Analysis of zz-sudoku-de-601842-base.sdk
Contents
Original Sudoku
level: medium
position: 8.1...6.7.4.7.1.8.9.......3..42.51...9.....6...56.73..7.......4.3.4.8.2.4.8...9.6 initial
Autosolve
position: 8.1...6.7.4.7.1.899......13..42.51.8.9.....651856.73.27.....8.4.394.8.214.8...9.6 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A2: 2,5 => SOL * DIS # A2: 3,6 => CTR => A2: 2,5 * DIS # B3: 2,5 => CTR => B3: 6,7 * DIS # E1: 2,5 => CTR => E1: 3,4 * DIS # G3: 2 => CTR => G3: 4,5 * PRF # G3: 2,5 => SOL * DIS # G3: 4 => CTR => G3: 2,5 * PRF # A2: 2,5 => SOL * DIS # A2: 3,6 => CTR => A2: 2,5 * DIS # E2: 2,5 => CTR => E2: 6 * PRF # E2: 6 => SOL * DIS # A2: 3,6 => CTR => A2: 2,5 * PRF # A2: 2,5 => SOL * DIS # B3: 2,5 => CTR => B3: 6,7 * DIS # C5: 2,3 => CTR => C5: 7 * PRF # C5: 7 => SOL * DIS # A2: 2,3 => CTR => A2: 5,6 * PRF # A2: 5,6 => SOL * DIS # F1: 3,4 => CTR => F1: 2,9 * DIS # B7: 2,6 => CTR => B7: 1,5 * DIS # E7: 2,6 => CTR => E7: 1,3,5 * DIS # C2: 2,6 => CTR => C2: 3 * PRF # C3: 2,6 => SOL * DIS # C3: 7 => CTR => C3: 2,6 * PRF # E8: 5,6 => SOL * DIS # E8: 7 => CTR => E8: 5,6 * PRF # A2: 5,6 => SOL * DIS # A2: 2,3 => CTR => A2: 5,6 * DIS # E7: 2,3 => CTR => E7: 1,5,6 * DIS # F7: 2,3 => CTR => F7: 6,9 * DIS # E9: 2,3 => CTR => E9: 1,5,7 * DIS # F1: 2,3 => CTR => F1: 4,9 * PRF # H9: 3,5 => SOL * DIS # H9: 7 => CTR => H9: 3,5 * DIS # D7: 3,5 => CTR => D7: 1,9 * DIS # H9: 3 => CTR => H9: 5,7 * PRF # E8: 5,7 => SOL * DIS # E8: 6 => CTR => E8: 5,7 * CNT 38 HDP CHAINS / 62 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A2: 2,5 => SOL * STA A2: 2,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 8.1...6.7.4.7.1.8.9.......3..42.51...9.....6...56.73..7.......4.3.4.8.2.4.8...9.6 | initial |
| 8.1...6.7.4.7.1.899......13..42.51.8.9.....651856.73.27.....8.4.394.8.214.8...9.6 | autosolve |
| 821539647543761289976824513364295178297183465185647392752916834639458721418372956 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) B1: 2,5 D3: 5,8 H1: 4,5 G2: 2,5 A4: 3,6 B4: 6,7 A5: 2,3 E4: 3,9 D5: 1,8 E5: 1,8 F5: 3,4 E6: 4,9 H4: 7,9 G5: 4,7 H6: 4,9 C7: 2,6 A8: 5,6 F9: 2,3 H7: 3,5 G8: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D5,E5: 1.. / D5 = 1 => 18 pairs (_) / E5 = 1 => 21 pairs (_) B7,B9: 1.. / B7 = 1 => 22 pairs (_) / B9 = 1 => 21 pairs (_) G2,G3: 2.. / G2 = 2 => 22 pairs (_) / G3 = 2 => 0 pairs (X) A5,C5: 2.. / A5 = 2 => 20 pairs (_) / C5 = 2 => 0 pairs (X) A2,A5: 2.. / A2 = 2 => 0 pairs (X) / A5 = 2 => 20 pairs (_) A2,C2: 3.. / A2 = 3 => 0 pairs (X) / C2 = 3 => 21 pairs (_) E4,F5: 3.. / E4 = 3 => 0 pairs (X) / F5 = 3 => 0 pairs (_) H7,H9: 3.. / H7 = 3 => 20 pairs (_) / H9 = 3 => 0 pairs (X) A4,E4: 3.. / A4 = 3 => 0 pairs (*) / E4 = 3 => 0 pairs (X) C2,C5: 3.. / C2 = 3 => 21 pairs (_) / C5 = 3 => 0 pairs (X) H1,G3: 4.. / H1 = 4 => 0 pairs (*) / G3 = 4 => 0 pairs (X) F5,E6: 4.. / F5 = 4 => 0 pairs (X) / E6 = 4 => 0 pairs (_) G5,H6: 4.. / G5 = 4 => 0 pairs (*) / H6 = 4 => 0 pairs (X) F5,G5: 4.. / F5 = 4 => 0 pairs (X) / G5 = 4 => 0 pairs (_) E6,H6: 4.. / E6 = 4 => 0 pairs (*) / H6 = 4 => 0 pairs (X) G3,G5: 4.. / G3 = 4 => 0 pairs (X) / G5 = 4 => 0 pairs (_) H1,H6: 4.. / H1 = 4 => 0 pairs (*) / H6 = 4 => 0 pairs (X) A2,A8: 5.. / A2 = 5 => 0 pairs (*) / A8 = 5 => 0 pairs (X) A4,B4: 6.. / A4 = 6 => 0 pairs (X) / B4 = 6 => 0 pairs (_) A8,E8: 6.. / A8 = 6 => 0 pairs (*) / E8 = 6 => 0 pairs (X) F3,F7: 6.. / F3 = 6 => 0 pairs (X) / F7 = 6 => 0 pairs (_) B3,C3: 7.. / B3 = 7 => 0 pairs (*) / C3 = 7 => 0 pairs (X) B4,C5: 7.. / B4 = 7 => 0 pairs (X) / C5 = 7 => 0 pairs (_) H4,G5: 7.. / H4 = 7 => 0 pairs (*) / G5 = 7 => 0 pairs (X) E8,E9: 7.. / E8 = 7 => 0 pairs (X) / E9 = 7 => 0 pairs (_) G8,H9: 7.. / G8 = 7 => 0 pairs (*) / H9 = 7 => 0 pairs (X) B4,H4: 7.. / B4 = 7 => 0 pairs (X) / H4 = 7 => 0 pairs (_) C5,G5: 7.. / C5 = 7 => 0 pairs (*) / G5 = 7 => 0 pairs (X) E8,G8: 7.. / E8 = 7 => 0 pairs (X) / G8 = 7 => 0 pairs (_) E9,H9: 7.. / E9 = 7 => 0 pairs (*) / H9 = 7 => 0 pairs (X) B3,B4: 7.. / B3 = 7 => 0 pairs (*) / B4 = 7 => 0 pairs (X) C3,C5: 7.. / C3 = 7 => 0 pairs (X) / C5 = 7 => 0 pairs (_) G5,G8: 7.. / G5 = 7 => 0 pairs (X) / G8 = 7 => 0 pairs (_) H4,H9: 7.. / H4 = 7 => 0 pairs (*) / H9 = 7 => 0 pairs (X) D3,E3: 8.. / D3 = 8 => 18 pairs (_) / E3 = 8 => 21 pairs (_) D5,E5: 8.. / D5 = 8 => 21 pairs (_) / E5 = 8 => 18 pairs (_) D3,D5: 8.. / D3 = 8 => 18 pairs (_) / D5 = 8 => 21 pairs (_) E3,E5: 8.. / E3 = 8 => 21 pairs (_) / E5 = 8 => 18 pairs (_) D1,F1: 9.. / D1 = 9 => 0 pairs (X) / F1 = 9 => 21 pairs (_) E4,E6: 9.. / E4 = 9 => 0 pairs (*) / E6 = 9 => 0 pairs (X) H4,H6: 9.. / H4 = 9 => 0 pairs (X) / H6 = 9 => 0 pairs (_) D7,F7: 9.. / D7 = 9 => 21 pairs (_) / F7 = 9 => 0 pairs (X) E4,H4: 9.. / E4 = 9 => 0 pairs (*) / H4 = 9 => 0 pairs (X) E6,H6: 9.. / E6 = 9 => 0 pairs (X) / H6 = 9 => 0 pairs (_) D1,D7: 9.. / D1 = 9 => 0 pairs (X) / D7 = 9 => 21 pairs (_) F1,F7: 9.. / F1 = 9 => 21 pairs (_) / F7 = 9 => 0 pairs (X) * DURATION: 0:01:13.943681 START: 07:12:30.893252 END: 07:13:44.836933 2017-05-01 * CP COUNT: (46) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,A8,B1,B4,C7,D3,D5,E4,E5,E6,F5,F9,G2,G5,G8,H1,H4,H6,H7) * 8.1...6.7.4.7.1.899......13..42.51.8.9.....651856.73.27.....8.4.394.8.214.8...9.6 * PAIR B1: 2,5 BLK 1 A2: 2,5,3,6 # reduction candidate for 2,5 A2: 2,5 => SOLVED * 821539647543761289976824513364295178297183465185647392752916834639458721418372956 A2: 3,6 => CTR * 8.1...6.7.4.7.1.899....6.13..42.5178297..34651856473927.....8.45394687214.8.729.6 B3: 2,5,6,7 # reduction candidate for 2,5 B3: 2,5 => CTR * 8.1...6.7.4.7.1.899.7....13.742.5198.9....765185697342762...8.45394.8.214.8...9.6 B3: 6,7 # 21 pairs * PAIR B1: 2,5 ROW 1 E1: 2,5,3,4 # reduction candidate for 2,5 E1: 2,5 => CTR * 8.1...647.4.7.1.899....4.13..4295178.97..34651856473927...36854639458721458172936 E1: 3,4 # 21 pairs * PAIR B1: 2,5 COL B B7: 2,5,1,6 # reduction candidate for 2,5 B7: 2,5 # 23 pairs B9: 2,5,1 # reduction candidate for 2,5 B9: 2,5 # 22 pairs * PAIR D3: 5,8 BLK 2 E3: 5,8,2,4,6 # reduction candidate for 5,8 E3: 5,8 # 24 pairs E3: 2,4,6 # 18 pairs * PAIR H1: 4,5 BLK 3 G3: 4,5,2 # reduction candidate for 4,5 G3: 2 => CTR * 8.1...647.4.7.15899.....213..42.51.8.9....4651856473927.....8.45394687214.8.7.9.6 G3: 4,5 # 22 pairs * PAIR H1: 4,5 ROW 1 E1: 4,5,2,3 # reduction candidate for 4,5 E1: 4,5 # 26 pairs E1: 2,3 # 21 pairs * PAIR G2: 2,5 BLK 3 G3: 2,5,4 # reduction candidate for 2,5 G3: 2,5 => SOLVED * 821539647543761289976824513364295178297183465185647392752916834639458721418372956 G3: 4 => CTR * 8.1.4.6575437.12899.....413..42.51.829...47651856973427.....8.4.394785214.8...976 * PAIR G2: 2,5 ROW 2 A2: 2,5,3,6 # reduction candidate for 2,5 A2: 2,5 => SOLVED * 821539647543761289976824513364295178297183465185647392752916834639458721418372956 A2: 3,6 => CTR * 8.1...6.7.4.7.1.899....6.13..42.5178297..34651856473927.....8.45394687214.8.729.6 E2: 2,5,6 # reduction candidate for 2,5 E2: 2,5 => CTR * 8.1...6.7.4.7.1.899....6.13..42.5178297..34651856473927.....8.45394687214.8.729.6 E2: 6 => SOLVED * 821539647543761289976824513364295178297183465185647392752916834639458721418372956 * PAIR A4: 3,6 COL A A2: 3,6,2,5 # reduction candidate for 3,6 A2: 3,6 => CTR * 8.1...6.7.4.7.1.899....6.13..42.5178297..34651856473927.....8.45394687214.8.729.6 A2: 2,5 => SOLVED * 821539647543761289976824513364295178297183465185647392752916834639458721418372956 * PAIR B4: 6,7 COL B B3: 6,7,2,5 # reduction candidate for 6,7 B3: 2,5 => CTR * 8.1...6.7.4.7.1.899.7....13.742.5198.9....765185697342762...8.45394.8.214.8...9.6 B3: 6,7 # 21 pairs * PAIR A5: 2,3 BLK 4 C5: 2,3,7 # reduction candidate for 2,3 C5: 2,3 => CTR * 8.1...657543761289967...4136742.5198.9....7651856973427.....8.4.394785214.8...976 C5: 7 => SOLVED * 821539647543761289976824513364295178297183465185647392752916834639458721418372956 * PAIR A5: 2,3 COL A A2: 2,3,5,6 # reduction candidate for 2,3 A2: 2,3 => CTR * 8.1...6.7.467.1.899....6.136.42.51.8.9.....651856.73.27.....8.45394687214.8.7.9.6 A2: 5,6 => SOLVED * 821539647543761289976824513364295178297183465185647392752916834639458721418372956 * PAIR F5: 3,4 COL F F1: 3,4,2,9 # reduction candidate for 3,4 F1: 3,4 => CTR * 8.19..6.7.4.7.1.899....6.13..42.5178297..34651856473927....98.4539468721418.729.6 F1: 2,9 # 21 pairs * PAIR C7: 2,6 BLK 7 B7: 2,6,1,5 # reduction candidate for 2,6 B7: 2,6 => CTR * 8.1...6.7.4.7.1.899....6.13..42.5178.97...4651856473927.....8.4539468721418.729.6 B7: 1,5 # 22 pairs * PAIR C7: 2,6 ROW 7 E7: 2,6,1,3,5 # reduction candidate for 2,6 E7: 2,6 => CTR * 8.1...6.7.4.7.1.899....6.13.642.5178.97...4651856473927.....8.4.394.87214.8.7.9.6 E7: 1,3,5 # 20 pairs F7: 2,6,3,9 # reduction candidate for 2,6 F7: 2,6 # 24 pairs * PAIR C7: 2,6 COL C C2: 2,6,3 # reduction candidate for 2,6 C2: 2,6 => CTR * 8.1...6.734.7.1.899......13674235198293..47651856973.27.....8.4.394.8.214.8...9.6 C2: 3 # 21 pairs C3: 2,6,7 # reduction candidate for 2,6 C3: 2,6 => SOLVED * 821539647543761289976824513364295178297183465185647392752916834639458721418372956 C3: 7 => CTR * 8.1...657543761289967...4136742.5198.9....7651856973427.....8.4.394785214.8...976 * PAIR A8: 5,6 BLK 7 B7: 5,6,1,2 # reduction candidate for 5,6 B7: 5,6 # 24 pairs B7: 1,2 # 22 pairs * PAIR A8: 5,6 ROW 8 E8: 5,6,7 # reduction candidate for 5,6 E8: 5,6 => SOLVED * 821539647543761289976824513364295178297183465185647392752916834639458721418372956 E8: 7 => CTR * 8.1...6.7.4.7.1.899......13..42.51.8.9.....651856.73.27.....8.46394785214.8...976 * PAIR A8: 5,6 COL A A2: 5,6,2,3 # reduction candidate for 5,6 A2: 5,6 => SOLVED * 821539647543761289976824513364295178297183465185647392752916834639458721418372956 A2: 2,3 => CTR * 8.1...6.7.467.1.899....6.136.42.51.8.9.....651856.73.27.....8.45394687214.8.7.9.6 * PAIR F9: 2,3 BLK 8 E7: 2,3,1,5,6 # reduction candidate for 2,3 E7: 2,3 => CTR * 8.13.96.75437612899.6....13364295178297..3465185647392712936854639458721458172936 E7: 1,5,6 # 20 pairs F7: 2,3,6,9 # reduction candidate for 2,3 F7: 2,3 => CTR * 8.1.4965754.7.1.899....6.13..42.51.8.9...47651856973427..9..8.4.394785214.8...976 F7: 6,9 # 21 pairs E9: 2,3,1,5,7 # reduction candidate for 2,3 E9: 2,3 => CTR * 8.1...6575437612899.....413.742.519829.....651856.73.27.....8.4.394785214.8...976 E9: 1,5,7 # 20 pairs * PAIR F9: 2,3 COL F F1: 2,3,4,9 # reduction candidate for 2,3 F1: 2,3 => CTR * 8.194365754.7.1.899....6.13..42.51.8.9...47651856973427....98.4.394785214.8...976 F1: 4,9 # 21 pairs * PAIR H7: 3,5 BLK 9 H9: 3,5,7 # reduction candidate for 3,5 H9: 3,5 => SOLVED * 821539647543761289976824513364295178297183465185647392752916834639458721418372956 H9: 7 => CTR * 8.1...6575437612899.....413.742.519829.....651856.73.27.....834.394.85214.8...976 * PAIR H7: 3,5 ROW 7 D7: 3,5,1,9 # reduction candidate for 3,5 D7: 3,5 => CTR * 8.19..6.7.4.7.1.899....6.13..42.51782971834651856473927...198.4539468721418.729.6 D7: 1,9 # 21 pairs E7: 3,5,1,2,6 # reduction candidate for 3,5 E7: 3,5 # 22 pairs * PAIR G8: 5,7 BLK 9 H9: 5,7,3 # reduction candidate for 5,7 H9: 3 => CTR * 82153.647.437.1.8997...4.13.64295178297..34651856473927....6854639458721458172936 H9: 5,7 # 20 pairs * PAIR G8: 5,7 ROW 8 E8: 5,7,6 # reduction candidate for 5,7 E8: 5,7 => SOLVED * 821539647543761289976824513364295178297183465185647392752916834639458721418372956 E8: 6 => CTR * 8.1...6.7.4.7.1.899....6.13..42.5178.97...4651856473927.....8.45394687214.8.7.9.6 * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-601842-base-pr-000.dot * REASONING * PRF # A2: 2,5 => SOL * DIS # A2: 3,6 => CTR => A2: 2,5 * DIS # B3: 2,5 => CTR => B3: 6,7 * DIS # E1: 2,5 => CTR => E1: 3,4 * DIS # G3: 2 => CTR => G3: 4,5 * PRF # G3: 2,5 => SOL * DIS # G3: 4 => CTR => G3: 2,5 * PRF # A2: 2,5 => SOL * DIS # A2: 3,6 => CTR => A2: 2,5 * DIS # E2: 2,5 => CTR => E2: 6 * PRF # E2: 6 => SOL * DIS # A2: 3,6 => CTR => A2: 2,5 * PRF # A2: 2,5 => SOL * DIS # B3: 2,5 => CTR => B3: 6,7 * DIS # C5: 2,3 => CTR => C5: 7 * PRF # C5: 7 => SOL * DIS # A2: 2,3 => CTR => A2: 5,6 * PRF # A2: 5,6 => SOL * DIS # F1: 3,4 => CTR => F1: 2,9 * DIS # B7: 2,6 => CTR => B7: 1,5 * DIS # E7: 2,6 => CTR => E7: 1,3,5 * DIS # C2: 2,6 => CTR => C2: 3 * PRF # C3: 2,6 => SOL * DIS # C3: 7 => CTR => C3: 2,6 * PRF # E8: 5,6 => SOL * DIS # E8: 7 => CTR => E8: 5,6 * PRF # A2: 5,6 => SOL * DIS # A2: 2,3 => CTR => A2: 5,6 * DIS # E7: 2,3 => CTR => E7: 1,5,6 * DIS # F7: 2,3 => CTR => F7: 6,9 * DIS # E9: 2,3 => CTR => E9: 1,5,7 * DIS # F1: 2,3 => CTR => F1: 4,9 * PRF # H9: 3,5 => SOL * DIS # H9: 7 => CTR => H9: 3,5 * DIS # D7: 3,5 => CTR => D7: 1,9 * DIS # H9: 3 => CTR => H9: 5,7 * PRF # E8: 5,7 => SOL * DIS # E8: 6 => CTR => E8: 5,7 * CNT 38 HDP CHAINS / 62 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,A8,B1,B4,C7,D3,D5,E4,E5,E6,F5,F9,G2,G5,G8,H1,H4,H6,H7) * 8.1...6.7.4.7.1.899......13..42.51.8.9.....651856.73.27.....8.4.394.8.214.8...9.6 * PAIR B1: 2,5 BLK 1 A2: 2,5,3,6 # reduction candidate for 2,5 A2: 2,5 => SOLVED * 821539647543761289976824513364295178297183465185647392752916834639458721418372956 * DURATION: 0:00:02.288791 START: 07:14:41.954331 END: 07:14:44.243122 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-601842-base-pr-001.dot * REASONING * PRF # A2: 2,5 => SOL * STA A2: 2,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokus.de/601842.html sehr schwierig level: medium * PAIR REDUCTION .. * ROUND 1: 8.1...6.7.4.7.1.899......13..42.51.8.9.....651856.73.27.....8.4.394.8.214.8...9.6 B1: 2,5 A2: 2,3,5,6 # reduction candidate for 2,5 A2: 2,5 => SOLVED * 821539647543761289976824513364295178297183465185647392752916834639458721418372956 * SOLVED! -------------------------------------------------- * AUTO .. H3 = 1 # set value G7 = 8 # set value I8 = 1 # set value Q1: 3.. = A2,C2: 3.. => E2 != 3 Q7: 1.. = B7,B9: 1.. => B6 != 1 Q5: 9.. = E4,E6: 9.. => E1,E2,E7,E8 != 9 I2: 9.. # hidden single C8: 9.. # hidden single I2 = 9 # set value I4: 8 # naked single I4 = 8 # set value I6: 2 # naked single I6 = 2 # set value I5: 5 # naked single A6: 1 # naked single B6: 8 # naked single C8 = 9 # set value I5 = 5 # set value A6 = 1 # set value B6 = 8 # set value D5,E5: 1,8.. => D5,E5 != 3,4 # hidden pair * UNSOLVED! |:step:| 00 -------------------------------------------------- highlight 4 E1: 2,3,4,5 H1: 4,5 H6: 4,9 E6: 4,9 => F1,E3 != 4 # x-wing (nested) highlight 6 B3 = 6 => A4 = 6 B3 = 6 => E2,F7,A8 = 6 => CTR => B3 != 6 # forced chain |:step:| 01 -------------------------------------------------- highlight 7 => full complementary chain * DISABLE VALUE:: C5 != 7 => A5,C5 = 2,3 => CTR * FORCE VALUE:: C5 = 7 |:step:| 01 --------------------------------------------------
Solution
position: 821539647543761289976824513364295178297183465185647392752916834639458721418372956 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:
* PRF # A2: 2,5 => SOL * DIS # A2: 3,6 => CTR => A2: 2,5 * DIS # B3: 2,5 => CTR => B3: 6,7 * INC # B3: 6,7 => UNS * DIS # E1: 2,5 => CTR => E1: 3,4 * INC # E1: 3,4 => UNS * INC # B7: 2,5 => UNS * INC # B9: 2,5 => UNS * INC # E3: 5,8 => UNS * INC # E3: 2,4,6 => UNS * INC # G3: 4,5 => UNS * DIS # G3: 2 => CTR => G3: 4,5 * INC # E1: 4,5 => UNS * INC # E1: 2,3 => UNS * PRF # G3: 2,5 => SOL * DIS # G3: 4 => CTR => G3: 2,5 * PRF # A2: 2,5 => SOL * DIS # A2: 3,6 => CTR => A2: 2,5 * DIS # E2: 2,5 => CTR => E2: 6 * PRF # E2: 6 => SOL * DIS # A2: 3,6 => CTR => A2: 2,5 * PRF # A2: 2,5 => SOL * INC # B3: 6,7 => UNS * DIS # B3: 2,5 => CTR => B3: 6,7 * DIS # C5: 2,3 => CTR => C5: 7 * PRF # C5: 7 => SOL * DIS # A2: 2,3 => CTR => A2: 5,6 * PRF # A2: 5,6 => SOL * DIS # F1: 3,4 => CTR => F1: 2,9 * INC # F1: 2,9 => UNS * DIS # B7: 2,6 => CTR => B7: 1,5 * INC # B7: 1,5 => UNS * DIS # E7: 2,6 => CTR => E7: 1,3,5 * INC # E7: 1,3,5 => UNS * INC # F7: 2,6 => UNS * DIS # C2: 2,6 => CTR => C2: 3 * INC # C2: 3 => UNS * PRF # C3: 2,6 => SOL * DIS # C3: 7 => CTR => C3: 2,6 * INC # B7: 5,6 => UNS * INC # B7: 1,2 => UNS * PRF # E8: 5,6 => SOL * DIS # E8: 7 => CTR => E8: 5,6 * PRF # A2: 5,6 => SOL * DIS # A2: 2,3 => CTR => A2: 5,6 * DIS # E7: 2,3 => CTR => E7: 1,5,6 * INC # E7: 1,5,6 => UNS * DIS # F7: 2,3 => CTR => F7: 6,9 * INC # F7: 6,9 => UNS * DIS # E9: 2,3 => CTR => E9: 1,5,7 * INC # E9: 1,5,7 => UNS * DIS # F1: 2,3 => CTR => F1: 4,9 * INC # F1: 4,9 => UNS * PRF # H9: 3,5 => SOL * DIS # H9: 7 => CTR => H9: 3,5 * DIS # D7: 3,5 => CTR => D7: 1,9 * INC # D7: 1,9 => UNS * INC # E7: 3,5 => UNS * INC # H9: 5,7 => UNS * DIS # H9: 3 => CTR => H9: 5,7 * PRF # E8: 5,7 => SOL * DIS # E8: 6 => CTR => E8: 5,7 * CNT 62 HDP CHAINS / 62 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A2: 2,5 => SOL * STA A2: 2,5 * CNT 1 HDP CHAINS / 1 HYP OPENED