Analysis of zz-www.sudokuoftheday.co.uk-20060502-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006
level: medium
position: .2....8..1...86.....95........859..3.....315.7.....9....7435..9.9.2......4.9.7.6. initial
Autosolve
position: .26.9.8..1...86.928.95........859..39....315.7.....9..6.74352.9.9.268....4.917.6. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 5 => CTR => B2: 3,7 * DIS # G3: 3,7 => CTR => G3: 4,6 * DIS # H3: 3,7 => CTR => H3: 1,4 * DIS # F3: 1,4 => CTR => F3: 2 * DIS # H1: 1,4 => CTR => H1: 3,7 * DIS # I1: 1,4 => CTR => I1: 5,7 * DIS # F6: 2 => CTR => F6: 1,4 * DIS # D1: 3,7 => CTR => D1: 1 * DIS # G2: 3,7 => CTR => G2: 4,5 * DIS # C4: 2,4 => CTR => C4: 1 * PRF # C4: 1 => SOL * PRF # C5: 2,4 => SOL * DIS # C5: 8 => CTR => C5: 2,4 * PRF # H4: 2,4 => SOL * DIS # H4: 7 => CTR => H4: 2,4 * DIS # B2: 3,5 => CTR => B2: 7 * DIS # C2: 3,5 => CTR => C2: 4 * PRF # C8: 3,5 => SOL * DIS # C8: 1 => CTR => C8: 3,5 * DIS # C9: 3,5 => CTR => C9: 2,8 * DIS # F6: 2,4 => CTR => F6: 1 * PRF # H6: 2,4 => SOL * DIS # H6: 8 => CTR => H6: 2,4 * DIS # E3: 2,4 => CTR => E3: 7 * DIS # G4: 4,6 => CTR => G4: 7 * PRF # G4: 7 => SOL * DIS # I6: 4,6 => CTR => I6: 8 * PRF # I6: 8 => SOL * PRF # I3: 4,6 => SOL * DIS # I3: 1,7 => CTR => I3: 4,6 * PRF # C8: 3,5 => SOL * DIS # C8: 1 => CTR => C8: 3,5 * DIS # A9: 3,5 => CTR => A9: 2 * DIS # C9: 3,5 => CTR => C9: 2,8 * DIS # G8: 3,5 => CTR => G8: 4,7 * DIS # A1: 4 => CTR => A1: 3,5 * DIS # G8: 3,5 => CTR => G8: 4,7 * DIS # A9: 3,5 => CTR => A9: 2 * DIS # C9: 3,5 => CTR => C9: 2,8 * DIS # G2: 4,7 => CTR => G2: 3,5 * DIS # C9: 2,3 => CTR => C9: 5,8 * CNT 41 HDP CHAINS / 66 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 5 => CTR => B2: 3,7 * DIS B2: 3,7 # G3: 3,7 => CTR => G3: 4,6 * DIS B2: 3,7 + G3: 4,6 # H3: 3,7 => CTR => H3: 1,4 * DIS B2: 3,7 + G3: 4,6 + H3: 1,4 # F3: 1,4 => CTR => F3: 2 * DIS B2: 3,7 + G3: 4,6 + H3: 1,4 + F3: 2 # C4: 2,4 => CTR => C4: 1 * PRF B2: 3,7 + G3: 4,6 + H3: 1,4 + F3: 2 + C4: 1 => SOL * STA B2: 3,7 + G3: 4,6 + H3: 1,4 + F3: 2 + C4: 1 * CNT 6 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2....8..1...86.....95........859..3.....315.7.....9....7435..9.9.2......4.9.7.6. | initial |
| .26.9.8..1...86.928.95........859..39....315.7.....9..6.74352.9.9.268....4.917.6. | autosolve |
| 526194837174386592839572614461859723982743156753621948617435289395268471248917365 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) B3: 3,7 F1: 1,4 D2: 3,7 A4: 2,4 B4: 1,6 B5: 6,8 B6: 3,5 C6: 3,5 D5: 6,7 D6: 1,6 E6: 2,4 I5: 4,6 B7: 1,8 A8: 3,5 H7: 1,8 G9: 3,5 I9: 5,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B4,C4: 1.. / B4 = 1 => 0 pairs (X) / C4 = 1 => 0 pairs (_) D6,F6: 1.. / D6 = 1 => 0 pairs (X) / F6 = 1 => 18 pairs (_) B7,C8: 1.. / B7 = 1 => 0 pairs (*) / C8 = 1 => 0 pairs (X) B7,H7: 1.. / B7 = 1 => 0 pairs (*) / H7 = 1 => 0 pairs (X) B4,B7: 1.. / B4 = 1 => 0 pairs (X) / B7 = 1 => 0 pairs (_) C4,C8: 1.. / C4 = 1 => 0 pairs (*) / C8 = 1 => 0 pairs (X) D1,D6: 1.. / D1 = 1 => 18 pairs (_) / D6 = 1 => 0 pairs (X) E3,F3: 2.. / E3 = 2 => 0 pairs (X) / F3 = 2 => 19 pairs (_) H4,H6: 2.. / H4 = 2 => 0 pairs (*) / H6 = 2 => 0 pairs (X) A9,C9: 2.. / A9 = 2 => 21 pairs (_) / C9 = 2 => 0 pairs (X) C5,E5: 2.. / C5 = 2 => 0 pairs (*) / E5 = 2 => 0 pairs (X) A4,A9: 2.. / A4 = 2 => 0 pairs (X) / A9 = 2 => 21 pairs (_) F3,F6: 2.. / F3 = 2 => 19 pairs (_) / F6 = 2 => 0 pairs (X) D1,D2: 3.. / D1 = 3 => 0 pairs (X) / D2 = 3 => 19 pairs (_) B6,C6: 3.. / B6 = 3 => 0 pairs (X) / C6 = 3 => 20 pairs (_) A1,C2: 4.. / A1 = 4 => 0 pairs (X) / C2 = 4 => 21 pairs (_) C2,G2: 4.. / C2 = 4 => 21 pairs (_) / G2 = 4 => 0 pairs (X) A1,A4: 4.. / A1 = 4 => 0 pairs (X) / A4 = 4 => 21 pairs (_) I1,G2: 5.. / I1 = 5 => 0 pairs (X) / G2 = 5 => 20 pairs (_) B6,C6: 5.. / B6 = 5 => 20 pairs (_) / C6 = 5 => 0 pairs (X) A1,I1: 5.. / A1 = 5 => 20 pairs (_) / I1 = 5 => 0 pairs (X) B2,B6: 5.. / B2 = 5 => 0 pairs (X) / B6 = 5 => 20 pairs (_) G3,I3: 6.. / G3 = 6 => 0 pairs (*) / I3 = 6 => 0 pairs (X) B4,B5: 6.. / B4 = 6 => 0 pairs (*) / B5 = 6 => 0 pairs (X) D5,D6: 6.. / D5 = 6 => 0 pairs (X) / D6 = 6 => 18 pairs (_) B4,G4: 6.. / B4 = 6 => 0 pairs (*) / G4 = 6 => 0 pairs (X) D6,I6: 6.. / D6 = 6 => 18 pairs (_) / I6 = 6 => 0 pairs (X) G3,G4: 6.. / G3 = 6 => 0 pairs (*) / G4 = 6 => 0 pairs (X) B2,B3: 7.. / B2 = 7 => 18 pairs (_) / B3 = 7 => 0 pairs (X) D5,E5: 7.. / D5 = 7 => 18 pairs (_) / E5 = 7 => 0 pairs (X) G4,H4: 7.. / G4 = 7 => 0 pairs (*) / H4 = 7 => 0 pairs (X) E3,E5: 7.. / E3 = 7 => 18 pairs (_) / E5 = 7 => 0 pairs (X) B5,C5: 8.. / B5 = 8 => 0 pairs (*) / C5 = 8 => 0 pairs (X) H6,I6: 8.. / H6 = 8 => 0 pairs (X) / I6 = 8 => 0 pairs (_) B7,C9: 8.. / B7 = 8 => 0 pairs (X) / C9 = 8 => 0 pairs (_) H7,I9: 8.. / H7 = 8 => 0 pairs (*) / I9 = 8 => 0 pairs (X) B7,H7: 8.. / B7 = 8 => 0 pairs (X) / H7 = 8 => 0 pairs (_) C9,I9: 8.. / C9 = 8 => 0 pairs (*) / I9 = 8 => 0 pairs (X) B5,B7: 8.. / B5 = 8 => 0 pairs (*) / B7 = 8 => 0 pairs (X) C5,C9: 8.. / C5 = 8 => 0 pairs (X) / C9 = 8 => 0 pairs (_) H6,H7: 8.. / H6 = 8 => 0 pairs (X) / H7 = 8 => 0 pairs (_) I6,I9: 8.. / I6 = 8 => 0 pairs (*) / I9 = 8 => 0 pairs (X) * DURATION: 0:00:47.219919 START: 22:49:24.133081 END: 22:50:11.353000 2019-04-30 * CP COUNT: (42) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A8,B3,B4,B5,B6,B7,C6,D2,D5,D6,E6,F1,G9,H7,I5,I9) * .26.9.8..1...86.928.95........859..39....315.7.....9..6.74352.9.9.268....4.917.6. * PAIR B3: 3,7 BLK 1 B2: 3,7,5 # reduction candidate for 3,7 B2: 5 => CTR * .26.9.8.515..86.928795........859..39.26731547351..9.66.74352.9.9.268..7248917.6. B2: 3,7 # 20 pairs * PAIR B3: 3,7 ROW 3 G3: 3,7,4,6 # reduction candidate for 3,7 G3: 3,7 => CTR * .26.9.8..1...86.928.95....6...8596739687231547..641928687435219.91268....4.917.65 G3: 4,6 # 18 pairs H3: 3,7,1,4 # reduction candidate for 3,7 H3: 3,7 => CTR * 526.9.8..1.4.865928.95.....4.1859.2398267315475....9..6.74352.9.9.268...248917365 H3: 1,4 # 18 pairs * PAIR F1: 1,4 BLK 2 F3: 1,4,2 # reduction candidate for 1,4 F3: 1,4 => CTR * .26.9.8..1...86.928.952.......859..39.2.731547...42986687435219.91268...24.917.68 F3: 2 # 19 pairs * PAIR F1: 1,4 ROW 1 H1: 1,4,3,7 # reduction candidate for 1,4 H1: 1,4 => CTR * .26.9.8..1.4.86.928.95.....4..859..39..6731547..1..9.66.74352.9.9.268...24.917.68 H1: 3,7 # 18 pairs I1: 1,4,5,7 # reduction candidate for 1,4 I1: 1,4 => CTR * 526.9.8..1.4.865928.95.....4..859..39..6731547531..9.66.74352.939.268...24.917368 I1: 5,7 # 18 pairs * PAIR F1: 1,4 COL F F6: 1,4,2 # reduction candidate for 1,4 F6: 2 => CTR * .26.9.8..1...86.928.95........859..39....315.7..1.29.66.74352.9.9.268....4.917.68 F6: 1,4 # 19 pairs * PAIR D2: 3,7 BLK 2 D1: 3,7,1 # reduction candidate for 3,7 D1: 3,7 => CTR * .26.9.8..1...86.928.95..6...61859..398...315.7..1..9.66.74352.9.9.268....4.917.68 D1: 1 # 18 pairs * PAIR D2: 3,7 ROW 2 B2: 3,7,5 # reduction candidate for 3,7 B2: 3,7 # 20 pairs G2: 3,7,4,5 # reduction candidate for 3,7 G2: 3,7 => CTR * 326.9.8.51543867928795.....4..8596739687.315.7.....9..6.74352.9.9.268...24.917.68 G2: 4,5 # 18 pairs * PAIR A4: 2,4 BLK 4 C4: 2,4,1 # reduction candidate for 2,4 C4: 2,4 => CTR * .26.9.8..1...86.928.95......1.8596739687231547..6419286874352.9.9.268....4.917.6. C4: 1 => SOLVED * 526194837174386592839572614461859723982743156753621948617435289395268471248917365 C5: 2,4,8 # reduction candidate for 2,4 C5: 2,4 => SOLVED * 526194837174386592839572614461859723982743156753621948617435289395268471248917365 C5: 8 => CTR * .26.9.8..1...86.928.95........859..39.8.231547...41928687435219.91268....4.917.65 * PAIR A4: 2,4 ROW 4 H4: 2,4,7 # reduction candidate for 2,4 H4: 2,4 => SOLVED * 526194837174386592839572614461859723982743156753621948617435289395268471248917365 H4: 7 => CTR * 526.9.8..1.4.865928.95.2...4.2859.739....315.7.....9286.7435289.9.268....48917.65 * PAIR B6: 3,5 COL B B2: 3,5,7 # reduction candidate for 3,5 B2: 3,5 => CTR * .26.9.8..1...86.928795........859..39.26731547..1..9.66.74352.9.9.268...248917365 B2: 7 # 18 pairs * PAIR C6: 3,5 COL C C2: 3,5,4 # reduction candidate for 3,5 C2: 3,5 => CTR * 426.918.51...864928.95.....2..859..39...2315.7..14.9..6.74352.9.9.268....4.917.6. C2: 4 # 21 pairs C8: 3,5,1 # reduction candidate for 3,5 C8: 3,5 => SOLVED * 526194837174386592839572614461859723982743156753621948617435289395268471248917365 C8: 1 => CTR * .26.9.8..1...86.928.95......1.8596739687231547..6419286874352.9.91268....4.917.6. C9: 3,5,2,8 # reduction candidate for 3,5 C9: 3,5 => CTR * .26.9.8..1...86.928.95........859..39.8.231547...41928687435219.91268...24.917.65 C9: 2,8 # 18 pairs * PAIR E6: 2,4 BLK 5 E5: 2,4,7 # reduction candidate for 2,4 E5: 2,4 # 18 pairs F6: 2,4,1 # reduction candidate for 2,4 F6: 2,4 => CTR * .26.9.8..1...86.928.95..6...61859..398...315.7..1..9.66.74352.9.9.268....4.917.68 F6: 1 # 18 pairs * PAIR E6: 2,4 ROW 6 H6: 2,4,8 # reduction candidate for 2,4 H6: 2,4 => SOLVED * 526194837174386592839572614461859723982743156753621948617435289395268471248917365 H6: 8 => CTR * .26.9.8..1...86.928.95........859.239.2..315.7.....98.687435219.91268...24.917.68 * PAIR E6: 2,4 COL E E3: 2,4,7 # reduction candidate for 2,4 E3: 2,4 => CTR * .26.9.8..1...86.928.95........859..39.26731547..1..9.66.74352.9.9.268...248917365 E3: 7 # 18 pairs * PAIR I5: 4,6 BLK 6 G4: 4,6,7 # reduction candidate for 4,6 G4: 4,6 => CTR * 526.9.8..1.4.865928.95.2...4.2859.739....315.7.....9286.7435289.9.268....48917.65 G4: 7 => SOLVED * 526194837174386592839572614461859723982743156753621948617435289395268471248917365 I6: 4,6,8 # reduction candidate for 4,6 I6: 4,6 => CTR * .26.9.8..1...86.928.95......1.8596.39....315.7.....98.687435219.91268....4.917.68 I6: 8 => SOLVED * 526194837174386592839572614461859723982743156753621948617435289395268471248917365 * PAIR I5: 4,6 COL I I3: 4,6,1,7 # reduction candidate for 4,6 I3: 4,6 => SOLVED * 526194837174386592839572614461859723982743156753621948617435289395268471248917365 I3: 1,7 => CTR * 526.9.8.41.4.865928.95.46..461859723982.4315675362.9486174352893952684..248917365 * PAIR A8: 3,5 BLK 7 C8: 3,5,1 # reduction candidate for 3,5 C8: 3,5 => SOLVED * 526194837174386592839572614461859723982743156753621948617435289395268471248917365 C8: 1 => CTR * .26.9.8..1...86.928.95......1.8596739687231547..6419286874352.9.91268....4.917.6. A9: 3,5,2 # reduction candidate for 3,5 A9: 3,5 => CTR * .26.9.8..1...86.928.95.....2..859..39...2315.7...419286.7435289.9.268....4.917.6. A9: 2 # 21 pairs C9: 3,5,2,8 # reduction candidate for 3,5 C9: 3,5 => CTR * .26.9.8..1...86.928.95........859..39.8.231547...41928687435219.91268...24.917.65 C9: 2,8 # 18 pairs * PAIR A8: 3,5 ROW 8 G8: 3,5,4,7 # reduction candidate for 3,5 G8: 3,5 => CTR * .26.9.8.51...86.928.95..6.1...859..39....315.7.....98.687435219.91268..7.4.917.68 G8: 4,7 # 18 pairs * PAIR A8: 3,5 COL A A1: 3,5,4 # reduction candidate for 3,5 A1: 4 => CTR * 426.918.51...864928.95.....2..859..39...2315.7..14.9..6.74352.9.9.268....4.917.6. A1: 3,5 # 21 pairs * PAIR G9: 3,5 BLK 9 G8: 3,5,4,7 # reduction candidate for 3,5 G8: 3,5 => CTR * .26.9.8.51...86.928.95..6.1...859..39....315.7.....98.687435219.91268..7.4.917.68 G8: 4,7 # 18 pairs * PAIR G9: 3,5 ROW 9 A9: 3,5,2 # reduction candidate for 3,5 A9: 3,5 => CTR * .26.9.8..1...86.928.95.....2..859..39...2315.7...419286.7435289.9.268....4.917.6. A9: 2 # 21 pairs C9: 3,5,2,8 # reduction candidate for 3,5 C9: 3,5 => CTR * .26.9.8..1...86.928.95........859..39.8.231547...41928687435219.91268...24.917.65 C9: 2,8 # 18 pairs * PAIR G9: 3,5 COL G G2: 3,5,4,7 # reduction candidate for 3,5 G2: 4,7 => CTR * .26.9.8.51...86.928.95........859..39.8.231547.....9..6.74352.9.9.268....4.917.68 G2: 3,5 # 23 pairs * PAIR I9: 5,8 ROW 9 C9: 5,8,2,3 # reduction candidate for 5,8 C9: 2,3 => CTR * .26.9.8..1...86.928.95........859..39.8.231547...41928687435219.91268....4.917.65 C9: 5,8 # 22 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060502-absurd-base-pr-000.dot * REASONING * DIS # B2: 5 => CTR => B2: 3,7 * DIS # G3: 3,7 => CTR => G3: 4,6 * DIS # H3: 3,7 => CTR => H3: 1,4 * DIS # F3: 1,4 => CTR => F3: 2 * DIS # H1: 1,4 => CTR => H1: 3,7 * DIS # I1: 1,4 => CTR => I1: 5,7 * DIS # F6: 2 => CTR => F6: 1,4 * DIS # D1: 3,7 => CTR => D1: 1 * DIS # G2: 3,7 => CTR => G2: 4,5 * DIS # C4: 2,4 => CTR => C4: 1 * PRF # C4: 1 => SOL * PRF # C5: 2,4 => SOL * DIS # C5: 8 => CTR => C5: 2,4 * PRF # H4: 2,4 => SOL * DIS # H4: 7 => CTR => H4: 2,4 * DIS # B2: 3,5 => CTR => B2: 7 * DIS # C2: 3,5 => CTR => C2: 4 * PRF # C8: 3,5 => SOL * DIS # C8: 1 => CTR => C8: 3,5 * DIS # C9: 3,5 => CTR => C9: 2,8 * DIS # F6: 2,4 => CTR => F6: 1 * PRF # H6: 2,4 => SOL * DIS # H6: 8 => CTR => H6: 2,4 * DIS # E3: 2,4 => CTR => E3: 7 * DIS # G4: 4,6 => CTR => G4: 7 * PRF # G4: 7 => SOL * DIS # I6: 4,6 => CTR => I6: 8 * PRF # I6: 8 => SOL * PRF # I3: 4,6 => SOL * DIS # I3: 1,7 => CTR => I3: 4,6 * PRF # C8: 3,5 => SOL * DIS # C8: 1 => CTR => C8: 3,5 * DIS # A9: 3,5 => CTR => A9: 2 * DIS # C9: 3,5 => CTR => C9: 2,8 * DIS # G8: 3,5 => CTR => G8: 4,7 * DIS # A1: 4 => CTR => A1: 3,5 * DIS # G8: 3,5 => CTR => G8: 4,7 * DIS # A9: 3,5 => CTR => A9: 2 * DIS # C9: 3,5 => CTR => C9: 2,8 * DIS # G2: 4,7 => CTR => G2: 3,5 * DIS # C9: 2,3 => CTR => C9: 5,8 * CNT 41 HDP CHAINS / 66 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A8,B3,B4,B5,B6,B7,C6,D2,D5,D6,E6,F1,G9,H7,I5,I9) * .26.9.8..1...86.928.95........859..39....315.7.....9..6.74352.9.9.268....4.917.6. * PAIR B3: 3,7 BLK 1 B2: 3,7,5 # reduction candidate for 3,7 B2: 5 => CTR * .26.9.8.515..86.928795........859..39.26731547351..9.66.74352.9.9.268..7248917.6. * PAIR B3: 3,7 ROW 3 G3: 3,7,4,6 # reduction candidate for 3,7 G3: 3,7 => CTR * .26.9.8..1...86.928.95....6...859673968723154753641928687435219.91268....4.917.65 H3: 3,7,1,4 # reduction candidate for 3,7 H3: 3,7 => CTR * 526.9.8..1.4.865928.95.....4.1859.239826731547531..9..6.74352.9.9.268...248917365 * PAIR RESTART * PAIR F1: 1,4 BLK 2 F3: 1,4,2 # reduction candidate for 1,4 F3: 1,4 => CTR * .26.9.83.17.386.9283952...7...859..39.2.73154753.42986687435219.91268..5245917368 * PAIR A4: 2,4 BLK 4 C4: 2,4,1 # reduction candidate for 2,4 C4: 2,4 => CTR * .26.9.83.17.386.928395.2....1.8596739687231547536419286874352.9.9.268....4.917.6. C4: 1 => SOLVED * 526194837174386592839572614461859723982743156753621948617435289395268471248917365 * DURATION: 0:00:05.921426 START: 22:50:53.653848 END: 22:50:59.575274 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060502-absurd-base-pr-001.dot * REASONING * DIS # B2: 5 => CTR => B2: 3,7 * DIS B2: 3,7 # G3: 3,7 => CTR => G3: 4,6 * DIS B2: 3,7 + G3: 4,6 # H3: 3,7 => CTR => H3: 1,4 * DIS B2: 3,7 + G3: 4,6 + H3: 1,4 # F3: 1,4 => CTR => F3: 2 * DIS B2: 3,7 + G3: 4,6 + H3: 1,4 + F3: 2 # C4: 2,4 => CTR => C4: 1 * PRF B2: 3,7 + G3: 4,6 + H3: 1,4 + F3: 2 + C4: 1 => SOL * STA B2: 3,7 + G3: 4,6 + H3: 1,4 + F3: 2 + C4: 1 * CNT 6 HDP CHAINS / 6 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060502, absurd
Solution
position: 526194837174386592839572614461859723982743156753621948617435289395268471248917365 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 # B2: 3,7 => UNS * DIS # B2: 5 => CTR => B2: 3,7 * DIS # G3: 3,7 => CTR => G3: 4,6 * INC # G3: 4,6 => UNS * DIS # H3: 3,7 => CTR => H3: 1,4 * INC # H3: 1,4 => UNS * DIS # F3: 1,4 => CTR => F3: 2 * INC # F3: 2 => UNS * DIS # H1: 1,4 => CTR => H1: 3,7 * INC # H1: 3,7 => UNS * DIS # I1: 1,4 => CTR => I1: 5,7 * INC # I1: 5,7 => UNS * INC # F6: 1,4 => UNS * DIS # F6: 2 => CTR => F6: 1,4 * DIS # D1: 3,7 => CTR => D1: 1 * INC # D1: 1 => UNS * INC # B2: 3,7 => UNS * DIS # G2: 3,7 => CTR => G2: 4,5 * INC # G2: 4,5 => UNS * DIS # C4: 2,4 => CTR => C4: 1 * PRF # C4: 1 => SOL * PRF # C5: 2,4 => SOL * DIS # C5: 8 => CTR => C5: 2,4 * PRF # H4: 2,4 => SOL * DIS # H4: 7 => CTR => H4: 2,4 * DIS # B2: 3,5 => CTR => B2: 7 * INC # B2: 7 => UNS * DIS # C2: 3,5 => CTR => C2: 4 * INC # C2: 4 => UNS * PRF # C8: 3,5 => SOL * DIS # C8: 1 => CTR => C8: 3,5 * DIS # C9: 3,5 => CTR => C9: 2,8 * INC # C9: 2,8 => UNS * INC # E5: 2,4 => UNS * DIS # F6: 2,4 => CTR => F6: 1 * INC # F6: 1 => UNS * PRF # H6: 2,4 => SOL * DIS # H6: 8 => CTR => H6: 2,4 * DIS # E3: 2,4 => CTR => E3: 7 * INC # E3: 7 => UNS * DIS # G4: 4,6 => CTR => G4: 7 * PRF # G4: 7 => SOL * DIS # I6: 4,6 => CTR => I6: 8 * PRF # I6: 8 => SOL * PRF # I3: 4,6 => SOL * DIS # I3: 1,7 => CTR => I3: 4,6 * PRF # C8: 3,5 => SOL * DIS # C8: 1 => CTR => C8: 3,5 * DIS # A9: 3,5 => CTR => A9: 2 * INC # A9: 2 => UNS * DIS # C9: 3,5 => CTR => C9: 2,8 * INC # C9: 2,8 => UNS * DIS # G8: 3,5 => CTR => G8: 4,7 * INC # G8: 4,7 => UNS * INC # A1: 3,5 => UNS * DIS # A1: 4 => CTR => A1: 3,5 * DIS # G8: 3,5 => CTR => G8: 4,7 * INC # G8: 4,7 => UNS * DIS # A9: 3,5 => CTR => A9: 2 * INC # A9: 2 => UNS * DIS # C9: 3,5 => CTR => C9: 2,8 * INC # C9: 2,8 => UNS * INC # G2: 3,5 => UNS * DIS # G2: 4,7 => CTR => G2: 3,5 * INC # C9: 5,8 => UNS * DIS # C9: 2,3 => CTR => C9: 5,8 * CNT 66 HDP CHAINS / 66 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 3,7 => UNS * DIS # B2: 5 => CTR => B2: 3,7 * DIS B2: 3,7 # G3: 3,7 => CTR => G3: 4,6 * DIS B2: 3,7 + G3: 4,6 # H3: 3,7 => CTR => H3: 1,4 * DIS B2: 3,7 + G3: 4,6 + H3: 1,4 # F3: 1,4 => CTR => F3: 2 * DIS B2: 3,7 + G3: 4,6 + H3: 1,4 + F3: 2 # C4: 2,4 => CTR => C4: 1 * PRF B2: 3,7 + G3: 4,6 + H3: 1,4 + F3: 2 + C4: 1 => SOL * STA B2: 3,7 + G3: 4,6 + H3: 1,4 + F3: 2 + C4: 1 * CNT 7 HDP CHAINS / 6 HYP OPENED