Analysis of zz-www.sudokuoftheday.co.uk-20060327-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006
level: medium
position: 96.8.2.4...4.5...2...9..7.62.....87.8492............6..9.5.....5....9.1...142...7 initial
Autosolve
position: 96.8.2.4...4.5...2...9..7.62.6..587.8492...........26.49.5..62.5....941.6.142...7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 1,3 => CTR => B2: 7,8 * DIS # E3: 1,3 => CTR => E3: 4 * DIS # A6: 1,3 => CTR => A6: 7 * PRF # F2: 6,7 => SOL * DIS # F2: 1,3 => CTR => F2: 6,7 * DIS # B3: 5,8 => CTR => B3: 2 * DIS # A6: 1,3 => CTR => A6: 7 * DIS # B6: 1,3 => CTR => B6: 5,7 * DIS # B2: 1,3 => CTR => B2: 7,8 * DIS # E6: 4,9 => CTR => E6: 8 * DIS # E8: 6,7 => CTR => E8: 3,8 * PRF # E8: 3,8 => SOL * PRF # F2: 6,7 => SOL * DIS # F2: 1,3 => CTR => F2: 6,7 * DIS # A6: 1,3 => CTR => A6: 7 * DIS # B6: 1,3 => CTR => B6: 5,7 * DIS # E6: 9 => CTR => E6: 4,8 * DIS # E6: 4,9 => CTR => E6: 8 * PRF # C7: 3,8 => SOL * DIS # C7: 7 => CTR => C7: 3,8 * DIS # B8: 3,8 => CTR => B8: 2,7 * DIS # C8: 3,8 => CTR => C8: 2,7 * DIS # B2: 1,7 => CTR => B2: 3,8 * DIS # E8: 6,7 => CTR => E8: 3,8 * PRF # E8: 3,8 => SOL * DIS # E7: 3,8 => CTR => E7: 1,7 * DIS # F7: 3,8 => CTR => F7: 1,7 * PRF # E8: 3,8 => SOL * DIS # E8: 6,7 => CTR => E8: 3,8 * PRF # C7: 3,8 => SOL * DIS # C7: 7 => CTR => C7: 3,8 * DIS # E7: 3,8 => CTR => E7: 1,7 * DIS # F7: 3,8 => CTR => F7: 1,7 * DIS # B8: 3,8 => CTR => B8: 2,7 * DIS # C8: 3,8 => CTR => C8: 2,7 * PRF # E8: 3,8 => SOL * DIS # E8: 6,7 => CTR => E8: 3,8 * CNT 37 HDP CHAINS / 67 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 1,3 => CTR => B2: 7,8 * DIS B2: 7,8 # A2: 7 => CTR => A2: 1,3 * DIS B2: 7,8 + A2: 1,3 # E3: 1,3 => CTR => E3: 4 * PRF B2: 7,8 + A2: 1,3 + E3: 4 # F2: 6,7 => SOL * STA B2: 7,8 + A2: 1,3 + E3: 4 + F2: 6,7 * CNT 4 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 96.8.2.4...4.5...2...9..7.62.....87.8492............6..9.5.....5....9.1...142...7 | initial |
| 96.8.2.4...4.5...2...9..7.62.6..587.8492...........26.49.5..62.5....941.6.142...7 | autosolve |
| 967812345384756192125943786216395874849267531753184269498571623572639418631428957 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (22) A3: 1,3 D2: 6,7 I1: 1,5 H3: 5,8 B4: 1,3 D4: 1,3 E4: 4,9 E5: 6,7 F5: 6,7 D6: 1,3 F6: 4,8 I4: 4,9 H5: 3,5 I5: 1,5 I6: 4,9 B9: 3,8 D8: 6,7 F9: 3,8 I7: 3,8 I8: 3,8 G9: 5,9 H9: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D4,D6: 1.. / D4 = 1 => 0 pairs (X) / D6 = 1 => 20 pairs (_) G5,I5: 1.. / G5 = 1 => 23 pairs (_) / I5 = 1 => 21 pairs (_) E7,F7: 1.. / E7 = 1 => 25 pairs (_) / F7 = 1 => 0 pairs (*) B4,D4: 1.. / B4 = 1 => 20 pairs (_) / D4 = 1 => 0 pairs (X) I1,I5: 1.. / I1 = 1 => 23 pairs (_) / I5 = 1 => 21 pairs (_) B3,C3: 2.. / B3 = 2 => 24 pairs (_) / C3 = 2 => 0 pairs (X) B8,C8: 2.. / B8 = 2 => 0 pairs (X) / C8 = 2 => 24 pairs (_) B3,B8: 2.. / B3 = 2 => 24 pairs (_) / B8 = 2 => 0 pairs (X) C3,C8: 2.. / C3 = 2 => 0 pairs (X) / C8 = 2 => 24 pairs (_) D4,D6: 3.. / D4 = 3 => 20 pairs (_) / D6 = 3 => 0 pairs (X) G5,H5: 3.. / G5 = 3 => 18 pairs (_) / H5 = 3 => 23 pairs (_) I7,I8: 3.. / I7 = 3 => 21 pairs (_) / I8 = 3 => 23 pairs (_) B4,D4: 3.. / B4 = 3 => 0 pairs (X) / D4 = 3 => 20 pairs (_) B9,F9: 3.. / B9 = 3 => 18 pairs (_) / F9 = 3 => 0 pairs (X) H2,H5: 3.. / H2 = 3 => 18 pairs (_) / H5 = 3 => 23 pairs (_) E3,F3: 4.. / E3 = 4 => 19 pairs (_) / F3 = 4 => 0 pairs (X) I4,I6: 4.. / I4 = 4 => 20 pairs (_) / I6 = 4 => 0 pairs (X) E4,I4: 4.. / E4 = 4 => 0 pairs (X) / I4 = 4 => 20 pairs (_) F3,F6: 4.. / F3 = 4 => 0 pairs (X) / F6 = 4 => 19 pairs (_) B6,C6: 5.. / B6 = 5 => 24 pairs (_) / C6 = 5 => 0 pairs (X) G9,H9: 5.. / G9 = 5 => 24 pairs (_) / H9 = 5 => 19 pairs (_) B3,B6: 5.. / B3 = 5 => 0 pairs (X) / B6 = 5 => 24 pairs (_) I1,I5: 5.. / I1 = 5 => 21 pairs (_) / I5 = 5 => 23 pairs (_) D2,F2: 6.. / D2 = 6 => 0 pairs (X) / F2 = 6 => 0 pairs (_) E5,F5: 6.. / E5 = 6 => 0 pairs (*) / F5 = 6 => 0 pairs (X) D8,E8: 6.. / D8 = 6 => 0 pairs (*) / E8 = 6 => 0 pairs (X) D2,D8: 6.. / D2 = 6 => 0 pairs (X) / D8 = 6 => 0 pairs (_) E5,E8: 6.. / E5 = 6 => 0 pairs (*) / E8 = 6 => 0 pairs (X) F2,F5: 6.. / F2 = 6 => 0 pairs (*) / F5 = 6 => 0 pairs (X) E5,F5: 7.. / E5 = 7 => 0 pairs (X) / F5 = 7 => 0 pairs (_) C1,E1: 7.. / C1 = 7 => 0 pairs (*) / E1 = 7 => 0 pairs (X) A2,A6: 7.. / A2 = 7 => 0 pairs (X) / A6 = 7 => 26 pairs (_) D2,D8: 7.. / D2 = 7 => 0 pairs (*) / D8 = 7 => 0 pairs (X) H2,H3: 8.. / H2 = 8 => 0 pairs (X) / H3 = 8 => 21 pairs (_) E6,F6: 8.. / E6 = 8 => 19 pairs (_) / F6 = 8 => 0 pairs (X) I7,I8: 8.. / I7 = 8 => 23 pairs (_) / I8 = 8 => 21 pairs (_) B2,H2: 8.. / B2 = 8 => 21 pairs (_) / H2 = 8 => 0 pairs (X) B9,F9: 8.. / B9 = 8 => 0 pairs (X) / F9 = 8 => 18 pairs (_) G2,H2: 9.. / G2 = 9 => 24 pairs (_) / H2 = 9 => 19 pairs (_) E4,E6: 9.. / E4 = 9 => 20 pairs (_) / E6 = 9 => 0 pairs (X) I4,I6: 9.. / I4 = 9 => 0 pairs (X) / I6 = 9 => 20 pairs (_) G9,H9: 9.. / G9 = 9 => 19 pairs (_) / H9 = 9 => 24 pairs (_) E4,I4: 9.. / E4 = 9 => 20 pairs (_) / I4 = 9 => 0 pairs (X) E6,I6: 9.. / E6 = 9 => 0 pairs (X) / I6 = 9 => 20 pairs (_) G2,G9: 9.. / G2 = 9 => 24 pairs (_) / G9 = 9 => 19 pairs (_) H2,H9: 9.. / H2 = 9 => 19 pairs (_) / H9 = 9 => 24 pairs (_) * DURATION: 0:01:06.208173 START: 21:56:36.498649 END: 21:57:42.706822 2019-04-30 * CP COUNT: (46) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B4,B9,D2,D4,D6,D8,E4,E5,F5,F6,F9,G9,H3,H5,H9,I1,I4,I5,I6,I7,I8) * 96.8.2.4...4.5...2...9..7.62.6..587.8492...........26.49.5..62.5....941.6.142...7 * PAIR A3: 1,3 BLK 1 A2: 1,3,7 # reduction candidate for 1,3 A2: 1,3 # 26 pairs B2: 1,3,7,8 # reduction candidate for 1,3 B2: 1,3 => CTR * 965872.4...4.5..82...9..7562.6..587.8492...35.5....26.49.5..62.5726.941.6.142.597 B2: 7,8 # 24 pairs * PAIR A3: 1,3 ROW 3 E3: 1,3,4 # reduction candidate for 1,3 E3: 1,3 => CTR * 965872341..4651.82..89.47562.6..587.8492...35.5...826.49.5..62.5.2..941.681423597 E3: 4 # 19 pairs F3: 1,3,4 # reduction candidate for 1,3 F3: 1,3 # 19 pairs * PAIR A3: 1,3 COL A A6: 1,3,7 # reduction candidate for 1,3 A6: 1,3 => CTR * 96.8.2.4.7.465...2...9..7.62.6..587.8492.6.........26.49.5.762.5....941.6.142...7 A6: 7 # 26 pairs * PAIR D2: 6,7 BLK 2 F2: 6,7,1,3 # reduction candidate for 6,7 F2: 6,7 => SOLVED * 967812345384756192125943786216395874849267531753184269498571623572639418631428957 F2: 1,3 => CTR * 96.8.2.4...465...2...9..7.62.6..587.8492.6.........26.49.5.762.5....941.6.142...7 * PAIR I1: 1,5 BLK 3 G1: 1,5,3 # reduction candidate for 1,5 G1: 3 # 26 pairs G1: 1,5 # 26 pairs * PAIR H3: 5,8 ROW 3 B3: 5,8,2 # reduction candidate for 5,8 B3: 5,8 => CTR * 96.872.4...465...2..29..7.62.6..587.84926..........26.49.5..62.52...941.6.142...7 B3: 2 # 24 pairs C3: 5,8,2 # reduction candidate for 5,8 C3: 5,8 # 24 pairs * PAIR B4: 1,3 BLK 4 A6: 1,3,7 # reduction candidate for 1,3 A6: 1,3 => CTR * 96.8.2.4.7.465...2...9..7.62.6..587.8492.6.........26.49.5.762.5....941.6.142...7 A6: 7 # 26 pairs B6: 1,3,5,7 # reduction candidate for 1,3 B6: 1,3 => CTR * 96.8.2.4...4.5...2.529..7862.6..587.8492.......5...26.49.5..62.52...941.6.142...7 B6: 5,7 # 23 pairs * PAIR B4: 1,3 COL B B2: 1,3,7,8 # reduction candidate for 1,3 B2: 1,3 => CTR * 965872.4...4.5..82...9..7562.6..587.8492...35.5....26.49.5..62.5726.941.6.142.597 B2: 7,8 # 24 pairs * PAIR E4: 4,9 BLK 5 E6: 4,9,8 # reduction candidate for 4,9 E6: 4,9 => CTR * 965872341..4651.82..89.47562.6..587.8492...35.5...826.49.5..62.5.2..941.681423597 E6: 8 # 19 pairs * PAIR E5: 6,7 COL E E8: 6,7,3,8 # reduction candidate for 6,7 E8: 6,7 => CTR * 9678.2.4...4.5...2...9..7.62.6..587.8492.....7.....26.49.5..62.5....941.6.142...7 E8: 3,8 => SOLVED * 967812345384756192125943786216395874849267531753184269498571623572639418631428957 * PAIR F5: 6,7 COL F F2: 6,7,1,3 # reduction candidate for 6,7 F2: 6,7 => SOLVED * 967812345384756192125943786216395874849267531753184269498571623572639418631428957 F2: 1,3 => CTR * 96.8.2.4...465...2...9..7.62.6..587.8492.6.........26.49.5.762.5....941.6.142...7 * PAIR D6: 1,3 ROW 6 A6: 1,3,7 # reduction candidate for 1,3 A6: 1,3 => CTR * 96.8.2.4.7.465...2...9..7.62.6..587.8492.6.........26.49.5.762.5....941.6.142...7 A6: 7 # 26 pairs B6: 1,3,5,7 # reduction candidate for 1,3 B6: 1,3 => CTR * 96.8.2.4...4.5...2.529..7862.6..587.8492.......5...26.49.5..62.52...941.6.142...7 B6: 5,7 # 23 pairs * PAIR F6: 4,8 BLK 5 E6: 4,8,9 # reduction candidate for 4,8 E6: 9 => CTR * 965872341..4651.82..89.47562.6.458798492...35.5..9826449.5..62.5.2..941.681423597 E6: 4,8 # 20 pairs * PAIR H5: 3,5 BLK 6 G5: 3,5,1 # reduction candidate for 3,5 G5: 1 # 23 pairs G5: 3,5 # 21 pairs * PAIR I5: 1,5 BLK 6 G5: 1,5,3 # reduction candidate for 1,5 G5: 1,5 # 23 pairs G5: 3 # 18 pairs * PAIR I6: 4,9 ROW 6 E6: 4,9,8 # reduction candidate for 4,9 E6: 4,9 => CTR * 965872341..4651.82..89.47562.6..587.8492...35.5...826.49.5..62.5.2..941.681423597 E6: 8 # 19 pairs * PAIR B9: 3,8 BLK 7 C7: 3,8,7 # reduction candidate for 3,8 C7: 3,8 => SOLVED * 967812345384756192125943786216395874849267531753184269498571623572639418631428957 C7: 7 => CTR * 96.872.4...465...2...9..7.62.6..587.84926..........26.4975..62.5....941.6.142...7 B8: 3,8,2,7 # reduction candidate for 3,8 B8: 3,8 => CTR * 96.8.2.4..7465..82.289..7562163.587.8492.6.357531..26.4975..62.5.276941.6.142.597 B8: 2,7 # 23 pairs C8: 3,8,2,7 # reduction candidate for 3,8 C8: 3,8 => CTR * 96.872.4...465...2..29..7.62163.587.8492...........26.4975..62.528..9413631428..7 C8: 2,7 # 23 pairs * PAIR B9: 3,8 COL B B2: 3,8,1,7 # reduction candidate for 3,8 B2: 1,7 => CTR * 965872341..465.982...9..7562.6..587.84926..35.5....26.49.5..62.5....941.6.142.597 B2: 3,8 # 24 pairs * PAIR D8: 6,7 BLK 8 E8: 6,7,3,8 # reduction candidate for 6,7 E8: 6,7 => CTR * 9678.2.4...4.5...2...9..7.62.6..587.8492.....7.....26.49.5..62.5....941.6.142...7 E8: 3,8 => SOLVED * 967812345384756192125943786216395874849267531753184269498571623572639418631428957 * PAIR F9: 3,8 BLK 8 E7: 3,8,1,7 # reduction candidate for 3,8 E7: 3,8 => CTR * 96.872.4...4653..2...9..7.62.6..587.8492...........26.4975.162.5....941.6.142...7 E7: 1,7 # 23 pairs F7: 3,8,1,7 # reduction candidate for 3,8 F7: 3,8 => CTR * 96.872.4...465...2...9..7.62.6..587.84926..........26.49751.62.5....941.6.142...7 F7: 1,7 # 23 pairs E8: 3,8,6,7 # reduction candidate for 3,8 E8: 3,8 => SOLVED * 967812345384756192125943786216395874849267531753184269498571623572639418631428957 E8: 6,7 => CTR * 9678.2.4...4.5...2...9..7.62.6..587.8492.....7.....26.49.5..62.5....941.6.142...7 * PAIR I7: 3,8 ROW 7 C7: 3,8,7 # reduction candidate for 3,8 C7: 3,8 => SOLVED * 967812345384756192125943786216395874849267531753184269498571623572639418631428957 C7: 7 => CTR * 96.872.4...465...2...9..7.62.6..587.84926..........26.4975..62.5....941.6.142...7 E7: 3,8,1,7 # reduction candidate for 3,8 E7: 3,8 => CTR * 96.872.4...4653..2...9..7.62.6..587.8492...........26.4975.162.5....941.6.142...7 E7: 1,7 # 23 pairs F7: 3,8,1,7 # reduction candidate for 3,8 F7: 3,8 => CTR * 96.872.4...465...2...9..7.62.6..587.84926..........26.49751.62.5....941.6.142...7 F7: 1,7 # 23 pairs * PAIR I8: 3,8 ROW 8 B8: 3,8,2,7 # reduction candidate for 3,8 B8: 3,8 => CTR * 96.8.2.4..7465..82.289..7562163.587.8492.6.357531..26.4975..62.5.276941.6.142.597 B8: 2,7 # 23 pairs C8: 3,8,2,7 # reduction candidate for 3,8 C8: 3,8 => CTR * 96.872.4...465...2..29..7.62163.587.8492...........26.4975..62.528..9413631428..7 C8: 2,7 # 23 pairs E8: 3,8,6,7 # reduction candidate for 3,8 E8: 3,8 => SOLVED * 967812345384756192125943786216395874849267531753184269498571623572639418631428957 E8: 6,7 => CTR * 9678.2.4...4.5...2...9..7.62.6..587.8492.....7.....26.49.5..62.5....941.6.142...7 * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060327-absurd-base-pr-000.dot * REASONING * DIS # B2: 1,3 => CTR => B2: 7,8 * DIS # E3: 1,3 => CTR => E3: 4 * DIS # A6: 1,3 => CTR => A6: 7 * PRF # F2: 6,7 => SOL * DIS # F2: 1,3 => CTR => F2: 6,7 * DIS # B3: 5,8 => CTR => B3: 2 * DIS # A6: 1,3 => CTR => A6: 7 * DIS # B6: 1,3 => CTR => B6: 5,7 * DIS # B2: 1,3 => CTR => B2: 7,8 * DIS # E6: 4,9 => CTR => E6: 8 * DIS # E8: 6,7 => CTR => E8: 3,8 * PRF # E8: 3,8 => SOL * PRF # F2: 6,7 => SOL * DIS # F2: 1,3 => CTR => F2: 6,7 * DIS # A6: 1,3 => CTR => A6: 7 * DIS # B6: 1,3 => CTR => B6: 5,7 * DIS # E6: 9 => CTR => E6: 4,8 * DIS # E6: 4,9 => CTR => E6: 8 * PRF # C7: 3,8 => SOL * DIS # C7: 7 => CTR => C7: 3,8 * DIS # B8: 3,8 => CTR => B8: 2,7 * DIS # C8: 3,8 => CTR => C8: 2,7 * DIS # B2: 1,7 => CTR => B2: 3,8 * DIS # E8: 6,7 => CTR => E8: 3,8 * PRF # E8: 3,8 => SOL * DIS # E7: 3,8 => CTR => E7: 1,7 * DIS # F7: 3,8 => CTR => F7: 1,7 * PRF # E8: 3,8 => SOL * DIS # E8: 6,7 => CTR => E8: 3,8 * PRF # C7: 3,8 => SOL * DIS # C7: 7 => CTR => C7: 3,8 * DIS # E7: 3,8 => CTR => E7: 1,7 * DIS # F7: 3,8 => CTR => F7: 1,7 * DIS # B8: 3,8 => CTR => B8: 2,7 * DIS # C8: 3,8 => CTR => C8: 2,7 * PRF # E8: 3,8 => SOL * DIS # E8: 6,7 => CTR => E8: 3,8 * CNT 37 HDP CHAINS / 67 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B4,B9,D2,D4,D6,D8,E4,E5,F5,F6,F9,G9,H3,H5,H9,I1,I4,I5,I6,I7,I8) * 96.8.2.4...4.5...2...9..7.62.6..587.8492...........26.49.5..62.5....941.6.142...7 * PAIR A3: 1,3 BLK 1 A2: 1,3,7 # reduction candidate for 1,3 A2: 1,3 # 26 pairs B2: 1,3,7,8 # reduction candidate for 1,3 B2: 1,3 => CTR * 965872.4...4.5..82...9..7562.6..587.8492...35.5....26.49.5..62.5726.941.6.142.597 * RESTART * PAIR A3: 1,3 BLK 1 A2: 1,3,7 # reduction candidate for 1,3 A2: 7 => CTR * 96.8.2.4.78465...21..9..7862.6..587.8492.6...3..1..26.49.5.762.5....941.6.142...7 * PAIR A3: 1,3 ROW 3 E3: 1,3,4 # reduction candidate for 1,3 E3: 1,3 => CTR * 96.8.2.4..74651.821.89347562.6..587.8492.6.357531.826.4975..62.5....941.681423..7 * RESTART * PAIR RESTART * PAIR D2: 6,7 BLK 2 F2: 6,7,1,3 # reduction candidate for 6,7 F2: 6,7 => SOLVED * 967812345384756192125943786216395874849267531753184269498571623572639418631428957 * DURATION: 0:00:06.020934 START: 21:58:34.610107 END: 21:58:40.631041 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060327-absurd-base-pr-001.dot * REASONING * DIS # B2: 1,3 => CTR => B2: 7,8 * DIS B2: 7,8 # A2: 7 => CTR => A2: 1,3 * DIS B2: 7,8 + A2: 1,3 # E3: 1,3 => CTR => E3: 4 * PRF B2: 7,8 + A2: 1,3 + E3: 4 # F2: 6,7 => SOL * STA B2: 7,8 + A2: 1,3 + E3: 4 + F2: 6,7 * CNT 4 HDP CHAINS / 6 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060327, absurd
Solution
position: 967812345384756192125943786216395874849267531753184269498571623572639418631428957 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 # A2: 1,3 => UNS * DIS # B2: 1,3 => CTR => B2: 7,8 * INC # B2: 7,8 => UNS * DIS # E3: 1,3 => CTR => E3: 4 * INC # E3: 4 => UNS * INC # F3: 1,3 => UNS * DIS # A6: 1,3 => CTR => A6: 7 * INC # A6: 7 => UNS * PRF # F2: 6,7 => SOL * DIS # F2: 1,3 => CTR => F2: 6,7 * INC # G1: 1,5 => UNS * INC # G1: 3 => UNS * DIS # B3: 5,8 => CTR => B3: 2 * INC # B3: 2 => UNS * INC # C3: 5,8 => UNS * DIS # A6: 1,3 => CTR => A6: 7 * INC # A6: 7 => UNS * DIS # B6: 1,3 => CTR => B6: 5,7 * INC # B6: 5,7 => UNS * DIS # B2: 1,3 => CTR => B2: 7,8 * INC # B2: 7,8 => UNS * DIS # E6: 4,9 => CTR => E6: 8 * INC # E6: 8 => UNS * DIS # E8: 6,7 => CTR => E8: 3,8 * PRF # E8: 3,8 => SOL * PRF # F2: 6,7 => SOL * DIS # F2: 1,3 => CTR => F2: 6,7 * DIS # A6: 1,3 => CTR => A6: 7 * INC # A6: 7 => UNS * DIS # B6: 1,3 => CTR => B6: 5,7 * INC # B6: 5,7 => UNS * INC # E6: 4,8 => UNS * DIS # E6: 9 => CTR => E6: 4,8 * INC # G5: 3,5 => UNS * INC # G5: 1 => UNS * INC # G5: 1,5 => UNS * INC # G5: 3 => UNS * DIS # E6: 4,9 => CTR => E6: 8 * INC # E6: 8 => UNS * PRF # C7: 3,8 => SOL * DIS # C7: 7 => CTR => C7: 3,8 * DIS # B8: 3,8 => CTR => B8: 2,7 * INC # B8: 2,7 => UNS * DIS # C8: 3,8 => CTR => C8: 2,7 * INC # C8: 2,7 => UNS * INC # B2: 3,8 => UNS * DIS # B2: 1,7 => CTR => B2: 3,8 * DIS # E8: 6,7 => CTR => E8: 3,8 * PRF # E8: 3,8 => SOL * DIS # E7: 3,8 => CTR => E7: 1,7 * INC # E7: 1,7 => UNS * DIS # F7: 3,8 => CTR => F7: 1,7 * INC # F7: 1,7 => UNS * PRF # E8: 3,8 => SOL * DIS # E8: 6,7 => CTR => E8: 3,8 * PRF # C7: 3,8 => SOL * DIS # C7: 7 => CTR => C7: 3,8 * DIS # E7: 3,8 => CTR => E7: 1,7 * INC # E7: 1,7 => UNS * DIS # F7: 3,8 => CTR => F7: 1,7 * INC # F7: 1,7 => UNS * DIS # B8: 3,8 => CTR => B8: 2,7 * INC # B8: 2,7 => UNS * DIS # C8: 3,8 => CTR => C8: 2,7 * INC # C8: 2,7 => UNS * PRF # E8: 3,8 => SOL * DIS # E8: 6,7 => CTR => E8: 3,8 * CNT 67 HDP CHAINS / 67 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 1,3 => UNS * DIS # B2: 1,3 => CTR => B2: 7,8 * INC B2: 7,8 # A2: 1,3 => UNS * DIS B2: 7,8 # A2: 7 => CTR => A2: 1,3 * DIS B2: 7,8 + A2: 1,3 # E3: 1,3 => CTR => E3: 4 * PRF B2: 7,8 + A2: 1,3 + E3: 4 # F2: 6,7 => SOL * STA B2: 7,8 + A2: 1,3 + E3: 4 + F2: 6,7 * CNT 6 HDP CHAINS / 6 HYP OPENED