Analysis of zz-sudoku-de-754055-base.sdk
Contents
Original Sudoku
level: medium
position: 45..9.7.2..7.....41....4.6...39.8...8...6...1...3.72...9.1....85.....1..2.1.3..45 initial
Autosolve
position: 45..9.7.2..7.....41....4.6...39.845.8...6...1..53.728..9.1....85.....1..2.1.3..45 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 2,3 => CTR => B2: 6,8 * DIS # C8: 4 => CTR => C8: 6,8 * DIS # H2: 1 => CTR => H2: 3,9 * DIS # D2: 6,8 => CTR => D2: 2,5 * DIS # H2: 1,3 => CTR => H2: 9 * PRF # H2: 9 => SOL * DIS # H2: 1,3 => CTR => H2: 9 * PRF # H2: 9 => SOL * DIS # D2: 5,8 => CTR => D2: 2,6 * DIS # E3: 5,8 => CTR => E3: 2,7 * DIS # H2: 1 => CTR => H2: 3,9 * PRF # I8: 3,9 => SOL * DIS # I8: 7 => CTR => I8: 3,9 * DIS # D5: 2,5 => CTR => D5: 4 * PRF # F7: 6 => SOL * PRF # H5: 3,9 => SOL * DIS # H5: 7 => CTR => H5: 3,9 * DIS # B8: 6,8 => CTR => B8: 3,7 * DIS # C8: 8 => CTR => C8: 4,6 * DIS # B8: 7,8 => CTR => B8: 3,6 * PRF # F8: 2 => SOL * CNT 21 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 2,3 => CTR => B2: 6,8 * DIS B2: 6,8 # C8: 4 => CTR => C8: 6,8 * DIS B2: 6,8 + C8: 6,8 # H2: 1 => CTR => H2: 3,9 * DIS B2: 6,8 + C8: 6,8 + H2: 3,9 # D2: 6,8 => CTR => D2: 2,5 * DIS B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 # E2: 2 => CTR => E2: 5,8 * DIS B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 + E2: 5,8 # E3: 5,8 => CTR => E3: 7 * PRF B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 + E2: 5,8 + E3: 7 # I8: 3,9 => SOL * STA B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 + E2: 5,8 + E3: 7 + I8: 3,9 * CNT 7 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 45..9.7.2..7.....41....4.6...39.8...8...6...1...3.72...9.1....85.....1..2.1.3..45 | initial |
| 45..9.7.2..7.....41....4.6...39.845.8...6...1..53.728..9.1....85.....1..2.1.3..45 | autosolve |
| 458693712367281594129574863613928457872465931945317286794156328536842179281739645 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (28) C1: 6,8 A2: 3,9 C3: 2,9 D1: 6,8 F1: 1,3 F2: 1,3 H1: 1,3 G2: 5,8 G3: 5,8 I3: 3,9 A4: 6,7 B4: 1,2 C5: 2,9 A6: 6,9 B6: 1,4 E4: 1,2 F5: 2,5 E6: 1,4 I4: 6,7 G5: 3,9 I6: 6,9 A7: 3,7 C7: 4,6 B9: 7,8 D9: 7,8 F9: 6,9 G7: 3,6 G9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F1,F2: 1.. / F1 = 1 => 0 pairs (X) / F2 = 1 => 26 pairs (_) H1,H2: 1.. / H1 = 1 => 26 pairs (_) / H2 = 1 => 0 pairs (X) B4,B6: 1.. / B4 = 1 => 23 pairs (_) / B6 = 1 => 0 pairs (X) E4,E6: 1.. / E4 = 1 => 0 pairs (X) / E6 = 1 => 23 pairs (_) F1,H1: 1.. / F1 = 1 => 0 pairs (X) / H1 = 1 => 26 pairs (_) F2,H2: 1.. / F2 = 1 => 26 pairs (_) / H2 = 1 => 0 pairs (X) B4,E4: 1.. / B4 = 1 => 23 pairs (_) / E4 = 1 => 0 pairs (X) B6,E6: 1.. / B6 = 1 => 0 pairs (X) / E6 = 1 => 23 pairs (_) H7,H8: 2.. / H7 = 2 => 29 pairs (_) / H8 = 2 => 29 pairs (_) B4,E4: 2.. / B4 = 2 => 0 pairs (X) / E4 = 2 => 23 pairs (_) C3,C5: 2.. / C3 = 2 => 0 pairs (X) / C5 = 2 => 0 pairs (_) F1,F2: 3.. / F1 = 3 => 26 pairs (_) / F2 = 3 => 0 pairs (X) G5,H5: 3.. / G5 = 3 => 27 pairs (_) / H5 = 3 => 0 pairs (*) A7,B8: 3.. / A7 = 3 => 0 pairs (X) / B8 = 3 => 0 pairs (_) F1,H1: 3.. / F1 = 3 => 26 pairs (_) / H1 = 3 => 0 pairs (X) B3,I3: 3.. / B3 = 3 => 0 pairs (X) / I3 = 3 => 0 pairs (_) A2,A7: 3.. / A2 = 3 => 0 pairs (*) / A7 = 3 => 0 pairs (X) G5,G7: 3.. / G5 = 3 => 27 pairs (_) / G7 = 3 => 0 pairs (*) I3,I8: 3.. / I3 = 3 => 0 pairs (*) / I8 = 3 => 0 pairs (X) B5,B6: 4.. / B5 = 4 => 0 pairs (X) / B6 = 4 => 23 pairs (_) D5,E6: 4.. / D5 = 4 => 23 pairs (_) / E6 = 4 => 0 pairs (X) C7,C8: 4.. / C7 = 4 => 29 pairs (_) / C8 = 4 => 0 pairs (X) B5,D5: 4.. / B5 = 4 => 0 pairs (X) / D5 = 4 => 23 pairs (_) B6,E6: 4.. / B6 = 4 => 23 pairs (_) / E6 = 4 => 0 pairs (X) C7,E7: 4.. / C7 = 4 => 29 pairs (_) / E7 = 4 => 0 pairs (X) D5,D8: 4.. / D5 = 4 => 23 pairs (_) / D8 = 4 => 0 pairs (X) G2,G3: 5.. / G2 = 5 => 31 pairs (_) / G3 = 5 => 28 pairs (_) D5,F5: 5.. / D5 = 5 => 0 pairs (X) / F5 = 5 => 31 pairs (_) E7,F7: 5.. / E7 = 5 => 31 pairs (_) / F7 = 5 => 0 pairs (X) F5,F7: 5.. / F5 = 5 => 31 pairs (_) / F7 = 5 => 0 pairs (X) C1,B2: 6.. / C1 = 6 => 0 pairs (X) / B2 = 6 => 28 pairs (_) D1,D2: 6.. / D1 = 6 => 28 pairs (_) / D2 = 6 => 0 pairs (X) A4,A6: 6.. / A4 = 6 => 0 pairs (*) / A6 = 6 => 0 pairs (X) I4,I6: 6.. / I4 = 6 => 0 pairs (X) / I6 = 6 => 0 pairs (_) G7,G9: 6.. / G7 = 6 => 27 pairs (_) / G9 = 6 => 0 pairs (*) C1,D1: 6.. / C1 = 6 => 0 pairs (X) / D1 = 6 => 28 pairs (_) B2,D2: 6.. / B2 = 6 => 28 pairs (_) / D2 = 6 => 0 pairs (X) A4,I4: 6.. / A4 = 6 => 0 pairs (*) / I4 = 6 => 0 pairs (X) A6,I6: 6.. / A6 = 6 => 0 pairs (X) / I6 = 6 => 0 pairs (_) F9,G9: 6.. / F9 = 6 => 27 pairs (_) / G9 = 6 => 0 pairs (*) B2,B8: 6.. / B2 = 6 => 28 pairs (_) / B8 = 6 => 0 pairs (X) D3,E3: 7.. / D3 = 7 => 0 pairs (X) / E3 = 7 => 28 pairs (_) A4,B5: 7.. / A4 = 7 => 0 pairs (X) / B5 = 7 => 0 pairs (_) I4,H5: 7.. / I4 = 7 => 0 pairs (*) / H5 = 7 => 0 pairs (X) A4,I4: 7.. / A4 = 7 => 0 pairs (X) / I4 = 7 => 0 pairs (_) B5,H5: 7.. / B5 = 7 => 0 pairs (*) / H5 = 7 => 0 pairs (X) B9,D9: 7.. / B9 = 7 => 0 pairs (X) / D9 = 7 => 28 pairs (_) A4,A7: 7.. / A4 = 7 => 0 pairs (X) / A7 = 7 => 0 pairs (_) I4,I8: 7.. / I4 = 7 => 0 pairs (*) / I8 = 7 => 0 pairs (X) G2,G3: 8.. / G2 = 8 => 28 pairs (_) / G3 = 8 => 31 pairs (_) C1,D1: 8.. / C1 = 8 => 28 pairs (_) / D1 = 8 => 0 pairs (X) B9,D9: 8.. / B9 = 8 => 28 pairs (_) / D9 = 8 => 0 pairs (X) C1,C8: 8.. / C1 = 8 => 28 pairs (_) / C8 = 8 => 0 pairs (X) A2,C3: 9.. / A2 = 9 => 0 pairs (X) / C3 = 9 => 0 pairs (_) H2,I3: 9.. / H2 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) C5,A6: 9.. / C5 = 9 => 0 pairs (X) / A6 = 9 => 0 pairs (_) F8,F9: 9.. / F8 = 9 => 27 pairs (_) / F9 = 9 => 0 pairs (*) A2,H2: 9.. / A2 = 9 => 0 pairs (X) / H2 = 9 => 0 pairs (_) C3,I3: 9.. / C3 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) A6,I6: 9.. / A6 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) F9,G9: 9.. / F9 = 9 => 0 pairs (*) / G9 = 9 => 0 pairs (X) A2,A6: 9.. / A2 = 9 => 0 pairs (X) / A6 = 9 => 0 pairs (_) C3,C5: 9.. / C3 = 9 => 0 pairs (*) / C5 = 9 => 0 pairs (X) G5,G9: 9.. / G5 = 9 => 0 pairs (*) / G9 = 9 => 0 pairs (X) * DURATION: 0:02:06.206642 START: 08:30:06.741033 END: 08:32:12.947675 2017-05-01 * CP COUNT: (64) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,A6,A7,B4,B6,B9,C1,C3,C5,C7,D1,D9,E4,E6,F1,F2,F5,F9,G2,G3,G5,G7,G9,H1,I3,I4,I6) * 45..9.7.2..7.....41....4.6...39.845.8...6...1..53.728..9.1....85.....1..2.1.3..45 * PAIR C1: 6,8 BLK 1 B2: 6,8,2,3 # reduction candidate for 6,8 B2: 2,3 => CTR * 45689.7.2..76..8.418...4563..39.845.8..562..1..534728..941....85.....1..2.1.3..45 B2: 6,8 # 30 pairs * PAIR C1: 6,8 COL C C8: 6,8,4 # reduction candidate for 6,8 C8: 4 => CTR * 45869.7.2.67.....41....4.6...39.845.8...6...1..53.728..96145328534..61..28173..45 C8: 6,8 # 29 pairs * PAIR A2: 3,9 ROW 2 H2: 3,9,1 # reduction candidate for 3,9 H2: 1 => CTR * 45..9.7.29.7....141.2..4.69..39.845.8.9.6.3716.53.728..9.1....85.....1..2.1.3..45 H2: 3,9 # 26 pairs * PAIR D1: 6,8 BLK 2 D2: 6,8,2,5 # reduction candidate for 6,8 D2: 6,8 => CTR * 45869.7.2.6782.5.41..57486..2391845.8.9.6537161534728979.1....85...8.1..28173..45 D2: 2,5 # 29 pairs * PAIR F2: 1,3 ROW 2 H2: 1,3,9 # reduction candidate for 1,3 H2: 1,3 => CTR * 45..9.7.29.7.....41.2..4.69..39.845.8.9.6.3716.53.728..9.1....85.....1..2.1.3..45 H2: 9 => SOLVED * 458693712367281594129574863613928457872465931945317286794156328536842179281739645 * PAIR H1: 1,3 BLK 3 H2: 1,3,9 # reduction candidate for 1,3 H2: 1,3 => CTR * 45..9.7.29.7.....41.2..4.69..39.845.8.9.6.3716.53.728..9.1....85.....1..2.1.3..45 H2: 9 => SOLVED * 458693712367281594129574863613928457872465931945317286794156328536842179281739645 * PAIR G2: 5,8 ROW 2 D2: 5,8,2,6 # reduction candidate for 5,8 D2: 5,8 => CTR * 45.69.7.2.67.2...41....4.6..2391845.8.9.6.371615347289.941..6.85.64..1.727183..45 D2: 2,6 # 29 pairs E2: 5,8,2 # reduction candidate for 5,8 E2: 5,8 # 31 pairs * PAIR G3: 5,8 ROW 3 D3: 5,8,2,7 # reduction candidate for 5,8 D3: 5,8 # 31 pairs E3: 5,8,2,7 # reduction candidate for 5,8 E3: 5,8 => CTR * 45869.7.2967.....413.7.4.6.7.39.84568...6..716.53.728939.175628586...1.7271836945 E3: 2,7 # 29 pairs * PAIR I3: 3,9 BLK 3 H2: 3,9,1 # reduction candidate for 3,9 H2: 1 => CTR * 45..9.7.29.7....141.2..4.69..39.845.8.9.6.3716.53.728..9.1....85.....1..2.1.3..45 H2: 3,9 # 26 pairs * PAIR I3: 3,9 COL I I8: 3,9,7 # reduction candidate for 3,9 I8: 3,9 => SOLVED * 458693712367281594129574863613928457872465931945317286794156328536842179281739645 I8: 7 => CTR * 45..937129.7.....41....4.63..39.845.8...6...1..53.7289.9.1....85.....1.72.1.3.945 * PAIR F5: 2,5 BLK 5 D5: 2,5,4 # reduction candidate for 2,5 D5: 2,5 => CTR * 45869.7.2.67.....41..7.4.637239.845.84..6..71.1534728..941....85..4..1.727183..45 D5: 4 # 23 pairs * PAIR F5: 2,5 COL F F7: 2,5,6 # reduction candidate for 2,5 F7: 6 => SOLVED * 458693712367281594129574863613928457872465931945317286794156328536842179281739645 F7: 2,5 # 30 pairs * PAIR G5: 3,9 BLK 6 H5: 3,9,7 # reduction candidate for 3,9 H5: 3,9 => SOLVED * 458693712367281594129574863613928457872465931945317286794156328536842179281739645 H5: 7 => CTR * 45869.7.2967.....413...4.6...39.845.8...6.371..53.7289.9.1..6.85.....1.7271836945 * PAIR A7: 3,7 BLK 7 B8: 3,7,6,8 # reduction candidate for 3,7 B8: 6,8 => CTR * 45869.7.2967.....4132..4.697.39.84568...6...1..53.728.39.1..6.85.....1..271836945 B8: 3,7 # 28 pairs * PAIR A7: 3,7 ROW 7 H7: 3,7,2 # reduction candidate for 3,7 H7: 3,7 # 29 pairs H7: 2 # 29 pairs * PAIR C7: 4,6 BLK 7 C8: 4,6,8 # reduction candidate for 4,6 C8: 8 => CTR * 45..9.7.2..7.....41....4.6...39.845.8...6...1..53.728..941....8568...1..27183..45 C8: 4,6 # 28 pairs * PAIR B9: 7,8 BLK 7 B8: 7,8,3,6 # reduction candidate for 7,8 B8: 7,8 => CTR * 45..9.7.2.67.....4132..4.69..39.845.8.9.6.3716.53.728..9.1....85.....1..2.1.3..45 B8: 3,6 # 29 pairs * PAIR D9: 7,8 BLK 8 D8: 7,8,2,4 # reduction candidate for 7,8 D8: 7,8 # 23 pairs E8: 7,8,2,4 # reduction candidate for 7,8 E8: 7,8 # 30 pairs * PAIR D9: 7,8 COL D D3: 7,8,2,5 # reduction candidate for 7,8 D3: 7,8 # 31 pairs D3: 2,5 # 29 pairs * PAIR F9: 6,9 BLK 8 F8: 6,9,2 # reduction candidate for 6,9 F8: 2 => SOLVED * 458693712367281594129574863613928457872465931945317286794156328536842179281739645 F8: 6,9 # 30 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-754055-base-pr-000.dot * REASONING * DIS # B2: 2,3 => CTR => B2: 6,8 * DIS # C8: 4 => CTR => C8: 6,8 * DIS # H2: 1 => CTR => H2: 3,9 * DIS # D2: 6,8 => CTR => D2: 2,5 * DIS # H2: 1,3 => CTR => H2: 9 * PRF # H2: 9 => SOL * DIS # H2: 1,3 => CTR => H2: 9 * PRF # H2: 9 => SOL * DIS # D2: 5,8 => CTR => D2: 2,6 * DIS # E3: 5,8 => CTR => E3: 2,7 * DIS # H2: 1 => CTR => H2: 3,9 * PRF # I8: 3,9 => SOL * DIS # I8: 7 => CTR => I8: 3,9 * DIS # D5: 2,5 => CTR => D5: 4 * PRF # F7: 6 => SOL * PRF # H5: 3,9 => SOL * DIS # H5: 7 => CTR => H5: 3,9 * DIS # B8: 6,8 => CTR => B8: 3,7 * DIS # C8: 8 => CTR => C8: 4,6 * DIS # B8: 7,8 => CTR => B8: 3,6 * PRF # F8: 2 => SOL * CNT 21 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,A6,A7,B4,B6,B9,C1,C3,C5,C7,D1,D9,E4,E6,F1,F2,F5,F9,G2,G3,G5,G7,G9,H1,I3,I4,I6) * 45..9.7.2..7.....41....4.6...39.845.8...6...1..53.728..9.1....85.....1..2.1.3..45 * PAIR C1: 6,8 BLK 1 B2: 6,8,2,3 # reduction candidate for 6,8 B2: 2,3 => CTR * 45689.7.2..76..8.418...4563..39.845.8..562..1..534728..941....85.....1..2.1.3..45 * PAIR C1: 6,8 COL C C8: 6,8,4 # reduction candidate for 6,8 C8: 4 => CTR * 45869.7.2.67.....41....4.6...39.845.8...6...1..53.728..96145328534..61..28173..45 * PAIR RESTART * PAIR A2: 3,9 ROW 2 H2: 3,9,1 # reduction candidate for 3,9 H2: 1 => CTR * 45..9.7.29.7..3.14132..4.69..39.845.8.9.6.3716.53.728..941....85.....1..2.1.3..45 * PAIR RESTART * PAIR D1: 6,8 BLK 2 D2: 6,8,2,5 # reduction candidate for 6,8 D2: 6,8 => CTR * 45..93712..7.215.41....486..2391845.8.9.6.371615347289.941..6.85..48.1.72.1.3..45 * PAIR G2: 5,8 ROW 2 E2: 5,8,2 # reduction candidate for 5,8 E2: 2 => CTR * 458693712.67.218.41....456..2391845.8.9.6.371615347289.9415.6.85.64..1.727183..45 * PAIR RESTART * PAIR G3: 5,8 ROW 3 D3: 5,8,7 # reduction candidate for 5,8 D3: 5,8 # 30 pairs E3: 5,8,7 # reduction candidate for 5,8 E3: 5,8 => CTR * 458693712.672.1..41.27.4.697239.845.8..562..1..534728..941.56.85.64.91..271836945 * RESTART * PAIR RESTART * PAIR I3: 3,9 COL I I8: 3,9,7 # reduction candidate for 3,9 I8: 3,9 => SOLVED * 458693712367281594129574863613928457872465931945317286794156328536842179281739645 * DURATION: 0:00:16.246296 START: 08:32:57.075160 END: 08:33:13.321456 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-754055-base-pr-001.dot * REASONING * DIS # B2: 2,3 => CTR => B2: 6,8 * DIS B2: 6,8 # C8: 4 => CTR => C8: 6,8 * DIS B2: 6,8 + C8: 6,8 # H2: 1 => CTR => H2: 3,9 * DIS B2: 6,8 + C8: 6,8 + H2: 3,9 # D2: 6,8 => CTR => D2: 2,5 * DIS B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 # E2: 2 => CTR => E2: 5,8 * DIS B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 + E2: 5,8 # E3: 5,8 => CTR => E3: 7 * PRF B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 + E2: 5,8 + E3: 7 # I8: 3,9 => SOL * STA B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 + E2: 5,8 + E3: 7 + I8: 3,9 * CNT 7 HDP CHAINS / 12 HYP OPENED
Header Info
http://www.sudokus.de/754055.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: 45..9.7.2..7.....41....4.6...39.845.8...6...1..53.728..9.1....85.....1..2.1.3..45 C1: 6,8 B2: 2,3,6,8 # reduction candidate for 6,8 B2: 2,3 => CTR * 45689.7.2..76..8.418...4563..39.845.8..562..1..534728..941....85.....1..2.1.3..45 C8: 4,6,8 # reduction candidate for 6,8 C8: 4 => CTR * 45869.7.2.67.....41....4.6...39.845.8...6...1..53.728..96145328534..61..28173..45 A2: 3,9 H2: 1,3,9 # reduction candidate for 3,9 H2: 1 => CTR * 45..9.7.29.7..3.14132..4.69..39.845.8.9.6.3716.53.728..941....85.....1..2.1.3..45 C3: 2,9 D1: 6,8 D2: 2,5,6,8 # reduction candidate for 6,8 D2: 6,8 => CTR * 45..93712..7.215.41....486..2391845.8.9.6.371615347289.941..6.85..48.1.72.1.3..45 G2: 5,8 E2: 2,5,8 # reduction candidate for 5,8 E2: 2 => CTR * 458693712.67.218.41....456..2391845.8.9.6.371615347289.9415.6.85.64..1.727183..45 G3: 5,8 D3: 5,7,8 # reduction candidate for 5,8 D3: 7 => CTR * 458693712.672.1..41.27.4.697239.845.8..562..1..534728..941.56.85.64.91..271836945 I3: 3,9 I8: 3,7,9 # reduction candidate for 3,9 I8: 3,9 => SOLVED * 458693712367281594129574863613928457872465931945317286794156328536842179281739645 * SOLVED! -------------------------------------------------- |:step:| 00 -------------------------------------------------- pair quad F1: 1,3 H1: 1,3 F2: 1,3 H2: 1,3,9 => H2 = 9 * SOLVED! |:step:| 01 --------------------------------------------------
Solution
position: 458693712367281594129574863613928457872465931945317286794156328536842179281739645 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 # B2: 6,8 => UNS * DIS # B2: 2,3 => CTR => B2: 6,8 * INC # C8: 6,8 => UNS * DIS # C8: 4 => CTR => C8: 6,8 * INC # H2: 3,9 => UNS * DIS # H2: 1 => CTR => H2: 3,9 * DIS # D2: 6,8 => CTR => D2: 2,5 * INC # D2: 2,5 => UNS * DIS # H2: 1,3 => CTR => H2: 9 * PRF # H2: 9 => SOL * DIS # H2: 1,3 => CTR => H2: 9 * PRF # H2: 9 => SOL * DIS # D2: 5,8 => CTR => D2: 2,6 * INC # D2: 2,6 => UNS * INC # E2: 5,8 => UNS * INC # D3: 5,8 => UNS * DIS # E3: 5,8 => CTR => E3: 2,7 * INC # E3: 2,7 => UNS * INC # H2: 3,9 => UNS * DIS # H2: 1 => CTR => H2: 3,9 * PRF # I8: 3,9 => SOL * DIS # I8: 7 => CTR => I8: 3,9 * DIS # D5: 2,5 => CTR => D5: 4 * INC # D5: 4 => UNS * INC # F7: 2,5 => UNS * PRF # F7: 6 => SOL * PRF # H5: 3,9 => SOL * DIS # H5: 7 => CTR => H5: 3,9 * INC # B8: 3,7 => UNS * DIS # B8: 6,8 => CTR => B8: 3,7 * INC # H7: 3,7 => UNS * INC # H7: 2 => UNS * INC # C8: 4,6 => UNS * DIS # C8: 8 => CTR => C8: 4,6 * DIS # B8: 7,8 => CTR => B8: 3,6 * INC # B8: 3,6 => UNS * INC # D8: 7,8 => UNS * INC # E8: 7,8 => UNS * INC # D3: 7,8 => UNS * INC # D3: 2,5 => UNS * INC # F8: 6,9 => UNS * PRF # F8: 2 => SOL * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 6,8 => UNS * DIS # B2: 2,3 => CTR => B2: 6,8 * INC B2: 6,8 # C8: 6,8 => UNS * DIS B2: 6,8 # C8: 4 => CTR => C8: 6,8 * INC B2: 6,8 + C8: 6,8 # H2: 3,9 => UNS * DIS B2: 6,8 + C8: 6,8 # H2: 1 => CTR => H2: 3,9 * DIS B2: 6,8 + C8: 6,8 + H2: 3,9 # D2: 6,8 => CTR => D2: 2,5 * INC B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 # E2: 5,8 => UNS * DIS B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 # E2: 2 => CTR => E2: 5,8 * INC B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 + E2: 5,8 # D3: 5,8 => UNS * DIS B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 + E2: 5,8 # E3: 5,8 => CTR => E3: 7 * PRF B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 + E2: 5,8 + E3: 7 # I8: 3,9 => SOL * STA B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 + E2: 5,8 + E3: 7 + I8: 3,9 * CNT 12 HDP CHAINS / 12 HYP OPENED