Analysis of zz-www.sudokuwiki.org-interesting-5x5-blank-center-base.sdk
Contents
Original Sudoku
level: medium
position: ...7.......24397...4.....6..9.....45.3.....1.76.....3..7.....2...58643.......2... initial
Autosolve
position: ...7.6...6.24397...47..1.6.2983176455346.8.17761.45.3..7...3.2..2586437.....72... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 3,9 => CTR => A1: 1,8 * DIS # I1: 3,9 => CTR => I1: 1,2,4,8 * DIS # C9: 6 => CTR => C9: 3,9 * DIS # E3: 2,5 => CTR => E3: 8 * DIS # G3: 8,9 => CTR => G3: 2,5 * DIS # G1: 5,8 => CTR => G1: 1,2,4,9 * DIS # H1: 5,8 => CTR => H1: 9 * PRF # G3: 5,8 => SOL * DIS # B2: 1 => CTR => B2: 5,8 * DIS # H9: 9 => CTR => H9: 5,8 * DIS # G1: 1,8 => CTR => G1: 2,4,5,9 * DIS # I1: 1,8 => CTR => I1: 2,3,4,9 * PRF # I7: 1,8 => SOL * DIS # I9: 1,8 => CTR => I9: 4,6,9 * DIS # G6: 2,9 => CTR => G6: 8 * DIS # G6: 2,9 => CTR => G6: 8 * PRF # G1: 2,9 => SOL * DIS # C9: 3 => CTR => C9: 6,9 * DIS # I7: 6,9 => CTR => I7: 1,4,8 * DIS # A7: 1,9 => CTR => A7: 4,8 * DIS # A9: 1,9 => CTR => A9: 3,4,8 * DIS # A1: 1,9 => CTR => A1: 3,8 * DIS # A7: 1,8 => CTR => A7: 4,9 * DIS # A9: 1,8 => CTR => A9: 3,4,9 * DIS # G9: 1,8 => CTR => G9: 4,5,9 * DIS # I9: 1,8 => CTR => I9: 4,6,9 * PRF # D7: 5,9 => SOL * PRF # G7: 1,9 => SOL * DIS # I7: 1,9 => CTR => I7: 4,6,8 * DIS # G9: 1,9 => CTR => G9: 4,5,8 * DIS # I9: 1,9 => CTR => I9: 4,6,8 * DIS # I1: 1,9 => CTR => I1: 2,3,4,8 * CNT 32 HDP CHAINS / 76 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 3,9 => CTR => A1: 1,8 * DIS A1: 1,8 # I1: 3,9 => CTR => I1: 1,2,4,8 * DIS A1: 1,8 + I1: 1,2,4,8 # G6: 2,9 => CTR => G6: 8 * PRF A1: 1,8 + I1: 1,2,4,8 + G6: 8 => SOL * STA A1: 1,8 + I1: 1,2,4,8 + G6: 8 * CNT 4 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...7.......24397...4.....6..9.....45.3.....1.76.....3..7.....2...58643.......2... | initial |
| ...7.6...6.24397...47..1.6.2983176455346.8.17761.45.3..7...3.2..2586437.....72... | autosolve |
| 813756294652439781947281563298317645534628917761945832476593128125864379389172456 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) C1: 3,9 D3: 2,5 H2: 5,8 I2: 1,8 E5: 2,9 D6: 2,9 G5: 2,9 C7: 6,9 A8: 1,9 B9: 1,8 E7: 5,9 I8: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D7,D9: 1.. / D7 = 1 => 13 pairs (_) / D9 = 1 => 0 pairs (*) B2,I2: 1.. / B2 = 1 => 0 pairs (X) / I2 = 1 => 16 pairs (_) A8,I8: 1.. / A8 = 1 => 16 pairs (_) / I8 = 1 => 0 pairs (X) E5,D6: 2.. / E5 = 2 => 0 pairs (*) / D6 = 2 => 0 pairs (X) E5,G5: 2.. / E5 = 2 => 0 pairs (*) / G5 = 2 => 0 pairs (X) D3,D6: 2.. / D3 = 2 => 0 pairs (*) / D6 = 2 => 0 pairs (X) I1,I3: 3.. / I1 = 3 => 0 pairs (X) / I3 = 3 => 13 pairs (_) A9,C9: 3.. / A9 = 3 => 16 pairs (_) / C9 = 3 => 0 pairs (X) A3,I3: 3.. / A3 = 3 => 0 pairs (X) / I3 = 3 => 13 pairs (_) C1,C9: 3.. / C1 = 3 => 16 pairs (_) / C9 = 3 => 0 pairs (X) G1,I1: 4.. / G1 = 4 => 0 pairs (X) / I1 = 4 => 0 pairs (_) A7,A9: 4.. / A7 = 4 => 16 pairs (_) / A9 = 4 => 0 pairs (X) B1,B2: 5.. / B1 = 5 => 16 pairs (_) / B2 = 5 => 16 pairs (_) B2,H2: 5.. / B2 = 5 => 16 pairs (_) / H2 = 5 => 16 pairs (_) C7,C9: 6.. / C7 = 6 => 12 pairs (_) / C9 = 6 => 0 pairs (X) I7,I9: 6.. / I7 = 6 => 0 pairs (X) / I9 = 6 => 12 pairs (_) C7,I7: 6.. / C7 = 6 => 12 pairs (_) / I7 = 6 => 0 pairs (X) C9,I9: 6.. / C9 = 6 => 0 pairs (X) / I9 = 6 => 12 pairs (_) E1,E3: 8.. / E1 = 8 => 0 pairs (X) / E3 = 8 => 15 pairs (_) G6,I6: 8.. / G6 = 8 => 13 pairs (_) / I6 = 8 => 0 pairs (X) E5,D6: 9.. / E5 = 9 => 0 pairs (X) / D6 = 9 => 0 pairs (_) E5,G5: 9.. / E5 = 9 => 0 pairs (X) / G5 = 9 => 0 pairs (_) A8,I8: 9.. / A8 = 9 => 0 pairs (X) / I8 = 9 => 16 pairs (_) E5,E7: 9.. / E5 = 9 => 0 pairs (X) / E7 = 9 => 0 pairs (_) H1,H9: 9.. / H1 = 9 => 16 pairs (_) / H9 = 9 => 0 pairs (X) * DURATION: 0:00:28.720072 START: 23:23:18.956326 END: 23:23:47.676398 2019-04-28 * CP COUNT: (25) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B9,C1,C7,D3,D6,E5,E7,G5,H2,I2,I8) * ...7.6...6.24397...47..1.6.2983176455346.8.17761.45.3..7...3.2..2586437.....72... * PAIR C1: 3,9 BLK 1 A1: 3,9,1,8 # reduction candidate for 3,9 A1: 3,9 => CTR * ...786...6.2439781847..1963298317645534698217761245839.7...3.2..2586437..8..72... A1: 1,8 # 14 pairs A3: 3,9,8 # reduction candidate for 3,9 A3: 3,9 # 14 pairs * PAIR C1: 3,9 ROW 1 I1: 3,9,1,2,4,8 # reduction candidate for 3,9 I1: 3,9 => CTR * .1.7.64..6.24397.1.47..1.6.2983176455346.8.17761.45.3..7...3.2.125864379.8..72.5. I1: 1,2,4,8 # 13 pairs * PAIR C1: 3,9 COL C C9: 3,9,6 # reduction candidate for 3,9 C9: 6 => CTR * ..37.6.9.6524397819475812632983176455346.8.17761.45.3..79.53.26125864379386972.5. C9: 3,9 # 12 pairs * PAIR D3: 2,5 BLK 2 E1: 2,5,8 # reduction candidate for 2,5 E1: 2,5 # 15 pairs E3: 2,5,8 # reduction candidate for 2,5 E3: 2,5 => CTR * ...7864.26.24397.1.47..1.632983176455346.8.17761.45.3..7...3.2.125864379.8..72.5. E3: 8 # 15 pairs * PAIR D3: 2,5 ROW 3 G3: 2,5,8,9 # reduction candidate for 2,5 G3: 8,9 => CTR * ...7.64..6.24397.1.47..1.6.2983176455346.8.17761.45.3..7...3.2.125864379.8..72.5. G3: 2,5 # 17 pairs * PAIR H2: 5,8 BLK 3 G1: 5,8,1,2,4,9 # reduction candidate for 5,8 G1: 5,8 => CTR * .1.726594652439781947581263298317645534698.17761.45.32.7...3.2.125864379.8..72.56 G1: 1,2,4,9 # 12 pairs H1: 5,8,9 # reduction candidate for 5,8 H1: 5,8 => CTR * ..97.61.4612439758.47..1.6.2983176455346.8.17761.45.3..7...3.2.925864371....72.9. H1: 9 # 16 pairs G3: 5,8,2,9 # reduction candidate for 5,8 G3: 5,8 => SOLVED * 813756294652439781947281563298317645534628917761945832476593128125864379389172456 G3: 2,9 # 15 pairs * PAIR H2: 5,8 ROW 2 B2: 5,8,1 # reduction candidate for 5,8 B2: 1 => CTR * .5.7.6...612439758.47..1.6.2983176455346.8.17761.4583.87...3.2..2586437.....72... B2: 5,8 # 16 pairs * PAIR H2: 5,8 COL H H9: 5,8,9 # reduction candidate for 5,8 H9: 9 => CTR * ..97.61.4612439758.47..1.6.2983176455346.8.17761.45.3..7...3.2.925864371....72.9. H9: 5,8 # 16 pairs * PAIR I2: 1,8 BLK 3 G1: 1,8,2,4,5,9 # reduction candidate for 1,8 G1: 1,8 => CTR * ...726..46.24397...47581263298317645534698.17761.45.32.7...3.2..2586437.....72... G1: 2,4,5,9 # 16 pairs I1: 1,8,2,3,4,9 # reduction candidate for 1,8 I1: 1,8 => CTR * ...7264..6.24397...47581263298317645534698.17761.45.32.7...3.2..2586437.....72... I1: 2,3,4,9 # 12 pairs * PAIR I2: 1,8 ROW 2 B2: 1,8,5 # reduction candidate for 1,8 B2: 5 # 16 pairs B2: 1,8 # 16 pairs * PAIR I2: 1,8 COL I I7: 1,8,4,6,9 # reduction candidate for 1,8 I7: 1,8 => SOLVED * 813756294652439781947281563298317645534628917761945832476593128125864379389172456 I7: 4,6,9 # 12 pairs I9: 1,8,4,6,9 # reduction candidate for 1,8 I9: 1,8 => CTR * ..37.6..46.24397...47..1.632983176455346.8.17761.45.32.79.53.26.2586437...6.72... I9: 4,6,9 # 12 pairs * PAIR D6: 2,9 ROW 6 G6: 2,9,8 # reduction candidate for 2,9 G6: 2,9 => CTR * 8137.6492652439781947281.632983176455346.8.17761.45.3847...3826125864379386972154 G6: 8 # 13 pairs I6: 2,9,8 # reduction candidate for 2,9 I6: 2,9 # 13 pairs * PAIR G5: 2,9 BLK 6 G6: 2,9,8 # reduction candidate for 2,9 G6: 2,9 => CTR * 8137.6492652439781947281.632983176455346.8.17761.45.3847...3826125864379386972154 G6: 8 # 13 pairs I6: 2,9,8 # reduction candidate for 2,9 I6: 2,9 # 13 pairs * PAIR G5: 2,9 COL G G1: 2,9,1,4,5,8 # reduction candidate for 2,9 G1: 2,9 => SOLVED * 813756294652439781947281563298317645534628917761945832476593128125864379389172456 G1: 1,4,5,8 # 12 pairs G3: 2,9,5,8 # reduction candidate for 2,9 G3: 2,9 # 15 pairs * PAIR C7: 6,9 BLK 7 C9: 6,9,3 # reduction candidate for 6,9 C9: 3 => CTR * ..97.61.4612439758.47..1.6.2983176455346.8.17761.45.3..76..3.2.925864371..3.72.96 C9: 6,9 # 16 pairs * PAIR C7: 6,9 ROW 7 I7: 6,9,1,4,8 # reduction candidate for 6,9 I7: 6,9 => CTR * ...7.6.9.6.24397..9475.1863298317645534698217761245938879153426.2586437....972... I7: 1,4,8 # 12 pairs * PAIR A8: 1,9 BLK 7 A7: 1,9,4,8 # reduction candidate for 1,9 A7: 1,9 => CTR * ..97.61.4612439758.47..1.6.2983176455346.8.17761.45.3..76..3.2.925864371483172596 A7: 4,8 # 13 pairs A9: 1,9,3,4,8 # reduction candidate for 1,9 A9: 1,9 => CTR * ..97.6..46.24397...47..1.632983176455346.8.17761.45.32476..3.2..2586437..83.72496 A9: 3,4,8 # 12 pairs * PAIR A8: 1,9 COL A A1: 1,9,3,8 # reduction candidate for 1,9 A1: 1,9 => CTR * ...7.6...6.24397...47..1.6.2983176455346.8.17761.45.3..7...3.2.925864371.1..72.9. A1: 3,8 # 16 pairs * PAIR B9: 1,8 BLK 7 A7: 1,8,4,9 # reduction candidate for 1,8 A7: 1,8 => CTR * ..97.61.4612439758.47..1.6.2983176455346.8.17761.45.3..76..3.2.9258643714.3.72.96 A7: 4,9 # 16 pairs A9: 1,8,3,4,9 # reduction candidate for 1,8 A9: 1,8 => CTR * ..97.6..46.24397...47..1.632983176455346.8.17761.45.32476..3.2.925864371..3.72496 A9: 3,4,9 # 12 pairs * PAIR B9: 1,8 ROW 9 G9: 1,8,4,5,9 # reduction candidate for 1,8 G9: 1,8 => CTR * .1.7.6.9.6524397819475812632983176455346.8.17761.45.3..7.1.3.2.125864379.8.97215. G9: 4,5,9 # 12 pairs I9: 1,8,4,6,9 # reduction candidate for 1,8 I9: 1,8 => CTR * ..37.6..46.24397...47..1.632983176455346.8.17761.45.32.79.53.26.2586437...6.72... I9: 4,6,9 # 12 pairs * PAIR B9: 1,8 COL B B1: 1,8,5 # reduction candidate for 1,8 B1: 1,8 # 16 pairs B2: 1,8,5 # reduction candidate for 1,8 B2: 1,8 # 16 pairs * PAIR E7: 5,9 BLK 8 D7: 5,9,1 # reduction candidate for 5,9 D7: 5,9 => SOLVED * 813756294652439781947281563298317645534628917761945832476593128125864379389172456 D7: 1 # 13 pairs D9: 5,9,1 # reduction candidate for 5,9 D9: 5,9 # 13 pairs * PAIR E7: 5,9 ROW 7 G7: 5,9,1,4,8 # reduction candidate for 5,9 G7: 5,9 # 18 pairs G7: 1,4,8 # 13 pairs * PAIR I8: 1,9 BLK 9 G7: 1,9,4,5,8 # reduction candidate for 1,9 G7: 1,9 => SOLVED * 813756294652439781947281563298317645534628917761945832476593128125864379389172456 G7: 4,5,8 # 12 pairs I7: 1,9,4,6,8 # reduction candidate for 1,9 I7: 1,9 => CTR * ...7.6..46.24397.8.472.1.63298317645534628917761.45.32.76..3.2..2586437.....72..6 I7: 4,6,8 # 12 pairs G9: 1,9,4,5,8 # reduction candidate for 1,9 G9: 1,9 => CTR * 8.37264916.24397..947..1.632983176455346.8.17761.45.3..79.53.26125864379.86972154 G9: 4,5,8 # 12 pairs I9: 1,9,4,6,8 # reduction candidate for 1,9 I9: 1,9 => CTR * ..37.6..46.24397...47..1.632983176455346.8.17761.45.32.79.53.26.2586437...6.72... I9: 4,6,8 # 12 pairs * PAIR I8: 1,9 COL I I1: 1,9,2,3,4,8 # reduction candidate for 1,9 I1: 1,9 => CTR * ...7264..6.24397...47581263298317645534698.17761.45.32.7...3.2..2586437.....72... I1: 2,3,4,8 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-interesting-5x5-blank-center-base-pr-000.dot * REASONING * DIS # A1: 3,9 => CTR => A1: 1,8 * DIS # I1: 3,9 => CTR => I1: 1,2,4,8 * DIS # C9: 6 => CTR => C9: 3,9 * DIS # E3: 2,5 => CTR => E3: 8 * DIS # G3: 8,9 => CTR => G3: 2,5 * DIS # G1: 5,8 => CTR => G1: 1,2,4,9 * DIS # H1: 5,8 => CTR => H1: 9 * PRF # G3: 5,8 => SOL * DIS # B2: 1 => CTR => B2: 5,8 * DIS # H9: 9 => CTR => H9: 5,8 * DIS # G1: 1,8 => CTR => G1: 2,4,5,9 * DIS # I1: 1,8 => CTR => I1: 2,3,4,9 * PRF # I7: 1,8 => SOL * DIS # I9: 1,8 => CTR => I9: 4,6,9 * DIS # G6: 2,9 => CTR => G6: 8 * DIS # G6: 2,9 => CTR => G6: 8 * PRF # G1: 2,9 => SOL * DIS # C9: 3 => CTR => C9: 6,9 * DIS # I7: 6,9 => CTR => I7: 1,4,8 * DIS # A7: 1,9 => CTR => A7: 4,8 * DIS # A9: 1,9 => CTR => A9: 3,4,8 * DIS # A1: 1,9 => CTR => A1: 3,8 * DIS # A7: 1,8 => CTR => A7: 4,9 * DIS # A9: 1,8 => CTR => A9: 3,4,9 * DIS # G9: 1,8 => CTR => G9: 4,5,9 * DIS # I9: 1,8 => CTR => I9: 4,6,9 * PRF # D7: 5,9 => SOL * PRF # G7: 1,9 => SOL * DIS # I7: 1,9 => CTR => I7: 4,6,8 * DIS # G9: 1,9 => CTR => G9: 4,5,8 * DIS # I9: 1,9 => CTR => I9: 4,6,8 * DIS # I1: 1,9 => CTR => I1: 2,3,4,8 * CNT 32 HDP CHAINS / 76 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B9,C1,C7,D3,D6,E5,E7,G5,H2,I2,I8) * ...7.6...6.24397...47..1.6.2983176455346.8.17761.45.3..7...3.2..2586437.....72... * PAIR C1: 3,9 BLK 1 A1: 3,9,1,8 # reduction candidate for 3,9 A1: 3,9 => CTR * ...786...6.2439781847..1963298317645534698217761245839.7...3.2..2586437..8..72... * RESTART * PAIR C1: 3,9 ROW 1 I1: 3,9,1,2,4,8 # reduction candidate for 3,9 I1: 3,9 => CTR * 81.7.64..6.24397.1.47..1.6.2983176455346.8.17761.45.3..7...3.2.125864379.8..72.5. * PAIR RESTART * PAIR D6: 2,9 ROW 6 G6: 2,9,8 # reduction candidate for 2,9 G6: 2,9 => CTR * 8137.6492652439781947281.632983176455346.8.17761.45.3847...3826125864379386972154 G6: 8 => SOLVED * 813756294652439781947281563298317645534628917761945832476593128125864379389172456 * DURATION: 0:00:04.444545 START: 23:24:32.119425 END: 23:24:36.563970 2019-04-28 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-interesting-5x5-blank-center-base-pr-001.dot * REASONING * DIS # A1: 3,9 => CTR => A1: 1,8 * DIS A1: 1,8 # I1: 3,9 => CTR => I1: 1,2,4,8 * DIS A1: 1,8 + I1: 1,2,4,8 # G6: 2,9 => CTR => G6: 8 * PRF A1: 1,8 + I1: 1,2,4,8 + G6: 8 => SOL * STA A1: 1,8 + I1: 1,2,4,8 + G6: 8 * CNT 4 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuwiki.org/Interesting_Sudokus Minimal at 24 Clues with a 5x5 blank space in the center Discovered by Klaus Brenner
Solution
position: 813756294652439781947281563298317645534628917761945832476593128125864379389172456 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 # A1: 3,9 => CTR => A1: 1,8 * INC # A1: 1,8 => UNS * INC # A3: 3,9 => UNS * DIS # I1: 3,9 => CTR => I1: 1,2,4,8 * INC # I1: 1,2,4,8 => UNS * INC # C9: 3,9 => UNS * DIS # C9: 6 => CTR => C9: 3,9 * INC # E1: 2,5 => UNS * DIS # E3: 2,5 => CTR => E3: 8 * INC # E3: 8 => UNS * INC # G3: 2,5 => UNS * DIS # G3: 8,9 => CTR => G3: 2,5 * DIS # G1: 5,8 => CTR => G1: 1,2,4,9 * INC # G1: 1,2,4,9 => UNS * DIS # H1: 5,8 => CTR => H1: 9 * INC # H1: 9 => UNS * PRF # G3: 5,8 => SOL * INC # G3: 2,9 => UNS * INC # B2: 5,8 => UNS * DIS # B2: 1 => CTR => B2: 5,8 * INC # H9: 5,8 => UNS * DIS # H9: 9 => CTR => H9: 5,8 * DIS # G1: 1,8 => CTR => G1: 2,4,5,9 * INC # G1: 2,4,5,9 => UNS * DIS # I1: 1,8 => CTR => I1: 2,3,4,9 * INC # I1: 2,3,4,9 => UNS * INC # B2: 1,8 => UNS * INC # B2: 5 => UNS * PRF # I7: 1,8 => SOL * INC # I7: 4,6,9 => UNS * DIS # I9: 1,8 => CTR => I9: 4,6,9 * INC # I9: 4,6,9 => UNS * DIS # G6: 2,9 => CTR => G6: 8 * INC # G6: 8 => UNS * INC # I6: 2,9 => UNS * DIS # G6: 2,9 => CTR => G6: 8 * INC # G6: 8 => UNS * INC # I6: 2,9 => UNS * PRF # G1: 2,9 => SOL * INC # G1: 1,4,5,8 => UNS * INC # G3: 2,9 => UNS * INC # C9: 6,9 => UNS * DIS # C9: 3 => CTR => C9: 6,9 * DIS # I7: 6,9 => CTR => I7: 1,4,8 * INC # I7: 1,4,8 => UNS * DIS # A7: 1,9 => CTR => A7: 4,8 * INC # A7: 4,8 => UNS * DIS # A9: 1,9 => CTR => A9: 3,4,8 * INC # A9: 3,4,8 => UNS * DIS # A1: 1,9 => CTR => A1: 3,8 * INC # A1: 3,8 => UNS * DIS # A7: 1,8 => CTR => A7: 4,9 * INC # A7: 4,9 => UNS * DIS # A9: 1,8 => CTR => A9: 3,4,9 * INC # A9: 3,4,9 => UNS * DIS # G9: 1,8 => CTR => G9: 4,5,9 * INC # G9: 4,5,9 => UNS * DIS # I9: 1,8 => CTR => I9: 4,6,9 * INC # I9: 4,6,9 => UNS * INC # B1: 1,8 => UNS * INC # B2: 1,8 => UNS * PRF # D7: 5,9 => SOL * INC # D7: 1 => UNS * INC # D9: 5,9 => UNS * INC # G7: 5,9 => UNS * INC # G7: 1,4,8 => UNS * PRF # G7: 1,9 => SOL * INC # G7: 4,5,8 => UNS * DIS # I7: 1,9 => CTR => I7: 4,6,8 * INC # I7: 4,6,8 => UNS * DIS # G9: 1,9 => CTR => G9: 4,5,8 * INC # G9: 4,5,8 => UNS * DIS # I9: 1,9 => CTR => I9: 4,6,8 * INC # I9: 4,6,8 => UNS * DIS # I1: 1,9 => CTR => I1: 2,3,4,8 * INC # I1: 2,3,4,8 => UNS * CNT 76 HDP CHAINS / 76 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 3,9 => CTR => A1: 1,8 * DIS A1: 1,8 # I1: 3,9 => CTR => I1: 1,2,4,8 * DIS A1: 1,8 + I1: 1,2,4,8 # G6: 2,9 => CTR => G6: 8 * PRF A1: 1,8 + I1: 1,2,4,8 + G6: 8 => SOL * STA A1: 1,8 + I1: 1,2,4,8 + G6: 8 * CNT 4 HDP CHAINS / 3 HYP OPENED