Analysis of xx-top95-039-base.sdk
Contents
Original Sudoku
level: medium
position: 249.6...3.3....2..8.......5.....6......2......1..4.82..9.5..7....4.....1.7...3... initial
Autosolve
position: 249.651.3.3....2..86......5.2...6....8.2......1..4.82..9.5..7...54.....1.7...3... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 5,7 => CTR => C2: 1 * DIS # A6: 9 => CTR => A6: 5,7 * DIS # C2: 5 => CTR => C2: 1,7 * DIS # E3: 1,7 => CTR => E3: 2,3,9 * DIS # F3: 1,7 => CTR => F3: 2,4,9 * DIS # D2: 7,8 => CTR => D2: 1,4,9 * DIS # F2: 7,8 => CTR => F2: 1,4,9 * PRF # D4: 7,8 => SOL * DIS # D4: 1,3,9 => CTR => D4: 7,8 * DIS # D8: 7,8 => CTR => D8: 6,9 * PRF # D8: 6,9 => SOL * DIS # H2: 7,8 => CTR => H2: 4,6,9 * DIS # H2: 4,9 => CTR => H2: 6,7,8 * DIS # I2: 4,9 => CTR => I2: 6,7,8 * DIS # D3: 4,9 => CTR => D3: 1,3,7 * DIS # F3: 4,9 => CTR => F3: 1,2,7 * DIS # G5: 4,9 => CTR => G5: 3,5,6 * DIS # C5: 3,7 => CTR => C5: 6 * DIS # C6: 3,7 => CTR => C6: 5,6 * PRF # D4: 3,7 => SOL * DIS # E4: 3,7 => CTR => E4: 1,5,8,9 * DIS # H4: 3,7 => CTR => H4: 1,4,5,9 * PRF # D4: 7,9 => SOL * DIS # E4: 7,9 => CTR => E4: 1,3,5,8 * DIS # E5: 7,9 => CTR => E5: 1,3,5 * DIS # F5: 7,9 => CTR => F5: 1 * DIS # D6: 7,9 => CTR => D6: 3 * DIS # I6: 7,9 => CTR => I6: 6 * DIS # F3: 7,9 => CTR => F3: 1,2,4 * PRF # I7: 4,6 => SOL * DIS # A7: 1 => CTR => A7: 3,6 * DIS # H8: 3,6 => CTR => H8: 8,9 * DIS # A7: 3 => CTR => A7: 1,6 * PRF # D9: 4,8,9 => SOL * DIS # I9: 4,6,9 => CTR => I9: 2,8 * PRF # F7: 1,8 => SOL * DIS # D9: 1,8 => CTR => D9: 4,6,9 * DIS # E9: 1,8 => CTR => E9: 9 * DIS # E2: 1,8 => CTR => E2: 7,9 * PRF # E4: 1,8 => SOL * DIS # E4: 3,5,7,9 => CTR => E4: 1,8 * CNT 41 HDP CHAINS / 86 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 5,7 => CTR => C2: 1 * DIS C2: 1 # D2: 7,8 => CTR => D2: 4,9 * DIS C2: 1 + D2: 4,9 # F2: 7,8 => CTR => F2: 4,9 * PRF C2: 1 + D2: 4,9 + F2: 4,9 # D4: 7,8 => SOL * STA C2: 1 + D2: 4,9 + F2: 4,9 + D4: 7,8 * CNT 4 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 249.6...3.3....2..8.......5.....6......2......1..4.82..9.5..7....4.....1.7...3... | initial |
| 249.651.3.3....2..86......5.2...6....8.2......1..4.82..9.5..7...54.....1.7...3... | autosolve |
| 249865173531974268867132495423786519986251347715349826692518734354627981178493652 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) A2: 5,7 C3: 1,7 D1: 7,8 H1: 7,8 G3: 4,9 C4: 3,7 F6: 7,9 C7: 2,8 A8: 3,6 A9: 1,6 C9: 2,8 E7: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,C3: 1.. / C2 = 1 => 13 pairs (_) / C3 = 1 => 0 pairs (X) H4,H5: 1.. / H4 = 1 => 12 pairs (_) / H5 = 1 => 0 pairs (X) A7,A9: 1.. / A7 = 1 => 0 pairs (X) / A9 = 1 => 13 pairs (_) E3,F3: 2.. / E3 = 2 => 0 pairs (X) / F3 = 2 => 12 pairs (_) C7,C9: 2.. / C7 = 2 => 11 pairs (_) / C9 = 2 => 11 pairs (_) E8,F8: 2.. / E8 = 2 => 12 pairs (_) / F8 = 2 => 0 pairs (X) I7,I9: 2.. / I7 = 2 => 11 pairs (_) / I9 = 2 => 11 pairs (_) C7,I7: 2.. / C7 = 2 => 11 pairs (_) / I7 = 2 => 11 pairs (_) C9,I9: 2.. / C9 = 2 => 11 pairs (_) / I9 = 2 => 11 pairs (_) E3,E8: 2.. / E3 = 2 => 0 pairs (X) / E8 = 2 => 12 pairs (_) F3,F8: 2.. / F3 = 2 => 12 pairs (_) / F8 = 2 => 0 pairs (X) D3,E3: 3.. / D3 = 3 => 0 pairs (X) / E3 = 3 => 12 pairs (_) A7,A8: 3.. / A7 = 3 => 0 pairs (X) / A8 = 3 => 13 pairs (_) C6,D6: 3.. / C6 = 3 => 0 pairs (X) / D6 = 3 => 12 pairs (_) A7,H7: 3.. / A7 = 3 => 0 pairs (X) / H7 = 3 => 13 pairs (_) A4,A5: 4.. / A4 = 4 => 14 pairs (_) / A5 = 4 => 13 pairs (_) F7,D9: 4.. / F7 = 4 => 12 pairs (_) / D9 = 4 => 0 pairs (*) A2,C2: 5.. / A2 = 5 => 13 pairs (_) / C2 = 5 => 0 pairs (X) A6,C6: 5.. / A6 = 5 => 0 pairs (X) / C6 = 5 => 13 pairs (_) E4,E5: 5.. / E4 = 5 => 0 pairs (X) / E5 = 5 => 12 pairs (_) G9,H9: 5.. / G9 = 5 => 16 pairs (_) / H9 = 5 => 12 pairs (_) A2,A6: 5.. / A2 = 5 => 13 pairs (_) / A6 = 5 => 0 pairs (X) C2,C6: 5.. / C2 = 5 => 0 pairs (X) / C6 = 5 => 13 pairs (_) H2,I2: 6.. / H2 = 6 => 12 pairs (_) / I2 = 6 => 0 pairs (X) C5,C6: 6.. / C5 = 6 => 13 pairs (_) / C6 = 6 => 0 pairs (X) D8,D9: 6.. / D8 = 6 => 0 pairs (*) / D9 = 6 => 0 pairs (X) C6,I6: 6.. / C6 = 6 => 0 pairs (X) / I6 = 6 => 13 pairs (_) D1,H1: 7.. / D1 = 7 => 0 pairs (X) / H1 = 7 => 0 pairs (_) D4,E4: 8.. / D4 = 8 => 0 pairs (X) / E4 = 8 => 0 pairs (_) C7,C9: 8.. / C7 = 8 => 11 pairs (_) / C9 = 8 => 11 pairs (_) D1,H1: 8.. / D1 = 8 => 0 pairs (*) / H1 = 8 => 0 pairs (X) * DURATION: 0:00:49.901207 START: 23:34:02.666315 END: 23:34:52.567522 2017-05-03 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,A9,C3,C4,C7,C9,D1,E7,F6,G3,H1) * 249.651.3.3....2..86......5.2...6....8.2......1..4.82..9.5..7...54.....1.7...3... * PAIR A2: 5,7 BLK 1 C2: 5,7,1 # reduction candidate for 5,7 C2: 5,7 => CTR * 249765183.3....2..861....75.2.8.6.1..8.2.1....1..4.82..9.5..7...54..8..1.7...3... C2: 1 # 13 pairs * PAIR A2: 5,7 COL A A6: 5,7,9 # reduction candidate for 5,7 A6: 9 => CTR * 249865173531479268867132..5.23986.1..862513..91534782669.51473235472869117.6.3... A6: 5,7 # 15 pairs * PAIR C3: 1,7 BLK 1 C2: 1,7,5 # reduction candidate for 1,7 C2: 5 => CTR * 249765183735...2..861....75.2.8.6.1..8.2.1...51..4.82..9.5..7...54..8..1.7...3... C2: 1,7 # 13 pairs * PAIR C3: 1,7 ROW 3 D3: 1,7,3,4,9 # reduction candidate for 1,7 D3: 1,7 # 14 pairs E3: 1,7,2,3,9 # reduction candidate for 1,7 E3: 1,7 => CTR * 249865173735...268861372..5.27.8635..862.....513.4.82669.5..73.354.2...117...3... E3: 2,3,9 # 12 pairs F3: 1,7,2,4,9 # reduction candidate for 1,7 F3: 1,7 => CTR * 249865173735...268861327..5.271.6....862.....51374982669.5..73.354.72..117...3... F3: 2,4,9 # 12 pairs * PAIR D1: 7,8 BLK 2 D2: 7,8,1,4,9 # reduction candidate for 7,8 D2: 7,8 => CTR * 249.651.3.3....2..86......5.2...6....8.2......1..4.82..9.5..7...54.....1.7...3... D2: 1,4,9 # 12 pairs E2: 7,8,1,9 # reduction candidate for 7,8 E2: 7,8 # 17 pairs F2: 7,8,1,4,9 # reduction candidate for 7,8 F2: 7,8 => CTR * 249765183.3...82..86......5.2.8.6.1..8.2.1....1..4.82..9.5.47...54.....1.7...3... F2: 1,4,9 # 17 pairs * PAIR D1: 7,8 COL D D4: 7,8,1,3,9 # reduction candidate for 7,8 D4: 7,8 => SOLVED * 249865173531974268867132495423786519986251347715349826692518734354627981178493652 D4: 1,3,9 => CTR * 249865173531.7.268867132..5.23986.1..86251..991534782669.514732.54728..117.693... D8: 7,8,6,9 # reduction candidate for 7,8 D8: 7,8 => CTR * 249865173531.79268867132945.23986.1..862513...1534.826.9.5147...5472869117.693... D8: 6,9 => SOLVED * 249865173531974268867132495423786519986251347715349826692518734354627981178493652 * PAIR H1: 7,8 BLK 3 H2: 7,8,4,6,9 # reduction candidate for 7,8 H2: 7,8 => CTR * 249865173735...286861732..5.2..86....8.2.....51634.82..9.5..7...54.2...1.7...3... H2: 4,6,9 # 12 pairs I2: 7,8,4,6,9 # reduction candidate for 7,8 I2: 7,8 # 14 pairs * PAIR G3: 4,9 BLK 3 H2: 4,9,6,7,8 # reduction candidate for 4,9 H2: 4,9 => CTR * 249765183735...2.6861.32.75.2...6....8.2.....516349827.9.5..7...54827..1.7.693... H2: 6,7,8 # 12 pairs I2: 4,9,6,7,8 # reduction candidate for 4,9 I2: 4,9 => CTR * 249765183.3..8.26.861....75.2.8.6.1..8.2.1....1..4.82.69.51473.3546...9117..93... I2: 6,7,8 # 12 pairs H3: 4,9,7 # reduction candidate for 4,9 H3: 4,9 # 13 pairs * PAIR G3: 4,9 ROW 3 D3: 4,9,1,3,7 # reduction candidate for 4,9 D3: 4,9 => CTR * 249765183.3...82..861.32.75.2..86....8.2......1..4982..9.5..7...54827..1.7.693... D3: 1,3,7 # 12 pairs F3: 4,9,1,2,7 # reduction candidate for 4,9 F3: 4,9 => CTR * 249765183735...26.86132..75.27..6....862.1..751394782669.51.73.354872.9117..93... F3: 1,2,7 # 12 pairs * PAIR G3: 4,9 COL G G4: 4,9,3,5 # reduction candidate for 4,9 G4: 4,9 # 17 pairs G5: 4,9,3,5,6 # reduction candidate for 4,9 G5: 4,9 => CTR * 2497651837351..26486143297542785631998327145651634982.69.51473.354...6.117.6.35.. G5: 3,5,6 # 12 pairs G9: 4,9,5,6 # reduction candidate for 4,9 G9: 4,9 # 16 pairs * PAIR C4: 3,7 BLK 4 C5: 3,7,6 # reduction candidate for 3,7 C5: 3,7 => CTR * 249.651.3735...2..861.32..5.2.8.6.1..8.2.1...516349827.9.5..7...54.27.81.7...3... C5: 6 # 13 pairs C6: 3,7,5,6 # reduction candidate for 3,7 C6: 3,7 => CTR * 2497651837351..26.861....75.2.8.6.1..862.1...51..4.82669.51.73.354..8.9117...3... C6: 5,6 # 13 pairs * PAIR C4: 3,7 ROW 4 D4: 3,7,1,8,9 # reduction candidate for 3,7 D4: 3,7 => SOLVED * 249865173531974268867132495423786519986251347715349826692518734354627981178493652 D4: 1,8,9 # 12 pairs E4: 3,7,1,5,8,9 # reduction candidate for 3,7 E4: 3,7 => CTR * 249765183.3....2..86......5.2.8.651..8.251....1..4.82..9.5147...54.....117..93.5. E4: 1,5,8,9 # 12 pairs H4: 3,7,1,4,5,9 # reduction candidate for 3,7 H4: 3,7 => CTR * 249.651.3.3..7.2..867132..5.23..65...8.25..1..1.34.82..9.5..7...54.28..1.7..93.5. H4: 1,4,5,9 # 12 pairs * PAIR F6: 7,9 BLK 5 D4: 7,9,1,3,8 # reduction candidate for 7,9 D4: 7,9 => SOLVED * 249865173531974268867132495423786519986251347715349826692518734354627981178493652 D4: 1,3,8 # 12 pairs E4: 7,9,1,3,5,8 # reduction candidate for 7,9 E4: 7,9 => CTR * 249765183.3....2..86..32..5.2.8.651..8.251....1.34.82..9.5..7...54.2...1.7...3.5. E4: 1,3,5,8 # 12 pairs E5: 7,9,1,3,5 # reduction candidate for 7,9 E5: 7,9 => CTR * 249765183.3....2..86..32..5.2.856.1..8.271....1.34982..9.5..7...54.2...1.7...3... E5: 1,3,5 # 12 pairs F5: 7,9,1 # reduction candidate for 7,9 F5: 7,9 => CTR * 249.651.3.3..7.2..867132..5.238.6....8.2......1.34.82..9.5..7...54.28..1.7...3... F5: 1 # 13 pairs D6: 7,9,3 # reduction candidate for 7,9 D6: 7,9 => CTR * 2497651837351..26.86132..75.278.6.1..862.1.4751394782669.51.73.354.....117.4.365. D6: 3 # 12 pairs * PAIR F6: 7,9 ROW 6 A6: 7,9,5 # reduction candidate for 7,9 A6: 7,9 # 13 pairs I6: 7,9,6 # reduction candidate for 7,9 I6: 7,9 => CTR * 249.651.3735...2..861.32..5.2.8.6.1..8.2.1...516349827.9.5..7...54.27.81.7...3... I6: 6 # 13 pairs * PAIR F6: 7,9 COL F F2: 7,9,1,4,8 # reduction candidate for 7,9 F2: 7,9 # 23 pairs F3: 7,9,1,2,4 # reduction candidate for 7,9 F3: 7,9 => CTR * 249.651.37351.426.86132...5.278.6.1..862.1..7513.4.82669.518734354.72.81178493652 F3: 1,2,4 # 12 pairs F8: 7,9,2,8 # reduction candidate for 7,9 F8: 7,9 # 15 pairs * PAIR C7: 2,8 ROW 7 I7: 2,8,4,6 # reduction candidate for 2,8 I7: 4,6 => SOLVED * 249865173531974268867132495423786519986251347715349826692518734354627981178493652 I7: 2,8 # 14 pairs * PAIR A8: 3,6 BLK 7 A7: 3,6,1 # reduction candidate for 3,6 A7: 1 => CTR * 249865173.3....26886....495.2...6....8.2..6...1634.82.1925847363546..981678..3542 A7: 3,6 # 13 pairs * PAIR A8: 3,6 ROW 8 G8: 3,6,9 # reduction candidate for 3,6 G8: 3,6 # 14 pairs H8: 3,6,8,9 # reduction candidate for 3,6 H8: 3,6 => CTR * 249.651.3.354.12..861.324.5.2.18635..8325.61.51634.82..9.5147...54.289.117.69354. H8: 8,9 # 13 pairs * PAIR A9: 1,6 BLK 7 A7: 1,6,3 # reduction candidate for 1,6 A7: 3 => CTR * 2497651837351982..861432..5.2...6....8.2.16..51634982739.5147..654.27..117.6.3... A7: 1,6 # 13 pairs * PAIR A9: 1,6 ROW 9 D9: 1,6,4,8,9 # reduction candidate for 1,6 D9: 4,8,9 => SOLVED * 249865173531974268867132495423786519986251347715349826692518734354627981178493652 D9: 1,6 # 14 pairs * PAIR C9: 2,8 ROW 9 I9: 2,8,4,6,9 # reduction candidate for 2,8 I9: 4,6,9 => CTR * 249865173531479268867132945.23.86....8625.....1534.826698514732354728691172693584 I9: 2,8 # 14 pairs * PAIR E7: 1,8 BLK 8 F7: 1,8,4 # reduction candidate for 1,8 F7: 1,8 => SOLVED * 249865173531974268867132495423786519986251347715349826692518734354627981178493652 F7: 4 # 12 pairs D9: 1,8,4,6,9 # reduction candidate for 1,8 D9: 1,8 => CTR * 249865173.3....2.886....495.2..86....8.25.....1..4.82..985147..3546..981.7..93... D9: 4,6,9 # 12 pairs E9: 1,8,9 # reduction candidate for 1,8 E9: 1,8 => CTR * 249.651.3.3...82..86......5.2.8.6.1..8.2.1....1..4.82..9.5.47...54....81.7...3... E9: 9 # 12 pairs * PAIR E7: 1,8 COL E E2: 1,8,7,9 # reduction candidate for 1,8 E2: 1,8 => CTR * 249765183.3....2..86......5.2.8.6.1..8.2.1....1..4.82..9.5..7...546.8..1.7..93... E2: 7,9 # 13 pairs E4: 1,8,3,5,7,9 # reduction candidate for 1,8 E4: 1,8 => SOLVED * 249865173531974268867132495423786519986251347715349826692518734354627981178493652 E4: 3,5,7,9 => CTR * 249765183.3....2..86......5.2.8.6.1..8.2......1..4.82..9.5147...54.....117..93... * INCONCLUSIVE * SAVE PR GRAPH xx-top95-039-base-pr-000.dot * REASONING * DIS # C2: 5,7 => CTR => C2: 1 * DIS # A6: 9 => CTR => A6: 5,7 * DIS # C2: 5 => CTR => C2: 1,7 * DIS # E3: 1,7 => CTR => E3: 2,3,9 * DIS # F3: 1,7 => CTR => F3: 2,4,9 * DIS # D2: 7,8 => CTR => D2: 1,4,9 * DIS # F2: 7,8 => CTR => F2: 1,4,9 * PRF # D4: 7,8 => SOL * DIS # D4: 1,3,9 => CTR => D4: 7,8 * DIS # D8: 7,8 => CTR => D8: 6,9 * PRF # D8: 6,9 => SOL * DIS # H2: 7,8 => CTR => H2: 4,6,9 * DIS # H2: 4,9 => CTR => H2: 6,7,8 * DIS # I2: 4,9 => CTR => I2: 6,7,8 * DIS # D3: 4,9 => CTR => D3: 1,3,7 * DIS # F3: 4,9 => CTR => F3: 1,2,7 * DIS # G5: 4,9 => CTR => G5: 3,5,6 * DIS # C5: 3,7 => CTR => C5: 6 * DIS # C6: 3,7 => CTR => C6: 5,6 * PRF # D4: 3,7 => SOL * DIS # E4: 3,7 => CTR => E4: 1,5,8,9 * DIS # H4: 3,7 => CTR => H4: 1,4,5,9 * PRF # D4: 7,9 => SOL * DIS # E4: 7,9 => CTR => E4: 1,3,5,8 * DIS # E5: 7,9 => CTR => E5: 1,3,5 * DIS # F5: 7,9 => CTR => F5: 1 * DIS # D6: 7,9 => CTR => D6: 3 * DIS # I6: 7,9 => CTR => I6: 6 * DIS # F3: 7,9 => CTR => F3: 1,2,4 * PRF # I7: 4,6 => SOL * DIS # A7: 1 => CTR => A7: 3,6 * DIS # H8: 3,6 => CTR => H8: 8,9 * DIS # A7: 3 => CTR => A7: 1,6 * PRF # D9: 4,8,9 => SOL * DIS # I9: 4,6,9 => CTR => I9: 2,8 * PRF # F7: 1,8 => SOL * DIS # D9: 1,8 => CTR => D9: 4,6,9 * DIS # E9: 1,8 => CTR => E9: 9 * DIS # E2: 1,8 => CTR => E2: 7,9 * PRF # E4: 1,8 => SOL * DIS # E4: 3,5,7,9 => CTR => E4: 1,8 * CNT 41 HDP CHAINS / 86 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,A9,C3,C4,C7,C9,D1,E7,F6,G3,H1) * 249.651.3.3....2..86......5.2...6....8.2......1..4.82..9.5..7...54.....1.7...3... * PAIR A2: 5,7 BLK 1 C2: 5,7,1 # reduction candidate for 5,7 C2: 5,7 => CTR * 249765183.3....2..861....75.2.8.6.1..8.2.1....1..4.82..9.5..7...54..8..1.7...3... * PAIR D1: 7,8 BLK 2 D2: 7,8,4,9 # reduction candidate for 7,8 D2: 7,8 => CTR * 249.651.3531.94268867132..5.23..65...8625.3...1534.8266925..73435462...117.4.3652 E2: 7,8,9 # reduction candidate for 7,8 E2: 7,8 # 20 pairs F2: 7,8,4,9 # reduction candidate for 7,8 F2: 7,8 => CTR * 249.651.3531498267867132..5.238.6....862.13...15349826698514732354.27.8117..83... * RESTART * PAIR D1: 7,8 COL D D4: 7,8,9 # reduction candidate for 7,8 D4: 7,8 => SOLVED * 249865173531974268867132495423786519986251347715349826692518734354627981178493652 * DURATION: 0:00:08.410386 START: 23:36:09.954061 END: 23:36:18.364447 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-039-base-pr-001.dot * REASONING * DIS # C2: 5,7 => CTR => C2: 1 * DIS C2: 1 # D2: 7,8 => CTR => D2: 4,9 * DIS C2: 1 + D2: 4,9 # F2: 7,8 => CTR => F2: 4,9 * PRF C2: 1 + D2: 4,9 + F2: 4,9 # D4: 7,8 => SOL * STA C2: 1 + D2: 4,9 + F2: 4,9 + D4: 7,8 * CNT 4 HDP CHAINS / 5 HYP OPENED
Header Info
Top 95 Sudokus 039 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 249865173531974268867132495423786519986251347715349826692518734354627981178493652 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:
* DIS # C2: 5,7 => CTR => C2: 1 * INC # C2: 1 => UNS * INC # A6: 5,7 => UNS * DIS # A6: 9 => CTR => A6: 5,7 * INC # C2: 1,7 => UNS * DIS # C2: 5 => CTR => C2: 1,7 * INC # D3: 1,7 => UNS * DIS # E3: 1,7 => CTR => E3: 2,3,9 * INC # E3: 2,3,9 => UNS * DIS # F3: 1,7 => CTR => F3: 2,4,9 * INC # F3: 2,4,9 => UNS * DIS # D2: 7,8 => CTR => D2: 1,4,9 * INC # D2: 1,4,9 => UNS * INC # E2: 7,8 => UNS * DIS # F2: 7,8 => CTR => F2: 1,4,9 * INC # F2: 1,4,9 => UNS * PRF # D4: 7,8 => SOL * DIS # D4: 1,3,9 => CTR => D4: 7,8 * DIS # D8: 7,8 => CTR => D8: 6,9 * PRF # D8: 6,9 => SOL * DIS # H2: 7,8 => CTR => H2: 4,6,9 * INC # H2: 4,6,9 => UNS * INC # I2: 7,8 => UNS * DIS # H2: 4,9 => CTR => H2: 6,7,8 * INC # H2: 6,7,8 => UNS * DIS # I2: 4,9 => CTR => I2: 6,7,8 * INC # I2: 6,7,8 => UNS * INC # H3: 4,9 => UNS * DIS # D3: 4,9 => CTR => D3: 1,3,7 * INC # D3: 1,3,7 => UNS * DIS # F3: 4,9 => CTR => F3: 1,2,7 * INC # F3: 1,2,7 => UNS * INC # G4: 4,9 => UNS * DIS # G5: 4,9 => CTR => G5: 3,5,6 * INC # G5: 3,5,6 => UNS * INC # G9: 4,9 => UNS * DIS # C5: 3,7 => CTR => C5: 6 * INC # C5: 6 => UNS * DIS # C6: 3,7 => CTR => C6: 5,6 * INC # C6: 5,6 => UNS * PRF # D4: 3,7 => SOL * INC # D4: 1,8,9 => UNS * DIS # E4: 3,7 => CTR => E4: 1,5,8,9 * INC # E4: 1,5,8,9 => UNS * DIS # H4: 3,7 => CTR => H4: 1,4,5,9 * INC # H4: 1,4,5,9 => UNS * PRF # D4: 7,9 => SOL * INC # D4: 1,3,8 => UNS * DIS # E4: 7,9 => CTR => E4: 1,3,5,8 * INC # E4: 1,3,5,8 => UNS * DIS # E5: 7,9 => CTR => E5: 1,3,5 * INC # E5: 1,3,5 => UNS * DIS # F5: 7,9 => CTR => F5: 1 * INC # F5: 1 => UNS * DIS # D6: 7,9 => CTR => D6: 3 * INC # D6: 3 => UNS * INC # A6: 7,9 => UNS * DIS # I6: 7,9 => CTR => I6: 6 * INC # I6: 6 => UNS * INC # F2: 7,9 => UNS * DIS # F3: 7,9 => CTR => F3: 1,2,4 * INC # F3: 1,2,4 => UNS * INC # F8: 7,9 => UNS * INC # I7: 2,8 => UNS * PRF # I7: 4,6 => SOL * INC # A7: 3,6 => UNS * DIS # A7: 1 => CTR => A7: 3,6 * INC # G8: 3,6 => UNS * DIS # H8: 3,6 => CTR => H8: 8,9 * INC # H8: 8,9 => UNS * INC # A7: 1,6 => UNS * DIS # A7: 3 => CTR => A7: 1,6 * INC # D9: 1,6 => UNS * PRF # D9: 4,8,9 => SOL * INC # I9: 2,8 => UNS * DIS # I9: 4,6,9 => CTR => I9: 2,8 * PRF # F7: 1,8 => SOL * INC # F7: 4 => UNS * DIS # D9: 1,8 => CTR => D9: 4,6,9 * INC # D9: 4,6,9 => UNS * DIS # E9: 1,8 => CTR => E9: 9 * INC # E9: 9 => UNS * DIS # E2: 1,8 => CTR => E2: 7,9 * INC # E2: 7,9 => UNS * PRF # E4: 1,8 => SOL * DIS # E4: 3,5,7,9 => CTR => E4: 1,8 * CNT 86 HDP CHAINS / 86 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C2: 5,7 => CTR => C2: 1 * DIS C2: 1 # D2: 7,8 => CTR => D2: 4,9 * INC C2: 1 + D2: 4,9 # E2: 7,8 => UNS * DIS C2: 1 + D2: 4,9 # F2: 7,8 => CTR => F2: 4,9 * PRF C2: 1 + D2: 4,9 + F2: 4,9 # D4: 7,8 => SOL * STA C2: 1 + D2: 4,9 + F2: 4,9 + D4: 7,8 * CNT 5 HDP CHAINS / 5 HYP OPENED