Analysis of zz-www.sudokuoftheday.co.uk-20060812-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006
level: medium
position: 1.9.4.8...6..9..7.........193..7..2.....5.4.9.2.......3...8..47.8..2.9.6.1.9...8. initial
Autosolve
position: 159.4.8...6..9..74.4.....9193..7..2..7..5.4.9.2..197..39..8..47.8..2.9.6.1.9...8. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 2,8 => CTR => C2: 3 * DIS # A3: 2,8 => CTR => A3: 7 * DIS # D1: 3,6 => CTR => D1: 2,7 * DIS # D3: 3,6 => CTR => D3: 2,5,8 * DIS # F3: 3,6 => CTR => F3: 2,5,8 * DIS # G3: 2,5 => CTR => G3: 3,6 * DIS # G3: 2,5 => CTR => G3: 3,6 * DIS # D1: 3,6 => CTR => D1: 2,7 * PRF # H5: 3,6 => SOL * DIS # H5: 1 => CTR => H5: 3,6 * DIS # H6: 3,6 => CTR => H6: 5 * PRF # H6: 5 => SOL * DIS # G2: 2,3 => CTR => G2: 5 * DIS # G3: 2,3 => CTR => G3: 5,6 * DIS # D1: 2,3 => CTR => D1: 6,7 * DIS # F1: 2,3 => CTR => F1: 6,7 * DIS # I9: 2,3 => CTR => I9: 5 * PRF # I9: 5 => SOL * DIS # C4: 6,8 => CTR => C4: 1,4,5 * DIS # C5: 6,8 => CTR => C5: 1 * PRF # C5: 1 => SOL * PRF # A6: 6,8 => SOL * DIS # C6: 6,8 => CTR => C6: 4,5 * DIS # D5: 6,8 => CTR => D5: 2,3 * DIS # F5: 6,8 => CTR => F5: 2,3 * DIS # H5: 3 => CTR => H5: 1,6 * DIS # C4: 1,6 => CTR => C4: 4,5,8 * PRF # C4: 4,5,8 => SOL * DIS # I6: 5,8 => CTR => I6: 3 * PRF # I6: 3 => SOL * PRF # C4: 5,8 => SOL * DIS # C4: 1,4,6 => CTR => C4: 5,8 * DIS # F9: 3,6 => CTR => F9: 4,5,7 * DIS # I9: 2,3 => CTR => I9: 5 * PRF # I9: 5 => SOL * DIS # G2: 2,3 => CTR => G2: 5 * DIS # G3: 2,3 => CTR => G3: 5,6 * CNT 37 HDP CHAINS / 63 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 2,8 => CTR => C2: 3 * DIS C2: 3 # A3: 2,8 => CTR => A3: 7 * DIS C2: 3 + A3: 7 # D1: 3,6 => CTR => D1: 2,7 * DIS C2: 3 + A3: 7 + D1: 2,7 # D3: 3,6 => CTR => D3: 2,5,8 * DIS C2: 3 + A3: 7 + D1: 2,7 + D3: 2,5,8 # F3: 3,6 => CTR => F3: 2,5,8 * PRF C2: 3 + A3: 7 + D1: 2,7 + D3: 2,5,8 + F3: 2,5,8 # H5: 3,6 => SOL * STA C2: 3 + A3: 7 + D1: 2,7 + D3: 2,5,8 + F3: 2,5,8 + H5: 3,6 * CNT 6 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.9.4.8...6..9..7.........193..7..2.....5.4.9.2.......3...8..47.8..2.9.6.1.9...8. | initial |
| 159.4.8...6..9..74.4.....9193..7..2..7..5.4.9.2..197..39..8..47.8..2.9.6.1.9...8. | autosolve |
| 159746832263198574748235691935674128871352469624819753396581247587423916412967385 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) A2: 2,8 E3: 3,6 H1: 3,6 I1: 2,3 A5: 6,8 G4: 1,6 I4: 5,8 E9: 3,6 G7: 1,2 G9: 2,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,F2: 1.. / D2 = 1 => 11 pairs (_) / F2 = 1 => 11 pairs (_) C4,C5: 1.. / C4 = 1 => 0 pairs (X) / C5 = 1 => 0 pairs (_) G4,H5: 1.. / G4 = 1 => 0 pairs (*) / H5 = 1 => 0 pairs (X) G7,H8: 1.. / G7 = 1 => 0 pairs (X) / H8 = 1 => 0 pairs (_) C4,G4: 1.. / C4 = 1 => 0 pairs (X) / G4 = 1 => 0 pairs (_) C5,H5: 1.. / C5 = 1 => 0 pairs (*) / H5 = 1 => 0 pairs (X) G4,G7: 1.. / G4 = 1 => 0 pairs (*) / G7 = 1 => 0 pairs (X) H5,H8: 1.. / H5 = 1 => 0 pairs (X) / H8 = 1 => 0 pairs (_) D5,F5: 2.. / D5 = 2 => 10 pairs (_) / F5 = 2 => 10 pairs (_) C7,G7: 2.. / C7 = 2 => 0 pairs (X) / G7 = 2 => 0 pairs (_) I1,I9: 2.. / I1 = 2 => 11 pairs (_) / I9 = 2 => 0 pairs (X) C2,C3: 3.. / C2 = 3 => 11 pairs (_) / C3 = 3 => 0 pairs (X) E3,E9: 3.. / E3 = 3 => 0 pairs (*) / E9 = 3 => 0 pairs (X) G2,G3: 5.. / G2 = 5 => 10 pairs (_) / G3 = 5 => 0 pairs (X) H8,I9: 5.. / H8 = 5 => 0 pairs (X) / I9 = 5 => 0 pairs (_) C4,I4: 5.. / C4 = 5 => 0 pairs (*) / I4 = 5 => 0 pairs (X) H6,H8: 5.. / H6 = 5 => 0 pairs (*) / H8 = 5 => 0 pairs (X) H1,G3: 6.. / H1 = 6 => 0 pairs (X) / G3 = 6 => 0 pairs (_) E3,E9: 6.. / E3 = 6 => 0 pairs (X) / E9 = 6 => 0 pairs (_) G3,G4: 6.. / G3 = 6 => 0 pairs (*) / G4 = 6 => 0 pairs (X) A3,C3: 7.. / A3 = 7 => 11 pairs (_) / C3 = 7 => 0 pairs (X) D1,F1: 7.. / D1 = 7 => 10 pairs (_) / F1 = 7 => 0 pairs (X) D1,D8: 7.. / D1 = 7 => 10 pairs (_) / D8 = 7 => 0 pairs (X) I4,I6: 8.. / I4 = 8 => 0 pairs (*) / I6 = 8 => 0 pairs (X) * DURATION: 0:00:27.060689 START: 01:44:24.317170 END: 01:44:51.377859 2019-05-01 * CP COUNT: (24) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,E3,E9,G4,G7,G9,H1,I1,I4) * 159.4.8...6..9..74.4.....9193..7..2..7..5.4.9.2..197..39..8..47.8..2.9.6.1.9...8. * PAIR A2: 2,8 BLK 1 C2: 2,8,3 # reduction candidate for 2,8 C2: 2,8 => CTR * 159.4.8...6..9..74.43.6..9193..7.62..7..5.419.2..197..39..8.147.8..2.9.6.1.93.285 C2: 3 # 11 pairs A3: 2,8,7 # reduction candidate for 2,8 A3: 2,8 => CTR * 159.4.8.2.63.9.574.47....91935.7.12.67..5.4.9.2..197.339..8..47.8..2.9.6.1.9...85 A3: 7 # 11 pairs C3: 2,8,3,7 # reduction candidate for 2,8 C3: 2,8 # 13 pairs * PAIR A2: 2,8 ROW 2 D2: 2,8,1,3,5 # reduction candidate for 2,8 D2: 2,8 # 12 pairs F2: 2,8,1,3,5 # reduction candidate for 2,8 F2: 2,8 # 12 pairs * PAIR E3: 3,6 BLK 2 D1: 3,6,2,7 # reduction candidate for 3,6 D1: 3,6 => CTR * 159.478.2.6..9..74.4.....9193547.128.71.5.469426819753392.8..4758472.9.6.1.9.4.85 D1: 2,7 # 11 pairs F1: 3,6,2,7 # reduction candidate for 3,6 F1: 3,6 # 12 pairs D3: 3,6,2,5,8 # reduction candidate for 3,6 D3: 3,6 => CTR * 159.4.863.63.9..74.4..3..91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.96.382 D3: 2,5,8 # 10 pairs F3: 3,6,2,5,8 # reduction candidate for 3,6 F3: 3,6 => CTR * 159.4.863.63.9..74.4..36.91931.7.625.7..5.419.2..1973839268.147.8..2.956.1.9..382 F3: 2,5,8 # 10 pairs * PAIR E3: 3,6 ROW 3 G3: 3,6,2,5 # reduction candidate for 3,6 G3: 2,5 => CTR * 159.4.86..6..9..74.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8. G3: 3,6 # 11 pairs * PAIR H1: 3,6 BLK 3 G3: 3,6,2,5 # reduction candidate for 3,6 G3: 2,5 => CTR * 159.4.86..6..9..74.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8. G3: 3,6 # 11 pairs * PAIR H1: 3,6 ROW 1 D1: 3,6,2,7 # reduction candidate for 3,6 D1: 3,6 => CTR * 159.478.2.6..9..74.4.....9193547.128.71.5.469426819753392.8..4758472.9.6.1.9.4.85 D1: 2,7 # 11 pairs F1: 3,6,2,7 # reduction candidate for 3,6 F1: 3,6 # 12 pairs * PAIR H1: 3,6 COL H H5: 3,6,1 # reduction candidate for 3,6 H5: 3,6 => SOLVED * 159746832263198574748235691935674128871352469624819753396581247587423916412967385 H5: 1 => CTR * 159.4.86..6..9..74.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8. H6: 3,6,5 # reduction candidate for 3,6 H6: 3,6 => CTR * 159.4.86..6..9..74.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8. H6: 5 => SOLVED * 159746832263198574748235691935674128871352469624819753396581247587423916412967385 * PAIR I1: 2,3 BLK 3 G2: 2,3,5 # reduction candidate for 2,3 G2: 2,3 => CTR * 159.4.86..6..9..74.4....591931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8. G2: 5 # 10 pairs G3: 2,3,5,6 # reduction candidate for 2,3 G3: 2,3 => CTR * 159.4.86..6..9.574.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8. G3: 5,6 # 11 pairs * PAIR I1: 2,3 ROW 1 D1: 2,3,6,7 # reduction candidate for 2,3 D1: 2,3 => CTR * 159.4786..6..9..74.4.....9193..7.62..7..5.419.2..197..39..8.147.8.721936.1.9.4285 D1: 6,7 # 11 pairs F1: 2,3,6,7 # reduction candidate for 2,3 F1: 2,3 => CTR * 15974.86..6..9..74.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8. F1: 6,7 # 11 pairs * PAIR I1: 2,3 COL I I9: 2,3,5 # reduction candidate for 2,3 I9: 2,3 => CTR * 159.4.86..6..9..74.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8. I9: 5 => SOLVED * 159746832263198574748235691935674128871352469624819753396581247587423916412967385 * PAIR A5: 6,8 BLK 4 C4: 6,8,1,4,5 # reduction candidate for 6,8 C4: 6,8 => CTR * 159.4.8...6..9..74.4.....9193..7.125.71.5.4.9.2..197.839..8.247.8..2.9.6.1.9...8. C4: 1,4,5 # 10 pairs C5: 6,8,1 # reduction candidate for 6,8 C5: 6,8 => CTR * 159.4.86..6..9..74.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8. C5: 1 => SOLVED * 159746832263198574748235691935674128871352469624819753396581247587423916412967385 A6: 6,8,4,5 # reduction candidate for 6,8 A6: 6,8 => SOLVED * 159746832263198574748235691935674128871352469624819753396581247587423916412967385 A6: 4,5 # 11 pairs C6: 6,8,4,5 # reduction candidate for 6,8 C6: 6,8 => CTR * 159.4.832.63.9.574.4..3.691935.7.128671.5.4.942..19753396.8.24758..2.916.1.96.385 C6: 4,5 # 11 pairs * PAIR A5: 6,8 ROW 5 D5: 6,8,2,3 # reduction candidate for 6,8 D5: 6,8 => CTR * 159.4.8...6..9..74.4.....9193..7..2..7..52439.2.3197..39..8..47.8..23916.1.96..85 D5: 2,3 # 11 pairs F5: 6,8,2,3 # reduction candidate for 6,8 F5: 6,8 => CTR * 159.4.8...6..9..74.4.....9193..7..2..7.25.439.2.3197..39..8..47.8..23916.1.96..85 F5: 2,3 # 11 pairs * PAIR G4: 1,6 BLK 6 H5: 1,6,3 # reduction candidate for 1,6 H5: 3 => CTR * 159.4.8...6..9..74.4.....9193..7.12..71.5.439.2.31976.39..8..47.8..2.9.6.1.9...8. H5: 1,6 # 14 pairs * PAIR G4: 1,6 ROW 4 C4: 1,6,4,5,8 # reduction candidate for 1,6 C4: 1,6 => CTR * 159.4.86..6..9..74.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8. C4: 4,5,8 => SOLVED * 159746832263198574748235691935674128871352469624819753396581247587423916412967385 * PAIR I4: 5,8 BLK 6 I6: 5,8,3 # reduction candidate for 5,8 I6: 5,8 => CTR * 159.4.86..6..9..74.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8. I6: 3 => SOLVED * 159746832263198574748235691935674128871352469624819753396581247587423916412967385 * PAIR I4: 5,8 ROW 4 C4: 5,8,1,4,6 # reduction candidate for 5,8 C4: 5,8 => SOLVED * 159746832263198574748235691935674128871352469624819753396581247587423916412967385 C4: 1,4,6 => CTR * 159.4.86..6..9..74.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8. * PAIR E9: 3,6 BLK 8 F9: 3,6,4,5,7 # reduction candidate for 3,6 F9: 3,6 => CTR * 159.4.8...6..9..74.4.....9193..7..2..7..5.4.9.2..197..39..8..47.8..2.9.6.1.9...8. F9: 4,5,7 # 10 pairs * PAIR G9: 2,3 BLK 9 I9: 2,3,5 # reduction candidate for 2,3 I9: 2,3 => CTR * 159.4.86..6..9..74.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8. I9: 5 => SOLVED * 159746832263198574748235691935674128871352469624819753396581247587423916412967385 * PAIR G9: 2,3 COL G G2: 2,3,5 # reduction candidate for 2,3 G2: 2,3 => CTR * 159.4.86..6..9..74.4....591931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8. G2: 5 # 10 pairs G3: 2,3,5,6 # reduction candidate for 2,3 G3: 2,3 => CTR * 159.4.86..6..9.574.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8. G3: 5,6 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060812-absurd-base-pr-000.dot * REASONING * DIS # C2: 2,8 => CTR => C2: 3 * DIS # A3: 2,8 => CTR => A3: 7 * DIS # D1: 3,6 => CTR => D1: 2,7 * DIS # D3: 3,6 => CTR => D3: 2,5,8 * DIS # F3: 3,6 => CTR => F3: 2,5,8 * DIS # G3: 2,5 => CTR => G3: 3,6 * DIS # G3: 2,5 => CTR => G3: 3,6 * DIS # D1: 3,6 => CTR => D1: 2,7 * PRF # H5: 3,6 => SOL * DIS # H5: 1 => CTR => H5: 3,6 * DIS # H6: 3,6 => CTR => H6: 5 * PRF # H6: 5 => SOL * DIS # G2: 2,3 => CTR => G2: 5 * DIS # G3: 2,3 => CTR => G3: 5,6 * DIS # D1: 2,3 => CTR => D1: 6,7 * DIS # F1: 2,3 => CTR => F1: 6,7 * DIS # I9: 2,3 => CTR => I9: 5 * PRF # I9: 5 => SOL * DIS # C4: 6,8 => CTR => C4: 1,4,5 * DIS # C5: 6,8 => CTR => C5: 1 * PRF # C5: 1 => SOL * PRF # A6: 6,8 => SOL * DIS # C6: 6,8 => CTR => C6: 4,5 * DIS # D5: 6,8 => CTR => D5: 2,3 * DIS # F5: 6,8 => CTR => F5: 2,3 * DIS # H5: 3 => CTR => H5: 1,6 * DIS # C4: 1,6 => CTR => C4: 4,5,8 * PRF # C4: 4,5,8 => SOL * DIS # I6: 5,8 => CTR => I6: 3 * PRF # I6: 3 => SOL * PRF # C4: 5,8 => SOL * DIS # C4: 1,4,6 => CTR => C4: 5,8 * DIS # F9: 3,6 => CTR => F9: 4,5,7 * DIS # I9: 2,3 => CTR => I9: 5 * PRF # I9: 5 => SOL * DIS # G2: 2,3 => CTR => G2: 5 * DIS # G3: 2,3 => CTR => G3: 5,6 * CNT 37 HDP CHAINS / 63 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,E3,E9,G4,G7,G9,H1,I1,I4) * 159.4.8...6..9..74.4.....9193..7..2..7..5.4.9.2..197..39..8..47.8..2.9.6.1.9...8. * PAIR A2: 2,8 BLK 1 C2: 2,8,3 # reduction candidate for 2,8 C2: 2,8 => CTR * 159.4.8...6..9..74.43.6..9193..7.62..7..5.419.2..197..39..8.147.8..2.9.6.1.93.285 A3: 2,8,7 # reduction candidate for 2,8 A3: 2,8 => CTR * 159.4.8.2.63.9.574.47....91935.7.12.67..5.4.9.2..197.339..8..47.8..2.9.6.1.9...85 * RESTART * PAIR A2: 2,8 ROW 2 D2: 2,8,1,5 # reduction candidate for 2,8 D2: 2,8 # 14 pairs F2: 2,8,1,5 # reduction candidate for 2,8 F2: 2,8 # 14 pairs * PAIR E3: 3,6 BLK 2 D1: 3,6,2,7 # reduction candidate for 3,6 D1: 3,6 => CTR * 159.478.2.63.9.57474.....9193547.128.71.5.469426819753392.8..4758472.9.6.179.4.85 F1: 3,6,2,7 # reduction candidate for 3,6 F1: 3,6 # 14 pairs D3: 3,6,2,5,8 # reduction candidate for 3,6 D3: 3,6 => CTR * 159.4.863263.9.574748.35291931.7.625.76.5.419.2.61973.392.8.147.8..2.956.1.9..382 F3: 3,6,2,5,8 # reduction candidate for 3,6 F3: 3,6 => CTR * 159.4.863263.9.574748536291931.7.625.76.5.419.2.61973.392.8.147.8..2.956.1.9..382 * RESTART * PAIR H1: 3,6 COL H H5: 3,6,1 # reduction candidate for 3,6 H5: 3,6 => SOLVED * 159746832263198574748235691935674128871352469624819753396581247587423916412967385 * DURATION: 0:00:07.126531 START: 01:45:29.340472 END: 01:45:36.467003 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060812-absurd-base-pr-001.dot * REASONING * DIS # C2: 2,8 => CTR => C2: 3 * DIS C2: 3 # A3: 2,8 => CTR => A3: 7 * DIS C2: 3 + A3: 7 # D1: 3,6 => CTR => D1: 2,7 * DIS C2: 3 + A3: 7 + D1: 2,7 # D3: 3,6 => CTR => D3: 2,5,8 * DIS C2: 3 + A3: 7 + D1: 2,7 + D3: 2,5,8 # F3: 3,6 => CTR => F3: 2,5,8 * PRF C2: 3 + A3: 7 + D1: 2,7 + D3: 2,5,8 + F3: 2,5,8 # H5: 3,6 => SOL * STA C2: 3 + A3: 7 + D1: 2,7 + D3: 2,5,8 + F3: 2,5,8 + H5: 3,6 * CNT 6 HDP CHAINS / 9 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060812, absurd
Solution
position: 159746832263198574748235691935674128871352469624819753396581247587423916412967385 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: 2,8 => CTR => C2: 3 * INC # C2: 3 => UNS * DIS # A3: 2,8 => CTR => A3: 7 * INC # A3: 7 => UNS * INC # C3: 2,8 => UNS * INC # D2: 2,8 => UNS * INC # F2: 2,8 => UNS * DIS # D1: 3,6 => CTR => D1: 2,7 * INC # D1: 2,7 => UNS * INC # F1: 3,6 => UNS * DIS # D3: 3,6 => CTR => D3: 2,5,8 * INC # D3: 2,5,8 => UNS * DIS # F3: 3,6 => CTR => F3: 2,5,8 * INC # F3: 2,5,8 => UNS * INC # G3: 3,6 => UNS * DIS # G3: 2,5 => CTR => G3: 3,6 * INC # G3: 3,6 => UNS * DIS # G3: 2,5 => CTR => G3: 3,6 * DIS # D1: 3,6 => CTR => D1: 2,7 * INC # D1: 2,7 => UNS * INC # F1: 3,6 => UNS * PRF # H5: 3,6 => SOL * DIS # H5: 1 => CTR => H5: 3,6 * DIS # H6: 3,6 => CTR => H6: 5 * PRF # H6: 5 => SOL * DIS # G2: 2,3 => CTR => G2: 5 * INC # G2: 5 => UNS * DIS # G3: 2,3 => CTR => G3: 5,6 * INC # G3: 5,6 => UNS * DIS # D1: 2,3 => CTR => D1: 6,7 * INC # D1: 6,7 => UNS * DIS # F1: 2,3 => CTR => F1: 6,7 * INC # F1: 6,7 => UNS * DIS # I9: 2,3 => CTR => I9: 5 * PRF # I9: 5 => SOL * DIS # C4: 6,8 => CTR => C4: 1,4,5 * INC # C4: 1,4,5 => UNS * DIS # C5: 6,8 => CTR => C5: 1 * PRF # C5: 1 => SOL * PRF # A6: 6,8 => SOL * INC # A6: 4,5 => UNS * DIS # C6: 6,8 => CTR => C6: 4,5 * INC # C6: 4,5 => UNS * DIS # D5: 6,8 => CTR => D5: 2,3 * INC # D5: 2,3 => UNS * DIS # F5: 6,8 => CTR => F5: 2,3 * INC # F5: 2,3 => UNS * INC # H5: 1,6 => UNS * DIS # H5: 3 => CTR => H5: 1,6 * DIS # C4: 1,6 => CTR => C4: 4,5,8 * PRF # C4: 4,5,8 => SOL * DIS # I6: 5,8 => CTR => I6: 3 * PRF # I6: 3 => SOL * PRF # C4: 5,8 => SOL * DIS # C4: 1,4,6 => CTR => C4: 5,8 * DIS # F9: 3,6 => CTR => F9: 4,5,7 * INC # F9: 4,5,7 => UNS * DIS # I9: 2,3 => CTR => I9: 5 * PRF # I9: 5 => SOL * DIS # G2: 2,3 => CTR => G2: 5 * INC # G2: 5 => UNS * DIS # G3: 2,3 => CTR => G3: 5,6 * INC # G3: 5,6 => UNS * CNT 63 HDP CHAINS / 63 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C2: 2,8 => CTR => C2: 3 * DIS C2: 3 # A3: 2,8 => CTR => A3: 7 * INC C2: 3 + A3: 7 # D2: 2,8 => UNS * INC C2: 3 + A3: 7 # F2: 2,8 => UNS * DIS C2: 3 + A3: 7 # D1: 3,6 => CTR => D1: 2,7 * INC C2: 3 + A3: 7 + D1: 2,7 # F1: 3,6 => UNS * DIS C2: 3 + A3: 7 + D1: 2,7 # D3: 3,6 => CTR => D3: 2,5,8 * DIS C2: 3 + A3: 7 + D1: 2,7 + D3: 2,5,8 # F3: 3,6 => CTR => F3: 2,5,8 * PRF C2: 3 + A3: 7 + D1: 2,7 + D3: 2,5,8 + F3: 2,5,8 # H5: 3,6 => SOL * STA C2: 3 + A3: 7 + D1: 2,7 + D3: 2,5,8 + F3: 2,5,8 + H5: 3,6 * CNT 9 HDP CHAINS / 9 HYP OPENED