Analysis of zz-www.sudokuoftheday.co.uk-20060403-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006
level: medium
position: .4..6......5.....99..2........18.2.3....75..8...34......34..65...1...9...6.5.7.34 initial
Autosolve
position: .4..6......5.....99..25....5..18.2.3....75..8...342.....34..65.451...9...6.5.7.34 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D1: 9 => CTR => D1: 7,8 * DIS # A2: 7,8 => CTR => A2: 1,2,3,6 * DIS # F1: 1,3 => CTR => F1: 8,9 * DIS # A2: 1,3 => CTR => A2: 2,6,7,8 * DIS # C4: 7,9 => CTR => C4: 4,6 * DIS # C4: 6,9 => CTR => C4: 4,7 * DIS # G2: 1,4 => CTR => G2: 3,7,8 * DIS # G3: 1,4 => CTR => G3: 3,7,8 * DIS # A2: 2,8 => CTR => A2: 1,3,6,7 * DIS # F1: 1,8 => CTR => F1: 3,9 * DIS # F8: 6,8 => CTR => F8: 3 * DIS # H8: 2,7 => CTR => H8: 8 * DIS # I1: 2,7 => CTR => I1: 1,5 * CNT 13 HDP CHAINS / 57 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D1: 9 => CTR => D1: 7,8 * DIS D1: 7,8 # A2: 7,8 => CTR => A2: 1,2,3,6 * DIS D1: 7,8 + A2: 1,2,3,6 # A2: 1,3 => CTR => A2: 2,6 * DIS D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 # C4: 7,9 => CTR => C4: 4 * DIS D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 # G2: 1,4 => CTR => G2: 3,7,8 * DIS D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 + G2: 3,7,8 # G3: 1,4 => CTR => G3: 3,7,8 * DIS D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 + G2: 3,7,8 + G3: 3,7,8 # A1: 2,8 => CTR => A1: 1,3,7 * DIS D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 + G2: 3,7,8 + G3: 3,7,8 + A1: 1,3,7 # H8: 2,7 => CTR => H8: 8 * PRF D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 + G2: 3,7,8 + G3: 3,7,8 + A1: 1,3,7 + H8: 8 # B3: 1,3 => SOL * STA D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 + G2: 3,7,8 + G3: 3,7,8 + A1: 1,3,7 + H8: 8 + B3: 1,3 * CNT 9 HDP CHAINS / 40 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .4..6......5.....99..2........18.2.3....75..8...34......34..65...1...9...6.5.7.34 | initial |
| .4..6......5.....99..25....5..18.2.3....75..8...342.....34..65.451...9...6.5.7.34 | autosolve |
| 347869521625731849918254376574186293236975418189342765793418652451623987862597134 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) D2: 7,8 E2: 1,3 B4: 7,9 F4: 6,9 D5: 6,9 G5: 1,4 A9: 2,8 F7: 1,8 D8: 6,8 E8: 2,3 I7: 1,2 I8: 2,7 G9: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I7,G9: 1.. / I7 = 1 => 0 pairs (X) / G9 = 1 => 14 pairs (_) E9,G9: 1.. / E9 = 1 => 0 pairs (X) / G9 = 1 => 14 pairs (_) A5,B5: 3.. / A5 = 3 => 13 pairs (_) / B5 = 3 => 13 pairs (_) E8,F8: 3.. / E8 = 3 => 0 pairs (X) / F8 = 3 => 14 pairs (_) E2,E8: 3.. / E2 = 3 => 14 pairs (_) / E8 = 3 => 0 pairs (X) F2,F3: 4.. / F2 = 4 => 13 pairs (_) / F3 = 4 => 13 pairs (_) C4,C5: 4.. / C4 = 4 => 13 pairs (_) / C5 = 4 => 0 pairs (X) C4,H4: 4.. / C4 = 4 => 13 pairs (_) / H4 = 4 => 0 pairs (X) G1,I1: 5.. / G1 = 5 => 15 pairs (_) / I1 = 5 => 15 pairs (_) G6,I6: 5.. / G6 = 5 => 15 pairs (_) / I6 = 5 => 15 pairs (_) G1,G6: 5.. / G1 = 5 => 15 pairs (_) / G6 = 5 => 15 pairs (_) I1,I6: 5.. / I1 = 5 => 15 pairs (_) / I6 = 5 => 15 pairs (_) A2,C3: 6.. / A2 = 6 => 14 pairs (_) / C3 = 6 => 0 pairs (X) F4,D5: 6.. / F4 = 6 => 12 pairs (_) / D5 = 6 => 0 pairs (X) D8,F8: 6.. / D8 = 6 => 12 pairs (_) / F8 = 6 => 0 pairs (X) A2,H2: 6.. / A2 = 6 => 14 pairs (_) / H2 = 6 => 0 pairs (X) D5,D8: 6.. / D5 = 6 => 0 pairs (X) / D8 = 6 => 12 pairs (_) F4,F8: 6.. / F4 = 6 => 12 pairs (_) / F8 = 6 => 0 pairs (X) I3,I6: 6.. / I3 = 6 => 14 pairs (_) / I6 = 6 => 0 pairs (X) D1,D2: 7.. / D1 = 7 => 11 pairs (_) / D2 = 7 => 13 pairs (_) A7,B7: 7.. / A7 = 7 => 13 pairs (_) / B7 = 7 => 16 pairs (_) H8,I8: 7.. / H8 = 7 => 0 pairs (X) / I8 = 7 => 14 pairs (_) H8,G9: 8.. / H8 = 8 => 14 pairs (_) / G9 = 8 => 0 pairs (X) D1,F1: 9.. / D1 = 9 => 0 pairs (X) / F1 = 9 => 12 pairs (_) F4,D5: 9.. / F4 = 9 => 0 pairs (X) / D5 = 9 => 12 pairs (_) B7,C9: 9.. / B7 = 9 => 14 pairs (_) / C9 = 9 => 14 pairs (_) E7,E9: 9.. / E7 = 9 => 14 pairs (_) / E9 = 9 => 14 pairs (_) B7,E7: 9.. / B7 = 9 => 14 pairs (_) / E7 = 9 => 14 pairs (_) C9,E9: 9.. / C9 = 9 => 14 pairs (_) / E9 = 9 => 14 pairs (_) D1,D5: 9.. / D1 = 9 => 0 pairs (X) / D5 = 9 => 12 pairs (_) F1,F4: 9.. / F1 = 9 => 12 pairs (_) / F4 = 9 => 0 pairs (X) * DURATION: 0:00:26.939483 START: 22:07:02.888912 END: 22:07:29.828395 2019-04-30 * CP COUNT: (31) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B4,D2,D5,D8,E2,E8,F4,F7,G5,G9,I7,I8) * .4..6......5.....99..25....5..18.2.3....75..8...342.....34..65.451...9...6.5.7.34 * PAIR D2: 7,8 BLK 2 D1: 7,8,9 # reduction candidate for 7,8 D1: 9 => CTR * .4.96......57....99..25....57.1892.3...675..8...342...78349165.4518.69...6.5.7834 D1: 7,8 # 12 pairs * PAIR D2: 7,8 ROW 2 A2: 7,8,1,2,3,6 # reduction candidate for 7,8 A2: 7,8 => CTR * 34..69..5.25....6991625...75.41862.3632975..81..342..6..34..65.4516..9...6.5.7.34 A2: 1,2,3,6 # 13 pairs B2: 7,8,1,2,3 # reduction candidate for 7,8 B2: 7,8 # 18 pairs G2: 7,8,1,3,4 # reduction candidate for 7,8 G2: 7,8 # 14 pairs H2: 7,8,1,2,4,6 # reduction candidate for 7,8 H2: 7,8 # 20 pairs * PAIR E2: 1,3 BLK 2 F1: 1,3,8,9 # reduction candidate for 1,3 F1: 1,3 => CTR * .4.96......57....99..25....57.1892.3...675..8...342...78349165.4518.69...6.5.7834 F1: 8,9 # 14 pairs F2: 1,3,4,8 # reduction candidate for 1,3 F2: 1,3 # 17 pairs F3: 1,3,4,8 # reduction candidate for 1,3 F3: 1,3 # 15 pairs * PAIR E2: 1,3 ROW 2 A2: 1,3,2,6,7,8 # reduction candidate for 1,3 A2: 1,3 => CTR * 14..69325325.1..699.625....5.41862.3632975..8...3425.6..34..65.4516..987.6.5.7134 A2: 2,6,7,8 # 13 pairs B2: 1,3,2,7,8 # reduction candidate for 1,3 B2: 1,3 # 17 pairs G2: 1,3,4,7,8 # reduction candidate for 1,3 G2: 1,3 # 17 pairs * PAIR B4: 7,9 BLK 4 C4: 7,9,4,6 # reduction candidate for 7,9 C4: 7,9 => CTR * .4..6......5.3...99..25....5..186243..4975168...342.9...349865145162397..6.517834 C4: 4,6 # 14 pairs B6: 7,9,1,8 # reduction candidate for 7,9 B6: 7,9 # 18 pairs C6: 7,9,6,8 # reduction candidate for 7,9 C6: 7,9 # 16 pairs * PAIR B4: 7,9 ROW 4 H4: 7,9,4,6 # reduction candidate for 7,9 H4: 7,9 # 14 pairs H4: 4,6 # 14 pairs * PAIR B4: 7,9 COL B B7: 7,9,2,8 # reduction candidate for 7,9 B7: 7,9 # 15 pairs B7: 2,8 # 15 pairs * PAIR F4: 6,9 ROW 4 C4: 6,9,4,7 # reduction candidate for 6,9 C4: 6,9 => CTR * .4..6......5.3...99..25....57.18.243..4.751.8...342...7834..651451...9...6.517834 C4: 4,7 # 14 pairs H4: 6,9,4,7 # reduction candidate for 6,9 H4: 6,9 # 13 pairs * PAIR D5: 6,9 ROW 5 C5: 6,9,2,4 # reduction candidate for 6,9 C5: 6,9 # 18 pairs H5: 6,9,1,4 # reduction candidate for 6,9 H5: 6,9 # 15 pairs * PAIR G5: 1,4 BLK 6 H5: 1,4,6,9 # reduction candidate for 1,4 H5: 6,9 # 15 pairs H5: 1,4 # 15 pairs * PAIR G5: 1,4 COL G G2: 1,4,3,7,8 # reduction candidate for 1,4 G2: 1,4 => CTR * .4..6......5.3...99..25....5..18.2.3....75..8...342.....349865145162397..6.517834 G2: 3,7,8 # 13 pairs G3: 1,4,3,7,8 # reduction candidate for 1,4 G3: 1,4 => CTR * .4..6......5.3.7.993725...65..18.2.33...75..8...3425.77834..651451...9...6.517834 G3: 3,7,8 # 13 pairs * PAIR A9: 2,8 BLK 7 A7: 2,8,7 # reduction candidate for 2,8 A7: 2,8 # 16 pairs B7: 2,8,7,9 # reduction candidate for 2,8 B7: 2,8 # 15 pairs C9: 2,8,9 # reduction candidate for 2,8 C9: 2,8 # 14 pairs * PAIR A9: 2,8 COL A A1: 2,8,1,3,7 # reduction candidate for 2,8 A1: 2,8 # 15 pairs A2: 2,8,1,3,6,7 # reduction candidate for 2,8 A2: 2,8 => CTR * 34..69125..5....699.625...75.41862.36329754181..3425.67.34..6514516..972.6.517834 A2: 1,3,6,7 # 13 pairs * PAIR F7: 1,8 COL F F1: 1,8,3,9 # reduction candidate for 1,8 F1: 1,8 => CTR * .4.96......57....99..25....57.1892.3...675..8...342...78349165.4518.69...6.5.7834 F1: 3,9 # 14 pairs F2: 1,8,3,4 # reduction candidate for 1,8 F2: 1,8 # 16 pairs F3: 1,8,3,4 # reduction candidate for 1,8 F3: 1,8 # 16 pairs * PAIR D8: 6,8 BLK 8 F8: 6,8,3 # reduction candidate for 6,8 F8: 6,8 => CTR * .4..6......5.1...99..25....5..18.2.3....75..8...342.....34.1652451.3.9.7.6.527134 F8: 3 # 14 pairs * PAIR I7: 1,2 ROW 7 E7: 1,2,9 # reduction candidate for 1,2 E7: 9 # 14 pairs E7: 1,2 # 14 pairs * PAIR I7: 1,2 COL I I1: 1,2,5,7 # reduction candidate for 1,2 I1: 1,2 # 16 pairs I1: 5,7 # 15 pairs * PAIR I8: 2,7 BLK 9 H8: 2,7,8 # reduction candidate for 2,7 H8: 2,7 => CTR * .4..6......5.....99..25....5..18.2.3....75..8...342.....34..651451...9..269517834 H8: 8 # 14 pairs * PAIR I8: 2,7 COL I I1: 2,7,1,5 # reduction candidate for 2,7 I1: 2,7 => CTR * .4..6.5..6.5.3...99..25.3.65..18.2.3.3..75..8...342..5..349865145162397..6.517834 I1: 1,5 # 15 pairs * PAIR G9: 1,8 COL G G1: 1,8,3,5,7 # reduction candidate for 1,8 G1: 1,8 # 17 pairs G2: 1,8,3,4,7 # reduction candidate for 1,8 G2: 1,8 # 15 pairs G3: 1,8,3,4,7 # reduction candidate for 1,8 G3: 1,8 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060403-absurd-base-pr-000.dot * REASONING * DIS # D1: 9 => CTR => D1: 7,8 * DIS # A2: 7,8 => CTR => A2: 1,2,3,6 * DIS # F1: 1,3 => CTR => F1: 8,9 * DIS # A2: 1,3 => CTR => A2: 2,6,7,8 * DIS # C4: 7,9 => CTR => C4: 4,6 * DIS # C4: 6,9 => CTR => C4: 4,7 * DIS # G2: 1,4 => CTR => G2: 3,7,8 * DIS # G3: 1,4 => CTR => G3: 3,7,8 * DIS # A2: 2,8 => CTR => A2: 1,3,6,7 * DIS # F1: 1,8 => CTR => F1: 3,9 * DIS # F8: 6,8 => CTR => F8: 3 * DIS # H8: 2,7 => CTR => H8: 8 * DIS # I1: 2,7 => CTR => I1: 1,5 * CNT 13 HDP CHAINS / 57 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B4,D2,D5,D8,E2,E8,F4,F7,G5,G9,I7,I8) * .4..6......5.....99..25....5..18.2.3....75..8...342.....34..65.451...9...6.5.7.34 * PAIR D2: 7,8 BLK 2 D1: 7,8,9 # reduction candidate for 7,8 D1: 9 => CTR * .4.96......57....99..25....57.1892.3...675..8...342...78349165.4518.69...6.5.7834 * PAIR D2: 7,8 ROW 2 A2: 7,8,1,2,3,6 # reduction candidate for 7,8 A2: 7,8 => CTR * 34..69..5.25....6991625...75.41862.3632975..81..342..6..34..65.4516..9...6.5.7.34 B2: 7,8,1,2,3 # reduction candidate for 7,8 B2: 7,8 # 17 pairs G2: 7,8,1,3,4 # reduction candidate for 7,8 G2: 7,8 # 13 pairs H2: 7,8,1,2,4,6 # reduction candidate for 7,8 H2: 7,8 # 22 pairs * PAIR RESTART * PAIR D2: 7,8 ROW 2 B2: 7,8,1,2,3 # reduction candidate for 7,8 B2: 7,8 # 17 pairs G2: 7,8,1,3,4 # reduction candidate for 7,8 G2: 7,8 # 13 pairs H2: 7,8,1,2,4,6 # reduction candidate for 7,8 H2: 7,8 # 22 pairs * PAIR E2: 1,3 BLK 2 F2: 1,3,4 # reduction candidate for 1,3 F2: 1,3 # 16 pairs F3: 1,3,4 # reduction candidate for 1,3 F3: 1,3 # 13 pairs * PAIR E2: 1,3 ROW 2 A2: 1,3,2,6 # reduction candidate for 1,3 A2: 1,3 => CTR * 14..69325325.1..699.625....5.41862.3632975..8...3425.6..34..65.4516..987.6.5.7134 B2: 1,3,2,7,8 # reduction candidate for 1,3 B2: 1,3 # 17 pairs G2: 1,3,4,7,8 # reduction candidate for 1,3 G2: 1,3 # 18 pairs * PAIR RESTART * PAIR E2: 1,3 BLK 2 F2: 1,3,4 # reduction candidate for 1,3 F2: 1,3 # 16 pairs F3: 1,3,4 # reduction candidate for 1,3 F3: 1,3 # 14 pairs * PAIR E2: 1,3 ROW 2 B2: 1,3,2,7,8 # reduction candidate for 1,3 B2: 1,3 # 17 pairs G2: 1,3,4,7,8 # reduction candidate for 1,3 G2: 1,3 # 18 pairs * PAIR B4: 7,9 BLK 4 C4: 7,9,4 # reduction candidate for 7,9 C4: 7,9 => CTR * .4..69...6.5.3...99..25...65..186243..4975168..6342.9...349.6514516..9...6.517834 B6: 7,9,1,8 # reduction candidate for 7,9 B6: 7,9 # 19 pairs C6: 7,9,6,8 # reduction candidate for 7,9 C6: 7,9 # 17 pairs * PAIR B4: 7,9 COL B B7: 7,9,2,8 # reduction candidate for 7,9 B7: 7,9 # 17 pairs B7: 2,8 # 17 pairs * PAIR G5: 1,4 BLK 6 H5: 1,4,6 # reduction candidate for 1,4 H5: 6 # 22 pairs H5: 1,4 # 18 pairs * PAIR G5: 1,4 COL G G2: 1,4,3,7,8 # reduction candidate for 1,4 G2: 1,4 => CTR * .4..69.....5.3...99..25....5.41862.3...975..8...342.....349.6514516..9...6.517834 G3: 1,4,3,7,8 # reduction candidate for 1,4 G3: 1,4 => CTR * .4..69.....5.3.7.993725..865.41862.33..975..8...3425.77834..6514516..9...6.517834 * PAIR RESTART * PAIR A9: 2,8 BLK 7 A7: 2,8,7 # reduction candidate for 2,8 A7: 2,8 # 20 pairs B7: 2,8,7,9 # reduction candidate for 2,8 B7: 2,8 # 17 pairs C9: 2,8,9 # reduction candidate for 2,8 C9: 2,8 # 15 pairs * PAIR A9: 2,8 COL A A1: 2,8,1,3,7 # reduction candidate for 2,8 A1: 2,8 => CTR * .4..693156.5....299..25..465.41862.33269754.81..3425..7.34..65.4516..9...6.5.7134 * PAIR RESTART * PAIR A9: 2,8 BLK 7 A7: 2,8,7 # reduction candidate for 2,8 A7: 2,8 # 20 pairs B7: 2,8,7,9 # reduction candidate for 2,8 B7: 2,8 # 18 pairs C9: 2,8,9 # reduction candidate for 2,8 C9: 2,8 # 16 pairs * PAIR I7: 1,2 ROW 7 E7: 1,2,9 # reduction candidate for 1,2 E7: 9 # 16 pairs E7: 1,2 # 16 pairs * PAIR I7: 1,2 COL I I1: 1,2,5,7 # reduction candidate for 1,2 I1: 1,2 # 18 pairs I1: 5,7 # 17 pairs * PAIR I8: 2,7 BLK 9 H8: 2,7,8 # reduction candidate for 2,7 H8: 2,7 => CTR * .4..69.....5.....99..25....5.41862.3...9754.8...342.....34.16524516.89...6.5.7834 * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A1,A2,A9,B2,B6,C5,C9,D1,D2,F2,F3,G2,G6,H5,I1,I3) * .4..69.....5.3...99..25....574186293...9754.8..9342...793418652451623987.6.597134 * PAIR A1: 1,3 BLK 1 B3: 1,3,8 # reduction candidate for 1,3 B3: 1,3 => SOLVED * 347869521625731849918254376574186293236975418189342765793418652451623987862597134 * DURATION: 0:00:25.162330 START: 22:07:56.001035 END: 22:08:21.163365 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060403-absurd-base-pr-001.dot * REASONING * DIS # D1: 9 => CTR => D1: 7,8 * DIS D1: 7,8 # A2: 7,8 => CTR => A2: 1,2,3,6 * DIS D1: 7,8 + A2: 1,2,3,6 # A2: 1,3 => CTR => A2: 2,6 * DIS D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 # C4: 7,9 => CTR => C4: 4 * DIS D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 # G2: 1,4 => CTR => G2: 3,7,8 * DIS D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 + G2: 3,7,8 # G3: 1,4 => CTR => G3: 3,7,8 * DIS D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 + G2: 3,7,8 + G3: 3,7,8 # A1: 2,8 => CTR => A1: 1,3,7 * DIS D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 + G2: 3,7,8 + G3: 3,7,8 + A1: 1,3,7 # H8: 2,7 => CTR => H8: 8 * PRF D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 + G2: 3,7,8 + G3: 3,7,8 + A1: 1,3,7 + H8: 8 # B3: 1,3 => SOL * STA D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 + G2: 3,7,8 + G3: 3,7,8 + A1: 1,3,7 + H8: 8 + B3: 1,3 * CNT 9 HDP CHAINS / 40 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060403, absurd
Solution
position: 347869521625731849918254376574186293236975418189342765793418652451623987862597134 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 # D1: 7,8 => UNS * DIS # D1: 9 => CTR => D1: 7,8 * DIS # A2: 7,8 => CTR => A2: 1,2,3,6 * INC # A2: 1,2,3,6 => UNS * INC # B2: 7,8 => UNS * INC # G2: 7,8 => UNS * INC # H2: 7,8 => UNS * DIS # F1: 1,3 => CTR => F1: 8,9 * INC # F1: 8,9 => UNS * INC # F2: 1,3 => UNS * INC # F3: 1,3 => UNS * DIS # A2: 1,3 => CTR => A2: 2,6,7,8 * INC # A2: 2,6,7,8 => UNS * INC # B2: 1,3 => UNS * INC # G2: 1,3 => UNS * DIS # C4: 7,9 => CTR => C4: 4,6 * INC # C4: 4,6 => UNS * INC # B6: 7,9 => UNS * INC # C6: 7,9 => UNS * INC # H4: 7,9 => UNS * INC # H4: 4,6 => UNS * INC # B7: 7,9 => UNS * INC # B7: 2,8 => UNS * DIS # C4: 6,9 => CTR => C4: 4,7 * INC # C4: 4,7 => UNS * INC # H4: 6,9 => UNS * INC # C5: 6,9 => UNS * INC # H5: 6,9 => UNS * INC # H5: 1,4 => UNS * INC # H5: 6,9 => UNS * DIS # G2: 1,4 => CTR => G2: 3,7,8 * INC # G2: 3,7,8 => UNS * DIS # G3: 1,4 => CTR => G3: 3,7,8 * INC # G3: 3,7,8 => UNS * INC # A7: 2,8 => UNS * INC # B7: 2,8 => UNS * INC # C9: 2,8 => UNS * INC # A1: 2,8 => UNS * DIS # A2: 2,8 => CTR => A2: 1,3,6,7 * INC # A2: 1,3,6,7 => UNS * DIS # F1: 1,8 => CTR => F1: 3,9 * INC # F1: 3,9 => UNS * INC # F2: 1,8 => UNS * INC # F3: 1,8 => UNS * DIS # F8: 6,8 => CTR => F8: 3 * INC # F8: 3 => UNS * INC # E7: 1,2 => UNS * INC # E7: 9 => UNS * INC # I1: 1,2 => UNS * INC # I1: 5,7 => UNS * DIS # H8: 2,7 => CTR => H8: 8 * INC # H8: 8 => UNS * DIS # I1: 2,7 => CTR => I1: 1,5 * INC # I1: 1,5 => UNS * INC # G1: 1,8 => UNS * INC # G2: 1,8 => UNS * INC # G3: 1,8 => UNS * CNT 57 HDP CHAINS / 57 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D1: 7,8 => UNS * DIS # D1: 9 => CTR => D1: 7,8 * DIS D1: 7,8 # A2: 7,8 => CTR => A2: 1,2,3,6 * INC D1: 7,8 + A2: 1,2,3,6 # B2: 7,8 => UNS * INC D1: 7,8 + A2: 1,2,3,6 # G2: 7,8 => UNS * INC D1: 7,8 + A2: 1,2,3,6 # H2: 7,8 => UNS * INC D1: 7,8 + A2: 1,2,3,6 # B2: 7,8 => UNS * INC D1: 7,8 + A2: 1,2,3,6 # G2: 7,8 => UNS * INC D1: 7,8 + A2: 1,2,3,6 # H2: 7,8 => UNS * INC D1: 7,8 + A2: 1,2,3,6 # F2: 1,3 => UNS * INC D1: 7,8 + A2: 1,2,3,6 # F3: 1,3 => UNS * DIS D1: 7,8 + A2: 1,2,3,6 # A2: 1,3 => CTR => A2: 2,6 * INC D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 # B2: 1,3 => UNS * INC D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 # G2: 1,3 => UNS * INC D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 # F2: 1,3 => UNS * INC D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 # F3: 1,3 => UNS * INC D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 # B2: 1,3 => UNS * INC D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 # G2: 1,3 => UNS * DIS D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 # C4: 7,9 => CTR => C4: 4 * INC D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 # B6: 7,9 => UNS * INC D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 # C6: 7,9 => UNS * INC D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 # B7: 7,9 => UNS * INC D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 # B7: 2,8 => UNS * INC D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 # H5: 1,4 => UNS * INC D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 # H5: 6 => UNS * DIS D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 # G2: 1,4 => CTR => G2: 3,7,8 * DIS D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 + G2: 3,7,8 # G3: 1,4 => CTR => G3: 3,7,8 * INC D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 + G2: 3,7,8 + G3: 3,7,8 # A7: 2,8 => UNS * INC D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 + G2: 3,7,8 + G3: 3,7,8 # B7: 2,8 => UNS * INC D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 + G2: 3,7,8 + G3: 3,7,8 # C9: 2,8 => UNS * DIS D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 + G2: 3,7,8 + G3: 3,7,8 # A1: 2,8 => CTR => A1: 1,3,7 * INC D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 + G2: 3,7,8 + G3: 3,7,8 + A1: 1,3,7 # A7: 2,8 => UNS * INC D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 + G2: 3,7,8 + G3: 3,7,8 + A1: 1,3,7 # B7: 2,8 => UNS * INC D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 + G2: 3,7,8 + G3: 3,7,8 + A1: 1,3,7 # C9: 2,8 => UNS * INC D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 + G2: 3,7,8 + G3: 3,7,8 + A1: 1,3,7 # E7: 1,2 => UNS * INC D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 + G2: 3,7,8 + G3: 3,7,8 + A1: 1,3,7 # E7: 9 => UNS * INC D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 + G2: 3,7,8 + G3: 3,7,8 + A1: 1,3,7 # I1: 1,2 => UNS * INC D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 + G2: 3,7,8 + G3: 3,7,8 + A1: 1,3,7 # I1: 5,7 => UNS * DIS D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 + G2: 3,7,8 + G3: 3,7,8 + A1: 1,3,7 # H8: 2,7 => CTR => H8: 8 * PRF D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 + G2: 3,7,8 + G3: 3,7,8 + A1: 1,3,7 + H8: 8 # B3: 1,3 => SOL * STA D1: 7,8 + A2: 1,2,3,6 + A2: 2,6 + C4: 4 + G2: 3,7,8 + G3: 3,7,8 + A1: 1,3,7 + H8: 8 + B3: 1,3 * CNT 40 HDP CHAINS / 40 HYP OPENED