Analysis of zz-www.sudokuoftheday.co.uk-20060819-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: 6...3589.5..9.......2..1...1....85.....2....1.3..57.84..........1..72.4.7..36.1.9 initial
Autosolve
position: 6.1.358925..926.1...2.81...1..6.85..8..2.3..1.3.157.84....19....1..72.4.7..3641.9 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 4,7 => CTR => B2: 8 * DIS # C2: 4,7 => CTR => C2: 3,8 * DIS # B3: 4,7 => CTR => B3: 9 * PRF # B4: 4,7 => SOL * DIS # B4: 2,9 => CTR => B4: 4,7 * DIS # B5: 4,7 => CTR => B5: 5,6,9 * DIS # B3: 4,7 => CTR => B3: 9 * DIS # G3: 4,7 => CTR => G3: 3,6 * DIS # G2: 3,7 => CTR => G2: 4 * PRF # H3: 3,7 => SOL * DIS # C2: 4,8 => CTR => C2: 3,7 * PRF # H3: 3,7 => SOL * DIS # B4: 2,9 => CTR => B4: 4,7 * PRF # B4: 4,7 => SOL * DIS # G6: 6 => CTR => G6: 2,9 * DIS # B5: 6,9 => CTR => B5: 4,5,7 * PRF # C5: 6,9 => SOL * PRF # G6: 6,9 => SOL * DIS # G6: 2 => CTR => G6: 6,9 * PRF # C8: 3,5 => SOL * PRF # B4: 4,9 => SOL * DIS # B5: 4,9 => CTR => B5: 5,6,7 * PRF # C5: 4,9 => SOL * DIS # H4: 3,7 => CTR => H4: 2 * PRF # H4: 2 => SOL * PRF # G5: 6,7 => SOL * DIS # H3: 6,7 => CTR => H3: 3,5 * DIS # C8: 3,9 => CTR => C8: 5,6 * PRF # C8: 5,6 => SOL * DIS # A3: 3,9 => CTR => A3: 4 * DIS # B9: 5,8 => CTR => B9: 2 * PRF # B9: 2 => SOL * DIS # I7: 6 => CTR => I7: 5,8 * PRF # I8: 6 => SOL * DIS # G7: 3,6 => CTR => G7: 2,7 * DIS # H7: 3,6 => CTR => H7: 2,5,7 * DIS # C8: 3,6 => CTR => C8: 5,9 * DIS # G3: 4,7 => CTR => G3: 3,6 * DIS # H7: 2,5 => CTR => H7: 3,6,7 * DIS # B9: 8 => CTR => B9: 2,5 * CNT 40 HDP CHAINS / 75 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 4,7 => CTR => B2: 8 * DIS B2: 8 # C2: 4,7 => CTR => C2: 3 * DIS B2: 8 + C2: 3 # I8: 8 => CTR => I8: 5,6 * PRF B2: 8 + C2: 3 + I8: 5,6 # C5: 7,9 => SOL * STA B2: 8 + C2: 3 + I8: 5,6 + C5: 7,9 * CNT 4 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6...3589.5..9.......2..1...1....85.....2....1.3..57.84..........1..72.4.7..36.1.9 | initial |
| 6.1.358925..926.1...2.81...1..6.85..8..2.3..1.3.157.84....19....1..72.4.7..3641.9 | autosolve |
| 671435892583926417492781635147698523859243761236157984364519278915872346728364159 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) B1: 4,7 D1: 4,7 D3: 4,7 I2: 3,7 I3: 5,6 A6: 2,9 C6: 6,9 E4: 4,9 E5: 4,9 I4: 3,7 H5: 6,7 A8: 3,9 C9: 5,8 D7: 5,8 D8: 5,8 G8: 3,6 H9: 2,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B4,A6: 2.. / B4 = 2 => 0 pairs (X) / A6 = 2 => 0 pairs (_) H4,G6: 2.. / H4 = 2 => 0 pairs (*) / G6 = 2 => 0 pairs (X) B4,H4: 2.. / B4 = 2 => 0 pairs (X) / H4 = 2 => 0 pairs (_) A6,G6: 2.. / A6 = 2 => 0 pairs (*) / G6 = 2 => 0 pairs (X) B9,H9: 2.. / B9 = 2 => 0 pairs (*) / H9 = 2 => 0 pairs (X) A6,A7: 2.. / A6 = 2 => 0 pairs (*) / A7 = 2 => 0 pairs (X) G6,G7: 2.. / G6 = 2 => 0 pairs (X) / G7 = 2 => 0 pairs (_) C2,A3: 3.. / C2 = 3 => 22 pairs (_) / A3 = 3 => 0 pairs (X) H4,I4: 3.. / H4 = 3 => 0 pairs (X) / I4 = 3 => 22 pairs (_) I2,I4: 3.. / I2 = 3 => 0 pairs (X) / I4 = 3 => 22 pairs (_) D1,D3: 4.. / D1 = 4 => 16 pairs (_) / D3 = 4 => 0 pairs (X) G2,G3: 4.. / G2 = 4 => 18 pairs (_) / G3 = 4 => 0 pairs (X) E4,E5: 4.. / E4 = 4 => 0 pairs (X) / E5 = 4 => 16 pairs (_) B1,D1: 4.. / B1 = 4 => 0 pairs (X) / D1 = 4 => 16 pairs (_) A3,A7: 4.. / A3 = 4 => 22 pairs (_) / A7 = 4 => 0 pairs (X) H3,I3: 5.. / H3 = 5 => 0 pairs (X) / I3 = 5 => 0 pairs (_) B5,C5: 5.. / B5 = 5 => 20 pairs (_) / C5 = 5 => 18 pairs (_) D7,D8: 5.. / D7 = 5 => 16 pairs (_) / D8 = 5 => 16 pairs (_) C6,G6: 6.. / C6 = 6 => 19 pairs (_) / G6 = 6 => 0 pairs (X) B5,B7: 6.. / B5 = 6 => 0 pairs (X) / B7 = 6 => 19 pairs (_) D1,D3: 7.. / D1 = 7 => 0 pairs (X) / D3 = 7 => 16 pairs (_) G7,H7: 7.. / G7 = 7 => 0 pairs (X) / H7 = 7 => 23 pairs (_) B1,D1: 7.. / B1 = 7 => 16 pairs (_) / D1 = 7 => 0 pairs (X) I2,I4: 7.. / I2 = 7 => 22 pairs (_) / I4 = 7 => 0 pairs (X) B2,C2: 8.. / B2 = 8 => 17 pairs (_) / C2 = 8 => 0 pairs (X) B9,C9: 8.. / B9 = 8 => 0 pairs (X) / C9 = 8 => 17 pairs (_) D7,D8: 8.. / D7 = 8 => 16 pairs (_) / D8 = 8 => 16 pairs (_) I7,I8: 8.. / I7 = 8 => 16 pairs (_) / I8 = 8 => 16 pairs (_) D7,I7: 8.. / D7 = 8 => 16 pairs (_) / I7 = 8 => 16 pairs (_) D8,I8: 8.. / D8 = 8 => 16 pairs (_) / I8 = 8 => 16 pairs (_) B2,B9: 8.. / B2 = 8 => 17 pairs (_) / B9 = 8 => 0 pairs (X) C2,C9: 8.. / C2 = 8 => 0 pairs (X) / C9 = 8 => 17 pairs (_) A3,B3: 9.. / A3 = 9 => 0 pairs (X) / B3 = 9 => 18 pairs (_) E4,E5: 9.. / E4 = 9 => 16 pairs (_) / E5 = 9 => 0 pairs (X) G5,G6: 9.. / G5 = 9 => 18 pairs (_) / G6 = 9 => 0 pairs (*) A8,C8: 9.. / A8 = 9 => 0 pairs (*) / C8 = 9 => 0 pairs (X) * DURATION: 0:00:44.100606 START: 01:54:24.734193 END: 01:55:08.834799 2019-05-01 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A8,B1,C6,C9,D1,D3,D7,D8,E4,E5,G8,H5,H9,I2,I3,I4) * 6.1.358925..926.1...2.81...1..6.85..8..2.3..1.3.157.84....19....1..72.4.7..3641.9 * PAIR B1: 4,7 BLK 1 B2: 4,7,8 # reduction candidate for 4,7 B2: 4,7 => CTR * 6.1.358925.8926.1.392.81...12.6.85..8..2.3..1.3.157.844...19...91..72.4.785364129 B2: 8 # 17 pairs C2: 4,7,3,8 # reduction candidate for 4,7 C2: 4,7 => CTR * 6.1.3589258.926.1.392.81...1..6.85..8..2.3..123.157.844...1927.91..7234.728364159 C2: 3,8 # 18 pairs B3: 4,7,9 # reduction candidate for 4,7 B3: 4,7 => CTR * 6.1.358925..926.1.9.2.81...1..6.85..8..2.3..123.157.844...1927.319.7264.728364159 B3: 9 # 18 pairs * PAIR B1: 4,7 COL B B4: 4,7,2,9 # reduction candidate for 4,7 B4: 4,7 => SOLVED * 671435892583926417492781635147698523859243761236157984364519278915872346728364159 B4: 2,9 => CTR * 6.1.35892583926417..2.8135612.6985738..2.3.61.36157.84.6..19.3.319.7264.758364129 B5: 4,7,5,6,9 # reduction candidate for 4,7 B5: 4,7 => CTR * 6.1.3589258.926.1...2.81...12.6.85..8.52.3..1936157284264.19...319.7264.758364129 B5: 5,6,9 # 17 pairs * PAIR D3: 4,7 ROW 3 B3: 4,7,9 # reduction candidate for 4,7 B3: 4,7 => CTR * 6.1.358925..926.1.9.2.81...1..6.85..8..2.3..123.157.844...1927.319.7264.728364159 B3: 9 # 18 pairs G3: 4,7,3,6 # reduction candidate for 4,7 G3: 4,7 => CTR * 6.1.358925..926.1.392.81...1..6.85..8..2.3..123.157.844...1927.91..7234.728364159 G3: 3,6 # 22 pairs * PAIR I2: 3,7 BLK 3 G2: 3,7,4 # reduction candidate for 3,7 G2: 3,7 => CTR * 67143589258492671339278146.1..6.85..8..2.3..123.157.844...1927..1..7234.728364159 G2: 4 # 18 pairs G3: 3,7,4,6 # reduction candidate for 3,7 G3: 3,7 # 20 pairs H3: 3,7,5,6 # reduction candidate for 3,7 H3: 3,7 => SOLVED * 671435892583926417492781635147698523859243761236157984364519278915872346728364159 H3: 5,6 # 18 pairs * PAIR I2: 3,7 ROW 2 C2: 3,7,4,8 # reduction candidate for 3,7 C2: 4,8 => CTR * 6.1.358925..926.1.392.81...1..6.85..8..2.3..123.157.844...1927.91..7234.728364159 C2: 3,7 # 18 pairs * PAIR I3: 5,6 BLK 3 H3: 5,6,3,7 # reduction candidate for 5,6 H3: 3,7 => SOLVED * 671435892583926417492781635147698523859243761236157984364519278915872346728364159 H3: 5,6 # 18 pairs * PAIR I3: 5,6 COL I I7: 5,6,8 # reduction candidate for 5,6 I7: 5,6 # 16 pairs I8: 5,6,8 # reduction candidate for 5,6 I8: 5,6 # 16 pairs * PAIR A6: 2,9 BLK 4 B4: 2,9,4,7 # reduction candidate for 2,9 B4: 2,9 => CTR * 6.1.35892583926417..2.8135612.6985738..2.3.61.36157.84.6..19.3.319.7264.758364129 B4: 4,7 => SOLVED * 671435892583926417492781635147698523859243761236157984364519278915872346728364159 * PAIR A6: 2,9 ROW 6 G6: 2,9,6 # reduction candidate for 2,9 G6: 6 => CTR * 6.1.358925..926.1...2.81...1..6.85238..2.3971239157684....19....1..72.4.7..3641.9 G6: 2,9 # 19 pairs * PAIR C6: 6,9 BLK 4 B5: 6,9,4,5,7 # reduction candidate for 6,9 B5: 6,9 => CTR * 6714358925839264174927816..1476985238.5243..123.157.84....1927..1..7234.728364159 B5: 4,5,7 # 19 pairs C5: 6,9,4,5,7 # reduction candidate for 6,9 C5: 6,9 => SOLVED * 671435892583926417492781635147698523859243761236157984364519278915872346728364159 C5: 4,5,7 # 17 pairs * PAIR C6: 6,9 ROW 6 G6: 6,9,2 # reduction candidate for 6,9 G6: 6,9 => SOLVED * 671435892583926417492781635147698523859243761236157984364519278915872346728364159 G6: 2 => CTR * 6.1.358925..926.1.492781...12.6.85..8..2.3961.36157284264.19....1..72.4.7..364129 * PAIR C6: 6,9 COL C C8: 6,9,3,5 # reduction candidate for 6,9 C8: 3,5 => SOLVED * 671435892583926417492781635147698523859243761236157984364519278915872346728364159 C8: 6,9 # 20 pairs * PAIR E4: 4,9 ROW 4 B4: 4,9,2,7 # reduction candidate for 4,9 B4: 4,9 => SOLVED * 671435892583926417492781635147698523859243761236157984364519278915872346728364159 B4: 2,7 # 19 pairs C4: 4,9,7 # reduction candidate for 4,9 C4: 4,9 # 19 pairs * PAIR E5: 4,9 ROW 5 B5: 4,9,5,6,7 # reduction candidate for 4,9 B5: 4,9 => CTR * 6.1.3589258.926.1...2.81...1276.85..8.52.3..1.36157.84.6..19....1..72.4.758364129 B5: 5,6,7 # 17 pairs C5: 4,9,5,6,7 # reduction candidate for 4,9 C5: 4,9 => SOLVED * 671435892583926417492781635147698523859243761236157984364519278915872346728364159 C5: 5,6,7 # 17 pairs * PAIR I4: 3,7 BLK 6 H4: 3,7,2 # reduction candidate for 3,7 H4: 3,7 => CTR * 6.1.358925..926.1...2.81...12.6.85..8..2.3..1936157284264.19...319.7264.7..364129 H4: 2 => SOLVED * 671435892583926417492781635147698523859243761236157984364519278915872346728364159 * PAIR H5: 6,7 BLK 6 G5: 6,7,9 # reduction candidate for 6,7 G5: 6,7 => SOLVED * 671435892583926417492781635147698523859243761236157984364519278915872346728364159 G5: 9 # 18 pairs * PAIR H5: 6,7 ROW 5 B5: 6,7,4,5,9 # reduction candidate for 6,7 B5: 6,7 # 20 pairs C5: 6,7,4,5,9 # reduction candidate for 6,7 C5: 6,7 # 22 pairs * PAIR H5: 6,7 COL H H3: 6,7,3,5 # reduction candidate for 6,7 H3: 6,7 => CTR * 6.1.358925..926.13392.81..51..6.85378..2.3.61.36157284....19....1..7234.7..3641.9 H3: 3,5 # 18 pairs H7: 6,7,2,3,5 # reduction candidate for 6,7 H7: 6,7 # 21 pairs * PAIR A8: 3,9 BLK 7 C8: 3,9,5,6 # reduction candidate for 3,9 C8: 3,9 => CTR * 6.1.358925..926.1.49278135612.6485.3845293.61.36157284264.19....1..7264.7..364129 C8: 5,6 => SOLVED * 671435892583926417492781635147698523859243761236157984364519278915872346728364159 * PAIR A8: 3,9 COL A A3: 3,9,4 # reduction candidate for 3,9 A3: 3,9 => CTR * 6.1.3589258.926.1.392.81.6.1..6.85..8..2.3..123.157.844...1927..1..7234.728364159 A3: 4 # 22 pairs * PAIR C9: 5,8 BLK 7 B9: 5,8,2 # reduction candidate for 5,8 B9: 5,8 => CTR * 6.1.358925..926.1...2.81...12.6.85..8..2.3..1936157284264.19...319.7264.7..364129 B9: 2 => SOLVED * 671435892583926417492781635147698523859243761236157984364519278915872346728364159 * PAIR D7: 5,8 ROW 7 I7: 5,8,6 # reduction candidate for 5,8 I7: 6 => CTR * 6.1.358925..926.1...2.81..51..6.85..865243971.39157684...819..6.165723487..3641.9 I7: 5,8 # 18 pairs * PAIR D8: 5,8 ROW 8 I8: 5,8,6 # reduction candidate for 5,8 I8: 6 => SOLVED * 671435892583926417492781635147698523859243761236157984364519278915872346728364159 I8: 5,8 # 18 pairs * PAIR G8: 3,6 BLK 9 G7: 3,6,2,7 # reduction candidate for 3,6 G7: 3,6 => CTR * 6.1.358925..926.1.492781.5612.6.85378..2.39.1.3.1572842...19.7..1..72.4.7..364129 G7: 2,7 # 18 pairs H7: 3,6,2,5,7 # reduction candidate for 3,6 H7: 3,6 => CTR * 6.1.358925..926.1...2.81.5612.6.85..8..2.3..1936157284264.1973.319.7264.7..364129 H7: 2,5,7 # 18 pairs * PAIR G8: 3,6 ROW 8 C8: 3,6,5,9 # reduction candidate for 3,6 C8: 3,6 => CTR * 6.1.3589258.926.1..92.81..51..6.85238..2.3761236157.84....1927.91..7234.728364159 C8: 5,9 # 19 pairs * PAIR G8: 3,6 COL G G3: 3,6,4,7 # reduction candidate for 3,6 G3: 4,7 => CTR * 6.1.358925..926.1.392.81...1..6.85..8..2.3..123.157.844...1927.91..7234.728364159 G3: 3,6 # 22 pairs * PAIR H9: 2,5 BLK 9 H7: 2,5,3,6,7 # reduction candidate for 2,5 H7: 2,5 => CTR * 6.1.358925..92641...2.816.51..6.85..8..2.3961.3615728426..197...1..7234.7..3641.9 H7: 3,6,7 # 17 pairs * PAIR H9: 2,5 ROW 9 B9: 2,5,8 # reduction candidate for 2,5 B9: 8 => CTR * 6.1.358925.8926.1.392.81...12.6.85..85.2.3..193.157.84....19....1..72.4.785364129 B9: 2,5 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060819-absurd-base-pr-000.dot * REASONING * DIS # B2: 4,7 => CTR => B2: 8 * DIS # C2: 4,7 => CTR => C2: 3,8 * DIS # B3: 4,7 => CTR => B3: 9 * PRF # B4: 4,7 => SOL * DIS # B4: 2,9 => CTR => B4: 4,7 * DIS # B5: 4,7 => CTR => B5: 5,6,9 * DIS # B3: 4,7 => CTR => B3: 9 * DIS # G3: 4,7 => CTR => G3: 3,6 * DIS # G2: 3,7 => CTR => G2: 4 * PRF # H3: 3,7 => SOL * DIS # C2: 4,8 => CTR => C2: 3,7 * PRF # H3: 3,7 => SOL * DIS # B4: 2,9 => CTR => B4: 4,7 * PRF # B4: 4,7 => SOL * DIS # G6: 6 => CTR => G6: 2,9 * DIS # B5: 6,9 => CTR => B5: 4,5,7 * PRF # C5: 6,9 => SOL * PRF # G6: 6,9 => SOL * DIS # G6: 2 => CTR => G6: 6,9 * PRF # C8: 3,5 => SOL * PRF # B4: 4,9 => SOL * DIS # B5: 4,9 => CTR => B5: 5,6,7 * PRF # C5: 4,9 => SOL * DIS # H4: 3,7 => CTR => H4: 2 * PRF # H4: 2 => SOL * PRF # G5: 6,7 => SOL * DIS # H3: 6,7 => CTR => H3: 3,5 * DIS # C8: 3,9 => CTR => C8: 5,6 * PRF # C8: 5,6 => SOL * DIS # A3: 3,9 => CTR => A3: 4 * DIS # B9: 5,8 => CTR => B9: 2 * PRF # B9: 2 => SOL * DIS # I7: 6 => CTR => I7: 5,8 * PRF # I8: 6 => SOL * DIS # G7: 3,6 => CTR => G7: 2,7 * DIS # H7: 3,6 => CTR => H7: 2,5,7 * DIS # C8: 3,6 => CTR => C8: 5,9 * DIS # G3: 4,7 => CTR => G3: 3,6 * DIS # H7: 2,5 => CTR => H7: 3,6,7 * DIS # B9: 8 => CTR => B9: 2,5 * CNT 40 HDP CHAINS / 75 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A8,B1,C6,C9,D1,D3,D7,D8,E4,E5,G8,H5,H9,I2,I3,I4) * 6.1.358925..926.1...2.81...1..6.85..8..2.3..1.3.157.84....19....1..72.4.7..3641.9 * PAIR B1: 4,7 BLK 1 B2: 4,7,8 # reduction candidate for 4,7 B2: 4,7 => CTR * 6.1.358925.8926.1.392.81...12.6.85..8..2.3..1.3.157.844...19...91..72.4.785364129 C2: 4,7,3 # reduction candidate for 4,7 C2: 4,7 => CTR * 6.1.3589258.926.1.392.81...1..6.85..8..2.3..123.157.844...1927.91..7234.728364159 * PAIR I3: 5,6 COL I I8: 5,6,8 # reduction candidate for 5,6 I8: 8 => CTR * 67143589258392641749278135612.64857384.2.3.61.36157.84.64.19..5.1.572648758364129 * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A6,A7,A8,B4,B5,B9,C4,C8,E4,E5,G3,G5,G6,G7,G8,H3,H4,H9,I3,I8) * 671435892583926417492781...1..6.85.38..2.3.61.36157.84.64519..8.1.872.4.7.83641.9 * PAIR C4: 7,9 BLK 4 C5: 7,9,5 # reduction candidate for 7,9 C5: 7,9 => SOLVED * 671435892583926417492781635147698523859243761236157984364519278915872346728364159 * DURATION: 0:00:05.786453 START: 01:56:02.021009 END: 01:56:07.807462 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060819-absurd-base-pr-001.dot * REASONING * DIS # B2: 4,7 => CTR => B2: 8 * DIS B2: 8 # C2: 4,7 => CTR => C2: 3 * DIS B2: 8 + C2: 3 # I8: 8 => CTR => I8: 5,6 * PRF B2: 8 + C2: 3 + I8: 5,6 # C5: 7,9 => SOL * STA B2: 8 + C2: 3 + I8: 5,6 + C5: 7,9 * CNT 4 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060819, absurd
Solution
position: 671435892583926417492781635147698523859243761236157984364519278915872346728364159 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 # B2: 4,7 => CTR => B2: 8 * INC # B2: 8 => UNS * DIS # C2: 4,7 => CTR => C2: 3,8 * INC # C2: 3,8 => UNS * DIS # B3: 4,7 => CTR => B3: 9 * INC # B3: 9 => UNS * PRF # B4: 4,7 => SOL * DIS # B4: 2,9 => CTR => B4: 4,7 * DIS # B5: 4,7 => CTR => B5: 5,6,9 * INC # B5: 5,6,9 => UNS * DIS # B3: 4,7 => CTR => B3: 9 * INC # B3: 9 => UNS * DIS # G3: 4,7 => CTR => G3: 3,6 * INC # G3: 3,6 => UNS * DIS # G2: 3,7 => CTR => G2: 4 * INC # G2: 4 => UNS * INC # G3: 3,7 => UNS * PRF # H3: 3,7 => SOL * INC # H3: 5,6 => UNS * INC # C2: 3,7 => UNS * DIS # C2: 4,8 => CTR => C2: 3,7 * INC # H3: 5,6 => UNS * PRF # H3: 3,7 => SOL * INC # I7: 5,6 => UNS * INC # I8: 5,6 => UNS * DIS # B4: 2,9 => CTR => B4: 4,7 * PRF # B4: 4,7 => SOL * INC # G6: 2,9 => UNS * DIS # G6: 6 => CTR => G6: 2,9 * DIS # B5: 6,9 => CTR => B5: 4,5,7 * INC # B5: 4,5,7 => UNS * PRF # C5: 6,9 => SOL * INC # C5: 4,5,7 => UNS * PRF # G6: 6,9 => SOL * DIS # G6: 2 => CTR => G6: 6,9 * INC # C8: 6,9 => UNS * PRF # C8: 3,5 => SOL * PRF # B4: 4,9 => SOL * INC # B4: 2,7 => UNS * INC # C4: 4,9 => UNS * DIS # B5: 4,9 => CTR => B5: 5,6,7 * INC # B5: 5,6,7 => UNS * PRF # C5: 4,9 => SOL * INC # C5: 5,6,7 => UNS * DIS # H4: 3,7 => CTR => H4: 2 * PRF # H4: 2 => SOL * PRF # G5: 6,7 => SOL * INC # G5: 9 => UNS * INC # B5: 6,7 => UNS * INC # C5: 6,7 => UNS * DIS # H3: 6,7 => CTR => H3: 3,5 * INC # H3: 3,5 => UNS * INC # H7: 6,7 => UNS * DIS # C8: 3,9 => CTR => C8: 5,6 * PRF # C8: 5,6 => SOL * DIS # A3: 3,9 => CTR => A3: 4 * INC # A3: 4 => UNS * DIS # B9: 5,8 => CTR => B9: 2 * PRF # B9: 2 => SOL * INC # I7: 5,8 => UNS * DIS # I7: 6 => CTR => I7: 5,8 * INC # I8: 5,8 => UNS * PRF # I8: 6 => SOL * DIS # G7: 3,6 => CTR => G7: 2,7 * INC # G7: 2,7 => UNS * DIS # H7: 3,6 => CTR => H7: 2,5,7 * INC # H7: 2,5,7 => UNS * DIS # C8: 3,6 => CTR => C8: 5,9 * INC # C8: 5,9 => UNS * INC # G3: 3,6 => UNS * DIS # G3: 4,7 => CTR => G3: 3,6 * DIS # H7: 2,5 => CTR => H7: 3,6,7 * INC # H7: 3,6,7 => UNS * INC # B9: 2,5 => UNS * DIS # B9: 8 => CTR => B9: 2,5 * CNT 75 HDP CHAINS / 75 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B2: 4,7 => CTR => B2: 8 * DIS B2: 8 # C2: 4,7 => CTR => C2: 3 * INC B2: 8 + C2: 3 # I8: 5,6 => UNS * DIS B2: 8 + C2: 3 # I8: 8 => CTR => I8: 5,6 * PRF B2: 8 + C2: 3 + I8: 5,6 # C5: 7,9 => SOL * STA B2: 8 + C2: 3 + I8: 5,6 + C5: 7,9 * CNT 5 HDP CHAINS / 5 HYP OPENED