 pairs H6: 4,6,1,2 # reduction candidate for 4,6 H6: 4,6 => CTR * 2..3.9.17673214598.197.5234528136749967.58321431927865794..215335247198.1.6.93472 H6: 1,2 # 13 pairs * PAIR H4: 4,6 COL H H1: 4,6,1,3,5 # reduction candidate for 4,6 H1: 4,6 # 18 pairs H3: 4,6,1,3 # reduction candidate for 4,6 H3: 4,6 # 15 pairs H7: 4,6,1,2,5 # reduction candidate for 4,6 H7: 4,6 # 18 pairs * PAIR A7: 5,7 BLK 7 C7: 5,7,4,8 # reduction candidate for 5,7 C7: 5,7 # 15 pairs C7: 4,8 # 13 pairs * PAIR A7: 5,7 COL A A4: 5,7,9 # reduction candidate for 5,7 A4: 9 # 13 pairs A4: 5,7 # 12 pairs * PAIR B8: 4,5 BLK 7 C7: 4,5,7,8 # reduction candidate for 4,5 C7: 4,5 # 11 pairs B9: 4,5,8 # reduction candidate for 4,5 B9: 4,5 # 14 pairs * PAIR B8: 4,5 ROW 8 D8: 4,5,6 # reduction candidate for 4,5 D8: 4,5 # 13 pairs G8: 4,5,1,6,9 # reduction candidate for 4,5 G8: 4,5 => CTR * 2....9..76....4.91..9..52.6.2.136.48.6......2.3.927..5.9...2..33.2671.891.6.93.74 G8: 1,6,9 # 12 pairs * PAIR B8: 4,5 COL B B1: 4,5,1,8 # reduction candidate for 4,5 B1: 4,5 # 15 pairs B1: 1,8 # 13 pairs * PAIR F8: 1,6 BLK 8 F7: 1,6,2,8 # reduction candidate for 1,6 F7: 1,6 => CTR * 2....9..76...24.9.4.9..52.6527138964961..27388349671257982...133.2.7..891.6893.72 F7: 2,8 # 11 pairs * PAIR F8: 1,6 ROW 8 G8: 1,6,4,5,9 # reduction candidate for 1,6 G8: 1,6 => CTR * 2..6.9..76..724.9..793.52...271389..96...27388349671257982...133.2.716891.6893.72 G8: 4,5,9 # 12 pairs I8: 1,6,4,9 # reduction candidate for 1,6 I8: 1,6 # 14 pairs * PAIR G9: 4,5 BLK 9 G7: 4,5,1,6 # reduction candidate for 4,5 G7: 4,5 => CTR * 2....9.576....4.9.8.9..52...2.13.....6.......43.9.7..5.9......33.2.7..8.186.93.72 G7: 1,6 # 13 pairs H7: 4,5,1,2,6 # reduction candidate for 4,5 H7: 4,5 # 14 pairs G8: 4,5,1,6,9 # reduction candidate for 4,5 G8: 4,5 => CTR * 2....9..76....4.91..9..52.6.2.136.48.6......2.3.927..5.9...2..33.2671.891.6.93.74 G8: 1,6,9 # 12 pairs * PAIR G9: 4,5 ROW 9 B9: 4,5,8 # reduction candidate for 4,5 B9: 4,5 # 14 pairs D9: 4,5,2,8 # reduction candidate for 4,5 D9: 4,5 # 12 pairs * PAIR G9: 4,5 COL G G1: 4,5,1,3,6,8 # reduction candidate for 4,5 G1: 4,5 # 14 pairs G1: 1,3,6,8 # 12 pairs * PAIR I9: 2,4 BLK 9 H7: 2,4,1,5,6 # reduction candidate for 2,4 H7: 2,4 # 15 pairs H7: 1,5,6 # 11 pairs * PAIR I9: 2,4 ROW 9 D9: 2,4,5,8 # reduction candidate for 2,4 D9: 2,4 # 13 pairs D9: 5,8 # 12 pairs * PAIR I9: 2,4 COL I I5: 2,4,1,8,9 # reduction candidate for 2,4 I5: 2,4 => CTR * 2....9..76....4.9...9..52...2.136.4..6......2.3.927..5.9...2..33.2.71.8.1.6.93.74 I5: 1,8,9 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190429-absurd-base-pr-000.dot * REASONING * DIS # E2: 1,8 => CTR => E2: 2 * DIS # D5: 2,8 => CTR => D5: 4,5 * DIS # E5: 2,8 => CTR => E5: 4,5 * DIS # F7: 1,6 => CTR => F7: 2,8 * DIS # G4: 4,6 => CTR => G4: 7,8,9 * DIS # I4: 4,6 => CTR => I4: 8,9 * DIS # H6: 4,6 => CTR => H6: 1,2 * DIS # G8: 4,5 => CTR => G8: 1,6,9 * DIS # F7: 1,6 => CTR => F7: 2,8 * DIS # G8: 1,6 => CTR => G8: 4,5,9 * DIS # G7: 4,5 => CTR => G7: 1,6 * DIS # G8: 4,5 => CTR => G8: 1,6,9 * DIS # I5: 2,4 => CTR => I5: 1,8,9 * CNT 13 HDP CHAINS / 78 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,A6,A7,B8,F4,F5,F8,G9,H4,I2,I9) * 2....9..76....4.9...9..52...2.13.....6........3.9.7..5.9......33.2.7..8.1.6.93.7. * PAIR A3: 4,8 BLK 1 B1: 4,8,1,5 # reduction candidate for 4,8 B1: 4,8 # 16 pairs C1: 4,8,3,5 # reduction candidate for 4,8 C1: 4,8 # 17 pairs B3: 4,8,1,7 # reduction candidate for 4,8 B3: 4,8 # 18 pairs * PAIR A3: 4,8 ROW 3 I3: 4,8,1,6 # reduction candidate for 4,8 I3: 4,8 # 15 pairs I3: 1,6 # 13 pairs * PAIR I2: 1,8 BLK 3 G1: 1,8,3,4,5,6 # reduction candidate for 1,8 G1: 1,8 # 15 pairs G2: 1,8,3,5 # reduction candidate for 1,8 G2: 1,8 # 16 pairs I3: 1,8,4,6 # reduction candidate for 1,8 I3: 1,8 # 14 pairs * PAIR I2: 1,8 ROW 2 B2: 1,8,5,7 # reduction candidate for 1,8 B2: 1,8 # 14 pairs E2: 1,8,2 # reduction candidate for 1,8 E2: 1,8 => CTR * 2.53.9..76732.459...97.523.52.136749967458321431927865794....533.2.7.98.1.6.93472 * RESTART * PAIR I2: 1,8 ROW 2 B2: 1,8,5,7 # reduction candidate for 1,8 B2: 1,8 # 14 pairs B2: 5,7 # 12 pairs * PAIR I2: 1,8 COL I I5: 1,8,4,9 # reduction candidate for 1,8 I5: 1,8 # 13 pairs I5: 4,9 # 12 pairs * PAIR RESTART * PAIR I2: 1,8 BLK 3 G1: 1,8,3,4,5,6 # reduction candidate for 1,8 G1: 1,8 # 14 pairs G2: 1,8,3,5 # reduction candidate for 1,8 G2: 1,8 # 16 pairs I3: 1,8,4,6 # reduction candidate for 1,8 I3: 1,8 => CTR * 2....96476..72459.8.96.523..2.13876..6...231..31967825.9.2.61.33.2.719861.6.93472 * PAIR I2: 1,8 ROW 2 B2: 1,8,5,7 # reduction candidate for 1,8 B2: 1,8 # 15 pairs B2: 5,7 # 13 pairs * PAIR I2: 1,8 COL I I5: 1,8,4,9 # reduction candidate for 1,8 I5: 4,9 # 13 pairs I5: 1,8 # 13 pairs * PAIR RESTART * PAIR I2: 1,8 BLK 3 G1: 1,8,3,4,5,6 # reduction candidate for 1,8 G1: 1,8 # 14 pairs G2: 1,8,3,5 # reduction candidate for 1,8 G2: 1,8 # 16 pairs * PAIR I2: 1,8 ROW 2 B2: 1,8,5,7 # reduction candidate for 1,8 B2: 1,8 # 15 pairs B2: 5,7 # 13 pairs * PAIR I2: 1,8 COL I I5: 1,8,4,9 # reduction candidate for 1,8 I5: 4,9 # 13 pairs I5: 1,8 # 13 pairs * PAIR A5: 7,9 BLK 4 A4: 7,9,5 # reduction candidate for 7,9 A4: 7,9 # 16 pairs A4: 5 # 10 pairs * PAIR A5: 7,9 ROW 5 G5: 7,9,1,3,4,8 # reduction candidate for 7,9 G5: 7,9 # 16 pairs G5: 1,3,4,8 # 13 pairs * PAIR A6: 4,8 BLK 4 C4: 4,8,5,7 # reduction candidate for 4,8 C4: 4,8 # 11 pairs C5: 4,8,1,7 # reduction candidate for 4,8 C5: 4,8 # 17 pairs C6: 4,8,1 # reduction candidate for 4,8 C6: 4,8 => CTR * 2..6.9..76..724.914793.52...27138...961..27388349671257982....33.2.7..8.1.6893.72 * PAIR A6: 4,8 ROW 6 E6: 4,8,6 # reduction candidate for 4,8 E6: 4,8 # 15 pairs G6: 4,8,6 # reduction candidate for 4,8 G6: 4,8 => CTR * 2.4..9..76...24.9...9..52...2.138....67..2...8319674257982...433.247..8.146893572 * RESTART * PAIR RESTART * PAIR A6: 4,8 BLK 4 C5: 4,8,7 # reduction candidate for 4,8 C5: 7 => SOLVED * 213869457675324891849715236528136749967542318431987625794258163352671984186493572 * DURATION: 0:00:21.940719 START: 05:42:05.925183 END: 05:42:27.865902 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190429-absurd-base-pr-001.dot * REASONING * DIS # E2: 1,8 => CTR => E2: 2 * DIS E2: 2 # I3: 1,8 => CTR => I3: 4,6 * DIS E2: 2 + I3: 4,6 # C6: 4,8 => CTR => C6: 1 * DIS E2: 2 + I3: 4,6 + C6: 1 # G6: 4,8 => CTR => G6: 6 * PRF E2: 2 + I3: 4,6 + C6: 1 + G6: 6 # C5: 7 => SOL * STA E2: 2 + I3: 4,6 + C6: 1 + G6: 6 + C5: 7 * CNT 5 HDP CHAINS / 38 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190429, absurd
Solution
position: 213869457675324891849715236528136749967542318431987625794258163352671984186493572 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 # B1: 4,8 => UNS * INC # C1: 4,8 => UNS * INC # B3: 4,8 => UNS * INC # I3: 4,8 => UNS * INC # I3: 1,6 => UNS * INC # G1: 1,8 => UNS * INC # G2: 1,8 => UNS * INC # I3: 1,8 => UNS * INC # B2: 1,8 => UNS * DIS # E2: 1,8 => CTR => E2: 2 * INC # E2: 2 => UNS * INC # I5: 1,8 => UNS * INC # I5: 2,4,9 => UNS * INC # A4: 7,9 => UNS * INC # A4: 5 => UNS * INC # G5: 7,9 => UNS * INC # G5: 1,3,4,8 => UNS * INC # C4: 4,8 => UNS * INC # C5: 4,8 => UNS * INC # C6: 4,8 => UNS * INC # E6: 4,8 => UNS * INC # G6: 4,8 => UNS * INC # E6: 6,8 => UNS * INC # E6: 2,4 => UNS * INC # G4: 6,8 => UNS * INC # I4: 6,8 => UNS * INC # F7: 6,8 => UNS * INC # F7: 1,2 => UNS * DIS # D5: 2,8 => CTR => D5: 4,5 * INC # D5: 4,5 => UNS * DIS # E5: 2,8 => CTR => E5: 4,5 * INC # E5: 4,5 => UNS * INC # E6: 2,8 => UNS * INC # I5: 2,8 => UNS * INC # I5: 1,4,9 => UNS * INC # F7: 2,8 => UNS * DIS # F7: 1,6 => CTR => F7: 2,8 * DIS # G4: 4,6 => CTR => G4: 7,8,9 * INC # G4: 7,8,9 => UNS * DIS # I4: 4,6 => CTR => I4: 8,9 * INC # I4: 8,9 => UNS * INC # G6: 4,6 => UNS * DIS # H6: 4,6 => CTR => H6: 1,2 * INC # H6: 1,2 => UNS * INC # H1: 4,6 => UNS * INC # H3: 4,6 => UNS * INC # H7: 4,6 => UNS * INC # C7: 5,7 => UNS * INC # C7: 4,8 => UNS * INC # A4: 5,7 => UNS * INC # A4: 9 => UNS * INC # C7: 4,5 => UNS * INC # B9: 4,5 => UNS * INC # D8: 4,5 => UNS * DIS # G8: 4,5 => CTR => G8: 1,6,9 * INC # G8: 1,6,9 => UNS * INC # B1: 4,5 => UNS * INC # B1: 1,8 => UNS * DIS # F7: 1,6 => CTR => F7: 2,8 * INC # F7: 2,8 => UNS * DIS # G8: 1,6 => CTR => G8: 4,5,9 * INC # G8: 4,5,9 => UNS * INC # I8: 1,6 => UNS * DIS # G7: 4,5 => CTR => G7: 1,6 * INC # G7: 1,6 => UNS * INC # H7: 4,5 => UNS * DIS # G8: 4,5 => CTR => G8: 1,6,9 * INC # G8: 1,6,9 => UNS * INC # B9: 4,5 => UNS * INC # D9: 4,5 => UNS * INC # G1: 4,5 => UNS * INC # G1: 1,3,6,8 => UNS * INC # H7: 2,4 => UNS * INC # H7: 1,5,6 => UNS * INC # D9: 2,4 => UNS * INC # D9: 5,8 => UNS * DIS # I5: 2,4 => CTR => I5: 1,8,9 * INC # I5: 1,8,9 => UNS * CNT 78 HDP CHAINS / 78 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 4,8 => UNS * INC # C1: 4,8 => UNS * INC # B3: 4,8 => UNS * INC # I3: 4,8 => UNS * INC # I3: 1,6 => UNS * INC # G1: 1,8 => UNS * INC # G2: 1,8 => UNS * INC # I3: 1,8 => UNS * INC # B2: 1,8 => UNS * DIS # E2: 1,8 => CTR => E2: 2 * INC E2: 2 # B2: 1,8 => UNS * INC E2: 2 # B2: 5,7 => UNS * INC E2: 2 # I5: 1,8 => UNS * INC E2: 2 # I5: 4,9 => UNS * INC E2: 2 # G1: 1,8 => UNS * INC E2: 2 # G2: 1,8 => UNS * DIS E2: 2 # I3: 1,8 => CTR => I3: 4,6 * INC E2: 2 + I3: 4,6 # B2: 1,8 => UNS * INC E2: 2 + I3: 4,6 # B2: 5,7 => UNS * INC E2: 2 + I3: 4,6 # I5: 1,8 => UNS * INC E2: 2 + I3: 4,6 # I5: 4,9 => UNS * INC E2: 2 + I3: 4,6 # G1: 1,8 => UNS * INC E2: 2 + I3: 4,6 # G2: 1,8 => UNS * INC E2: 2 + I3: 4,6 # B2: 1,8 => UNS * INC E2: 2 + I3: 4,6 # B2: 5,7 => UNS * INC E2: 2 + I3: 4,6 # I5: 1,8 => UNS * INC E2: 2 + I3: 4,6 # I5: 4,9 => UNS * INC E2: 2 + I3: 4,6 # A4: 7,9 => UNS * INC E2: 2 + I3: 4,6 # A4: 5 => UNS * INC E2: 2 + I3: 4,6 # G5: 7,9 => UNS * INC E2: 2 + I3: 4,6 # G5: 1,3,4,8 => UNS * INC E2: 2 + I3: 4,6 # C4: 4,8 => UNS * INC E2: 2 + I3: 4,6 # C5: 4,8 => UNS * DIS E2: 2 + I3: 4,6 # C6: 4,8 => CTR => C6: 1 * INC E2: 2 + I3: 4,6 + C6: 1 # E6: 4,8 => UNS * DIS E2: 2 + I3: 4,6 + C6: 1 # G6: 4,8 => CTR => G6: 6 * INC E2: 2 + I3: 4,6 + C6: 1 + G6: 6 # C5: 4,8 => UNS * PRF E2: 2 + I3: 4,6 + C6: 1 + G6: 6 # C5: 7 => SOL * STA E2: 2 + I3: 4,6 + C6: 1 + G6: 6 + C5: 7 * CNT 38 HDP CHAINS / 38 HYP OPENED