Analysis of xx-top95-004-base.sdk
Contents
Original Sudoku
level: medium
position: 48.3............71.2.......7.5....6....2..8.............1.76...3.....4......5.... initial
Autosolve
position: 4873...9....6..271126.9.3847.5...162...2..8..........9..1.769233..1..45.....53.18 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 3 => CTR => B2: 5,9 * PRF # B2: 3,9 => SOL * DIS # B2: 5 => CTR => B2: 3,9 * DIS # C5: 3,9 => CTR => C5: 4 * PRF # C5: 4 => SOL * DIS # E4: 3 => CTR => E4: 4,8 * DIS # F4: 4,8 => CTR => F4: 9 * PRF # F4: 9 => SOL * DIS # B5: 3,4 => CTR => B5: 1,6,9 * DIS # B6: 3,4 => CTR => B6: 1,6 * DIS # E4: 8 => CTR => E4: 3,4 * DIS # B5: 6,9 => CTR => B5: 1,3,4 * PRF # A9: 6,9 => SOL * DIS # A9: 2 => CTR => A9: 6,9 * DIS # F4: 4 => CTR => F4: 8,9 * DIS # E5: 1,4 => CTR => E5: 3,6 * DIS # E6: 1,4 => CTR => E6: 3,6 * DIS # B6: 1,4 => CTR => B6: 3,6 * DIS # B5: 3,4 => CTR => B5: 1,6,9 * DIS # E5: 3,4 => CTR => E5: 1,6 * DIS # B6: 3,4 => CTR => B6: 1,6 * PRF # E6: 3,4 => SOL * PRF # B9: 4,9 => SOL * DIS # F8: 2 => CTR => F8: 8,9 * PRF # F8: 2,8 => SOL * DIS # F8: 9 => CTR => F8: 2,8 * PRF # B9: 4,9 => SOL * DIS # C9: 4,9 => CTR => C9: 2 * PRF # C9: 2 => SOL * PRF # B9: 4,9 => SOL * CNT 30 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 3 => CTR => B2: 5,9 * DIS B2: 5,9 # E4: 3 => CTR => E4: 4,8 * DIS B2: 5,9 + E4: 4,8 # F4: 4,8 => CTR => F4: 9 * PRF B2: 5,9 + E4: 4,8 + F4: 9 => SOL * STA B2: 5,9 + E4: 4,8 + F4: 9 * CNT 4 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 48.3............71.2.......7.5....6....2..8.............1.76...3.....4......5.... | initial |
| 4873...9....6..271126.9.3847.5...162...2..8..........9..1.769233..1..45.....53.18 | autosolve |
| 487312695593684271126597384735849162914265837268731549851476923379128456642953718 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (31) A2: 5,9 C2: 3,9 E1: 1,2 F1: 1,2 E2: 4,8 F2: 4,8 D3: 5,7 F3: 5,7 G1: 5,6 I1: 5,6 B4: 3,4 A5: 6,9 A6: 2,8 C6: 2,8 D4: 8,9 F5: 5,7 D6: 5,7 F6: 1,4 H5: 3,4 I5: 5,7 G6: 5,7 H6: 3,4 A7: 5,8 B7: 4,5 B8: 6,7 C8: 8,9 D7: 4,8 E8: 2,8 D9: 4,9 I8: 6,7 G9: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,F1: 1.. / E1 = 1 => 28 pairs (_) / F1 = 1 => 0 pairs (X) B5,B6: 1.. / B5 = 1 => 31 pairs (_) / B6 = 1 => 0 pairs (X) B5,E5: 1.. / B5 = 1 => 31 pairs (_) / E5 = 1 => 0 pairs (X) F1,F6: 1.. / F1 = 1 => 0 pairs (X) / F6 = 1 => 28 pairs (_) E1,F1: 2.. / E1 = 2 => 0 pairs (X) / F1 = 2 => 28 pairs (_) A6,C6: 2.. / A6 = 2 => 0 pairs (*) / C6 = 2 => 0 pairs (X) A9,C9: 2.. / A9 = 2 => 0 pairs (X) / C9 = 2 => 0 pairs (_) E8,F8: 2.. / E8 = 2 => 28 pairs (_) / F8 = 2 => 0 pairs (X) A6,A9: 2.. / A6 = 2 => 0 pairs (*) / A9 = 2 => 0 pairs (X) C6,C9: 2.. / C6 = 2 => 0 pairs (X) / C9 = 2 => 0 pairs (_) E1,E8: 2.. / E1 = 2 => 0 pairs (X) / E8 = 2 => 28 pairs (_) F1,F8: 2.. / F1 = 2 => 28 pairs (_) / F8 = 2 => 0 pairs (X) B2,C2: 3.. / B2 = 3 => 0 pairs (X) / C2 = 3 => 32 pairs (_) H5,H6: 3.. / H5 = 3 => 30 pairs (_) / H6 = 3 => 0 pairs (X) B4,E4: 3.. / B4 = 3 => 32 pairs (_) / E4 = 3 => 0 pairs (X) C2,C5: 3.. / C2 = 3 => 32 pairs (_) / C5 = 3 => 0 pairs (X) E2,F2: 4.. / E2 = 4 => 32 pairs (_) / F2 = 4 => 28 pairs (_) H5,H6: 4.. / H5 = 4 => 0 pairs (X) / H6 = 4 => 30 pairs (_) D7,D9: 4.. / D7 = 4 => 0 pairs (*) / D9 = 4 => 0 pairs (X) B7,D7: 4.. / B7 = 4 => 0 pairs (X) / D7 = 4 => 0 pairs (_) C5,C9: 4.. / C5 = 4 => 0 pairs (*) / C9 = 4 => 0 pairs (X) A2,B2: 5.. / A2 = 5 => 0 pairs (*) / B2 = 5 => 0 pairs (X) D3,F3: 5.. / D3 = 5 => 20 pairs (_) / F3 = 5 => 20 pairs (_) G1,I1: 5.. / G1 = 5 => 20 pairs (_) / I1 = 5 => 20 pairs (_) F5,D6: 5.. / F5 = 5 => 20 pairs (_) / D6 = 5 => 20 pairs (_) I5,G6: 5.. / I5 = 5 => 20 pairs (_) / G6 = 5 => 20 pairs (_) A7,B7: 5.. / A7 = 5 => 0 pairs (X) / B7 = 5 => 0 pairs (_) F5,I5: 5.. / F5 = 5 => 20 pairs (_) / I5 = 5 => 20 pairs (_) D6,G6: 5.. / D6 = 5 => 20 pairs (_) / G6 = 5 => 20 pairs (_) A2,A7: 5.. / A2 = 5 => 0 pairs (*) / A7 = 5 => 0 pairs (X) B2,B7: 5.. / B2 = 5 => 0 pairs (X) / B7 = 5 => 0 pairs (_) D3,D6: 5.. / D3 = 5 => 20 pairs (_) / D6 = 5 => 20 pairs (_) F3,F5: 5.. / F3 = 5 => 20 pairs (_) / F5 = 5 => 20 pairs (_) G1,G6: 5.. / G1 = 5 => 20 pairs (_) / G6 = 5 => 20 pairs (_) I1,I5: 5.. / I1 = 5 => 20 pairs (_) / I5 = 5 => 20 pairs (_) G1,I1: 6.. / G1 = 6 => 20 pairs (_) / I1 = 6 => 20 pairs (_) E5,E6: 6.. / E5 = 6 => 0 pairs (*) / E6 = 6 => 0 pairs (X) I8,G9: 6.. / I8 = 6 => 20 pairs (_) / G9 = 6 => 20 pairs (_) B6,E6: 6.. / B6 = 6 => 0 pairs (*) / E6 = 6 => 0 pairs (X) B8,I8: 6.. / B8 = 6 => 20 pairs (_) / I8 = 6 => 20 pairs (_) A5,A9: 6.. / A5 = 6 => 32 pairs (_) / A9 = 6 => 0 pairs (*) G1,G9: 6.. / G1 = 6 => 20 pairs (_) / G9 = 6 => 20 pairs (_) I1,I8: 6.. / I1 = 6 => 20 pairs (_) / I8 = 6 => 20 pairs (_) D3,F3: 7.. / D3 = 7 => 20 pairs (_) / F3 = 7 => 20 pairs (_) F5,D6: 7.. / F5 = 7 => 20 pairs (_) / D6 = 7 => 20 pairs (_) I5,G6: 7.. / I5 = 7 => 20 pairs (_) / G6 = 7 => 20 pairs (_) B8,B9: 7.. / B8 = 7 => 20 pairs (_) / B9 = 7 => 20 pairs (_) I8,G9: 7.. / I8 = 7 => 20 pairs (_) / G9 = 7 => 20 pairs (_) F5,I5: 7.. / F5 = 7 => 20 pairs (_) / I5 = 7 => 20 pairs (_) D6,G6: 7.. / D6 = 7 => 20 pairs (_) / G6 = 7 => 20 pairs (_) B8,I8: 7.. / B8 = 7 => 20 pairs (_) / I8 = 7 => 20 pairs (_) B9,G9: 7.. / B9 = 7 => 20 pairs (_) / G9 = 7 => 20 pairs (_) D3,D6: 7.. / D3 = 7 => 20 pairs (_) / D6 = 7 => 20 pairs (_) F3,F5: 7.. / F3 = 7 => 20 pairs (_) / F5 = 7 => 20 pairs (_) G6,G9: 7.. / G6 = 7 => 20 pairs (_) / G9 = 7 => 20 pairs (_) I5,I8: 7.. / I5 = 7 => 20 pairs (_) / I8 = 7 => 20 pairs (_) E2,F2: 8.. / E2 = 8 => 28 pairs (_) / F2 = 8 => 32 pairs (_) A6,C6: 8.. / A6 = 8 => 0 pairs (X) / C6 = 8 => 0 pairs (_) A7,C8: 8.. / A7 = 8 => 0 pairs (*) / C8 = 8 => 0 pairs (X) A7,D7: 8.. / A7 = 8 => 0 pairs (*) / D7 = 8 => 0 pairs (X) A6,A7: 8.. / A6 = 8 => 0 pairs (X) / A7 = 8 => 0 pairs (_) C6,C8: 8.. / C6 = 8 => 0 pairs (*) / C8 = 8 => 0 pairs (X) D4,D7: 8.. / D4 = 8 => 0 pairs (*) / D7 = 8 => 0 pairs (X) D4,F4: 9.. / D4 = 9 => 0 pairs (X) / F4 = 9 => 0 pairs (_) F8,D9: 9.. / F8 = 9 => 0 pairs (X) / D9 = 9 => 0 pairs (_) C8,F8: 9.. / C8 = 9 => 0 pairs (*) / F8 = 9 => 0 pairs (X) D4,D9: 9.. / D4 = 9 => 0 pairs (X) / D9 = 9 => 0 pairs (_) F4,F8: 9.. / F4 = 9 => 0 pairs (*) / F8 = 9 => 0 pairs (X) * DURATION: 0:03:12.780410 START: 22:48:10.158188 END: 22:51:22.938598 2017-05-03 * CP COUNT: (68) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,A6,A7,B4,B7,B8,C2,C6,C8,D3,D4,D6,D7,D9,E1,E2,E8,F1,F2,F3,F5,F6,G1,G6,G9,H5,H6,I1,I5,I8) * 4873...9....6..271126.9.3847.5...162...2..8..........9..1.769233..1..45.....53.18 * PAIR A2: 5,9 BLK 1 B2: 5,9,3 # reduction candidate for 5,9 B2: 3 => CTR * 4873...9.5396..271126.9.384745.3.162..32..84........398.1.769233..1..45.....53.18 B2: 5,9 # 32 pairs * PAIR C2: 3,9 BLK 1 B2: 3,9,5 # reduction candidate for 3,9 B2: 3,9 => SOLVED * 487312695593684271126597384735849162914265837268731549851476923379128456642953718 B2: 5 => CTR * 487312.9.9536..271126.9.3847359..16261.2..8..........95418769233.812945....453.18 * PAIR C2: 3,9 COL C C5: 3,9,4 # reduction candidate for 3,9 C5: 3,9 => CTR * 4873...9....6..271126.9.3847.58.9162...2..8....2.....98.1.769233..1..45...4953.18 C5: 4 => SOLVED * 487312695593684271126597384735849162914265837268731549851476923379128456642953718 * PAIR E2: 4,8 COL E E4: 4,8,3 # reduction candidate for 4,8 E4: 3 => CTR * 4873...9.5..6..271126.9.3847458391629.32..84...2....398514769233..1..45...4953.18 E4: 4,8 # 32 pairs * PAIR F2: 4,8 COL F F4: 4,8,9 # reduction candidate for 4,8 F4: 4,8 => CTR * 487312.9....6..271126.9.3847.59..162.142..83.8.2..1.495418769233.812945.2.9453.18 F4: 9 => SOLVED * 487312695593684271126597384735849162914265837268731549851476923379128456642953718 * PAIR B4: 3,4 BLK 4 B5: 3,4,1,6,9 # reduction candidate for 3,4 B5: 3,4 => CTR * 487321.9....648271126.9.384745.3916263921.84..1..64.39.514769233.81..45.....53.18 B5: 1,6,9 # 31 pairs C5: 3,4,9 # reduction candidate for 3,4 C5: 3,4 # 34 pairs B6: 3,4,1,6 # reduction candidate for 3,4 B6: 3,4 => CTR * 487312.9....6..271126.9.3847.5...1626192..8......61..9..1.769233.812945...4.53.18 B6: 1,6 # 32 pairs * PAIR B4: 3,4 ROW 4 E4: 3,4,8 # reduction candidate for 3,4 E4: 8 => CTR * 487312.9...3648271126.9.384735984162.142..83.862.31.495.18769233.812945....453.18 E4: 3,4 # 33 pairs * PAIR A5: 6,9 BLK 4 B5: 6,9,1,3,4 # reduction candidate for 6,9 B5: 6,9 => CTR * 487321.9....648271126.9.384745.39162..321.84..1..64.39.514769233.91..45.....53.18 B5: 1,3,4 # 31 pairs * PAIR A5: 6,9 COL A A9: 6,9,2 # reduction candidate for 6,9 A9: 6,9 => SOLVED * 487312695593684271126597384735849162914265837268731549851476923379128456642953718 A9: 2 => CTR * 487312.9.9536..271126.9.384735...1626..2..8..8.2.6...95418769233.812945.2.9453.18 * PAIR D4: 8,9 BLK 5 F4: 8,9,4 # reduction candidate for 8,9 F4: 4 => CTR * 487312.9....648271126.9.384735984162.142..83.862.31.495.18769233.812945....453.18 F4: 8,9 # 33 pairs * PAIR F6: 1,4 BLK 5 E5: 1,4,3,6 # reduction candidate for 1,4 E5: 1,4 => CTR * 4873...9.5..6..271126.9.38474583916296321.84..1..6...9.514769233..1..45...4953.18 E5: 3,6 # 32 pairs E6: 1,4,3,6 # reduction candidate for 1,4 E6: 1,4 => CTR * 4873..695...6..271126.9.3847.5.3.16291.26.8...6.....39..1.7692337.1..4566.2.53718 E6: 3,6 # 32 pairs * PAIR F6: 1,4 ROW 6 B6: 1,4,3,6 # reduction candidate for 1,4 B6: 1,4 => CTR * 4873...9....6..271126.9.3847.58.9162...2..84...2.6..398.1.769233..1..45...4953.18 B6: 3,6 # 32 pairs * PAIR H5: 3,4 ROW 5 B5: 3,4,1,6,9 # reduction candidate for 3,4 B5: 3,4 => CTR * 487321.9....648271126.9.384745.3916263921.84..1..64.39.514769233.81..45.....53.18 B5: 1,6,9 # 31 pairs C5: 3,4,9 # reduction candidate for 3,4 C5: 3,4 # 34 pairs E5: 3,4,1,6 # reduction candidate for 3,4 E5: 3,4 => CTR * 487312.9....6..271126.9.3847.5...1626192..8......61..9..1.769233.812945...4.53.18 E5: 1,6 # 32 pairs * PAIR H6: 3,4 ROW 6 B6: 3,4,1,6 # reduction candidate for 3,4 B6: 3,4 => CTR * 487312.9....6..271126.9.3847.5...1626192..8......61..9..1.769233.812945...4.53.18 B6: 1,6 # 32 pairs E6: 3,4,1,6 # reduction candidate for 3,4 E6: 3,4 => SOLVED * 487312695593684271126597384735849162914265837268731549851476923379128456642953718 E6: 1,6 # 32 pairs * PAIR B8: 6,7 BLK 7 B9: 6,7,4,9 # reduction candidate for 6,7 B9: 4,9 => SOLVED * 487312695593684271126597384735849162914265837268731549851476923379128456642953718 B9: 6,7 # 32 pairs * PAIR C8: 8,9 ROW 8 F8: 8,9,2 # reduction candidate for 8,9 F8: 2 => CTR * 487321.9...3648271126.9.384745..9162...2..8..........9..1.769233.918245....953.18 F8: 8,9 # 28 pairs * PAIR E8: 2,8 BLK 8 F8: 2,8,9 # reduction candidate for 2,8 F8: 2,8 => SOLVED * 487312695593684271126597384735849162914265837268731549851476923379128456642953718 F8: 9 => CTR * 487312.9..536..271126.9.3847359..1629142..83......1.49.418769233.812945....453.18 * PAIR D9: 4,9 ROW 9 B9: 4,9,6,7 # reduction candidate for 4,9 B9: 4,9 => SOLVED * 487312695593684271126597384735849162914265837268731549851476923379128456642953718 B9: 6,7 # 32 pairs C9: 4,9,2 # reduction candidate for 4,9 C9: 4,9 => CTR * 487312.9....6..271126.9.3847.59..16261.2..8....2.....9..1.769233.812945.2..453.18 C9: 2 => SOLVED * 487312695593684271126597384735849162914265837268731549851476923379128456642953718 * PAIR G9: 6,7 ROW 9 B9: 6,7,4,9 # reduction candidate for 6,7 B9: 4,9 => SOLVED * 487312695593684271126597384735849162914265837268731549851476923379128456642953718 B9: 6,7 # 32 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-004-base-pr-000.dot * REASONING * DIS # B2: 3 => CTR => B2: 5,9 * PRF # B2: 3,9 => SOL * DIS # B2: 5 => CTR => B2: 3,9 * DIS # C5: 3,9 => CTR => C5: 4 * PRF # C5: 4 => SOL * DIS # E4: 3 => CTR => E4: 4,8 * DIS # F4: 4,8 => CTR => F4: 9 * PRF # F4: 9 => SOL * DIS # B5: 3,4 => CTR => B5: 1,6,9 * DIS # B6: 3,4 => CTR => B6: 1,6 * DIS # E4: 8 => CTR => E4: 3,4 * DIS # B5: 6,9 => CTR => B5: 1,3,4 * PRF # A9: 6,9 => SOL * DIS # A9: 2 => CTR => A9: 6,9 * DIS # F4: 4 => CTR => F4: 8,9 * DIS # E5: 1,4 => CTR => E5: 3,6 * DIS # E6: 1,4 => CTR => E6: 3,6 * DIS # B6: 1,4 => CTR => B6: 3,6 * DIS # B5: 3,4 => CTR => B5: 1,6,9 * DIS # E5: 3,4 => CTR => E5: 1,6 * DIS # B6: 3,4 => CTR => B6: 1,6 * PRF # E6: 3,4 => SOL * PRF # B9: 4,9 => SOL * DIS # F8: 2 => CTR => F8: 8,9 * PRF # F8: 2,8 => SOL * DIS # F8: 9 => CTR => F8: 2,8 * PRF # B9: 4,9 => SOL * DIS # C9: 4,9 => CTR => C9: 2 * PRF # C9: 2 => SOL * PRF # B9: 4,9 => SOL * CNT 30 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,A6,A7,B4,B7,B8,C2,C6,C8,D3,D4,D6,D7,D9,E1,E2,E8,F1,F2,F3,F5,F6,G1,G6,G9,H5,H6,I1,I5,I8) * 4873...9....6..271126.9.3847.5...162...2..8..........9..1.769233..1..45.....53.18 * PAIR A2: 5,9 BLK 1 B2: 5,9,3 # reduction candidate for 5,9 B2: 3 => CTR * 4873...9.5396..271126.9.384745.3.162..32..84........398.1.769233..1..45.....53.18 * PAIR E2: 4,8 COL E E4: 4,8,3 # reduction candidate for 4,8 E4: 3 => CTR * 4873...9...36..271126.9.384745.3.162..92..8..........9.514769233.81..45.....53.18 * PAIR RESTART * PAIR F2: 4,8 COL F F4: 4,8,9 # reduction candidate for 4,8 F4: 4,8 => CTR * 487312.9...36..271126.9.3847359..162.142..83.862.31.495.18769233.812945....453.18 F4: 9 => SOLVED * 487312695593684271126597384735849162914265837268731549851476923379128456642953718 * DURATION: 0:00:11.038861 START: 22:52:44.262451 END: 22:52:55.301312 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-004-base-pr-001.dot * REASONING * DIS # B2: 3 => CTR => B2: 5,9 * DIS B2: 5,9 # E4: 3 => CTR => E4: 4,8 * DIS B2: 5,9 + E4: 4,8 # F4: 4,8 => CTR => F4: 9 * PRF B2: 5,9 + E4: 4,8 + F4: 9 => SOL * STA B2: 5,9 + E4: 4,8 + F4: 9 * CNT 4 HDP CHAINS / 5 HYP OPENED
Header Info
Top 95 Sudokus 004 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 487312695593684271126597384735849162914265837268731549851476923379128456642953718 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: 5,9 => UNS * DIS # B2: 3 => CTR => B2: 5,9 * PRF # B2: 3,9 => SOL * DIS # B2: 5 => CTR => B2: 3,9 * DIS # C5: 3,9 => CTR => C5: 4 * PRF # C5: 4 => SOL * INC # E4: 4,8 => UNS * DIS # E4: 3 => CTR => E4: 4,8 * DIS # F4: 4,8 => CTR => F4: 9 * PRF # F4: 9 => SOL * DIS # B5: 3,4 => CTR => B5: 1,6,9 * INC # B5: 1,6,9 => UNS * INC # C5: 3,4 => UNS * DIS # B6: 3,4 => CTR => B6: 1,6 * INC # B6: 1,6 => UNS * INC # E4: 3,4 => UNS * DIS # E4: 8 => CTR => E4: 3,4 * DIS # B5: 6,9 => CTR => B5: 1,3,4 * INC # B5: 1,3,4 => UNS * PRF # A9: 6,9 => SOL * DIS # A9: 2 => CTR => A9: 6,9 * INC # F4: 8,9 => UNS * DIS # F4: 4 => CTR => F4: 8,9 * DIS # E5: 1,4 => CTR => E5: 3,6 * INC # E5: 3,6 => UNS * DIS # E6: 1,4 => CTR => E6: 3,6 * INC # E6: 3,6 => UNS * DIS # B6: 1,4 => CTR => B6: 3,6 * INC # B6: 3,6 => UNS * DIS # B5: 3,4 => CTR => B5: 1,6,9 * INC # B5: 1,6,9 => UNS * INC # C5: 3,4 => UNS * DIS # E5: 3,4 => CTR => E5: 1,6 * INC # E5: 1,6 => UNS * DIS # B6: 3,4 => CTR => B6: 1,6 * INC # B6: 1,6 => UNS * PRF # E6: 3,4 => SOL * INC # E6: 1,6 => UNS * INC # B9: 6,7 => UNS * PRF # B9: 4,9 => SOL * INC # F8: 8,9 => UNS * DIS # F8: 2 => CTR => F8: 8,9 * PRF # F8: 2,8 => SOL * DIS # F8: 9 => CTR => F8: 2,8 * PRF # B9: 4,9 => SOL * INC # B9: 6,7 => UNS * DIS # C9: 4,9 => CTR => C9: 2 * PRF # C9: 2 => SOL * INC # B9: 6,7 => UNS * PRF # B9: 4,9 => SOL * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 5,9 => UNS * DIS # B2: 3 => CTR => B2: 5,9 * INC B2: 5,9 # E4: 4,8 => UNS * DIS B2: 5,9 # E4: 3 => CTR => E4: 4,8 * DIS B2: 5,9 + E4: 4,8 # F4: 4,8 => CTR => F4: 9 * PRF B2: 5,9 + E4: 4,8 + F4: 9 => SOL * STA B2: 5,9 + E4: 4,8 + F4: 9 * CNT 6 HDP CHAINS / 5 HYP OPENED