Analysis of zz-www.sudokuoftheday.co.uk-20060818-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: .71.....2..8..9.5....2....6..7.8...4.2.........5..3.9....3.657.....9.84..3..7.... initial
Autosolve
position: .71....322.8.39.57...2.7.86..7.8...482......5..5.23.98.823.657.7.6.92843.3..7.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D2: 1 => CTR => D2: 4,6 * DIS # B6: 1 => CTR => B6: 4,6 * DIS # F9: 4,8 => CTR => F9: 1,5 * DIS # G3: 1 => CTR => G3: 4,9 * DIS # G3: 9 => CTR => G3: 1,4 * DIS # A4: 3,9 => CTR => A4: 1,6 * PRF # A4: 1,6 => SOL * DIS # C3: 4 => CTR => C3: 3,9 * PRF # D4: 1,5 => SOL * DIS # F9: 4,8 => CTR => F9: 1,5 * DIS # E5: 1,4 => CTR => E5: 6 * PRF # F9: 1,4 => SOL * DIS # H4: 1,6 => CTR => H4: 2 * DIS # E5: 4 => CTR => E5: 1,6 * DIS # D6: 1 => CTR => D6: 6,7 * DIS # A9: 4,9 => CTR => A9: 1,5 * DIS # A9: 4,9 => CTR => A9: 1,5 * PRF # C3: 4,9 => SOL * DIS # C3: 3 => CTR => C3: 4,9 * DIS # D9: 1,4 => CTR => D9: 5,8 * PRF # F9: 1,4 => SOL * DIS # E5: 1,4 => CTR => E5: 6 * DIS # D9: 1,5 => CTR => D9: 4,8 * PRF # D4: 1,5 => SOL * DIS # A7: 4 => CTR => A7: 1,9 * DIS # G4: 2,6 => CTR => G4: 3 * PRF # G4: 3 => SOL * DIS # H4: 1 => CTR => H4: 2,6 * DIS # A9: 1,9 => CTR => A9: 4,5 * CNT 29 HDP CHAINS / 65 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D2: 1 => CTR => D2: 4,6 * DIS D2: 4,6 # B6: 1 => CTR => B6: 4,6 * DIS D2: 4,6 + B6: 4,6 # A1: 9 => CTR => A1: 4,6 * PRF D2: 4,6 + B6: 4,6 + A1: 4,6 # D4: 1,5 => SOL * STA D2: 4,6 + B6: 4,6 + A1: 4,6 + D4: 1,5 * CNT 4 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .71.....2..8..9.5....2....6..7.8...4.2.........5..3.9....3.657.....9.84..3..7.... | initial |
| .71....322.8.39.57...2.7.86..7.8...482......5..5.23.98.823.657.7.6.92843.3..7.... | autosolve |
| 471658932268439157359217486697185324823964715145723698982346571716592843534871269 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) B2: 4,6 F1: 4,8 G1: 4,9 G2: 1,4 C5: 3,9 F4: 1,5 D5: 7,9 F5: 1,4 G5: 3,7 H5: 1,6 G6: 6,7 B8: 1,5 C9: 4,9 E7: 1,4 D8: 1,5 I7: 1,9 G9: 2,6 H9: 2,6 I9: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,E3: 1.. / D2 = 1 => 0 pairs (X) / E3 = 1 => 21 pairs (_) G2,G3: 1.. / G2 = 1 => 21 pairs (_) / G3 = 1 => 0 pairs (X) H4,H5: 1.. / H4 = 1 => 0 pairs (X) / H5 = 1 => 21 pairs (_) I7,I9: 1.. / I7 = 1 => 20 pairs (_) / I9 = 1 => 27 pairs (_) D2,G2: 1.. / D2 = 1 => 0 pairs (X) / G2 = 1 => 21 pairs (_) E3,G3: 1.. / E3 = 1 => 21 pairs (_) / G3 = 1 => 0 pairs (X) B8,D8: 1.. / B8 = 1 => 0 pairs (*) / D8 = 1 => 0 pairs (X) G4,H4: 2.. / G4 = 2 => 0 pairs (X) / H4 = 2 => 19 pairs (_) G9,H9: 2.. / G9 = 2 => 19 pairs (_) / H9 = 2 => 0 pairs (X) G4,G9: 2.. / G4 = 2 => 0 pairs (X) / G9 = 2 => 19 pairs (_) H4,H9: 2.. / H4 = 2 => 19 pairs (_) / H9 = 2 => 0 pairs (X) A3,C3: 3.. / A3 = 3 => 0 pairs (*) / C3 = 3 => 0 pairs (X) A4,C5: 3.. / A4 = 3 => 0 pairs (X) / C5 = 3 => 0 pairs (_) G4,G5: 3.. / G4 = 3 => 0 pairs (*) / G5 = 3 => 0 pairs (X) A4,G4: 3.. / A4 = 3 => 0 pairs (X) / G4 = 3 => 0 pairs (_) C5,G5: 3.. / C5 = 3 => 0 pairs (*) / G5 = 3 => 0 pairs (X) A3,A4: 3.. / A3 = 3 => 0 pairs (*) / A4 = 3 => 0 pairs (X) C3,C5: 3.. / C3 = 3 => 0 pairs (X) / C5 = 3 => 0 pairs (_) A6,B6: 4.. / A6 = 4 => 25 pairs (_) / B6 = 4 => 22 pairs (_) E5,F5: 4.. / E5 = 4 => 0 pairs (X) / F5 = 4 => 22 pairs (_) A7,E7: 4.. / A7 = 4 => 0 pairs (X) / E7 = 4 => 22 pairs (_) C3,C9: 4.. / C3 = 4 => 0 pairs (X) / C9 = 4 => 22 pairs (_) E1,E3: 5.. / E1 = 5 => 21 pairs (_) / E3 = 5 => 0 pairs (X) D4,F4: 5.. / D4 = 5 => 0 pairs (X) / F4 = 5 => 18 pairs (_) B8,A9: 5.. / B8 = 5 => 0 pairs (X) / A9 = 5 => 0 pairs (_) A1,E1: 5.. / A1 = 5 => 0 pairs (X) / E1 = 5 => 21 pairs (_) B8,D8: 5.. / B8 = 5 => 0 pairs (X) / D8 = 5 => 0 pairs (_) B3,B8: 5.. / B3 = 5 => 0 pairs (*) / B8 = 5 => 0 pairs (X) F4,F9: 5.. / F4 = 5 => 18 pairs (_) / F9 = 5 => 0 pairs (X) A1,B2: 6.. / A1 = 6 => 20 pairs (_) / B2 = 6 => 21 pairs (_) G9,H9: 6.. / G9 = 6 => 0 pairs (X) / H9 = 6 => 19 pairs (_) B2,D2: 6.. / B2 = 6 => 21 pairs (_) / D2 = 6 => 20 pairs (_) E5,H5: 6.. / E5 = 6 => 21 pairs (_) / H5 = 6 => 0 pairs (X) E1,E5: 6.. / E1 = 6 => 0 pairs (X) / E5 = 6 => 21 pairs (_) D5,D6: 7.. / D5 = 7 => 0 pairs (X) / D6 = 7 => 0 pairs (_) G5,G6: 7.. / G5 = 7 => 0 pairs (*) / G6 = 7 => 0 pairs (X) D5,G5: 7.. / D5 = 7 => 0 pairs (X) / G5 = 7 => 0 pairs (_) D6,G6: 7.. / D6 = 7 => 0 pairs (*) / G6 = 7 => 0 pairs (X) D1,F1: 8.. / D1 = 8 => 0 pairs (X) / F1 = 8 => 21 pairs (_) D9,F9: 8.. / D9 = 8 => 21 pairs (_) / F9 = 8 => 0 pairs (X) D1,D9: 8.. / D1 = 8 => 0 pairs (X) / D9 = 8 => 21 pairs (_) F1,F9: 8.. / F1 = 8 => 21 pairs (_) / F9 = 8 => 0 pairs (X) G1,G3: 9.. / G1 = 9 => 19 pairs (_) / G3 = 9 => 0 pairs (X) D4,D5: 9.. / D4 = 9 => 0 pairs (X) / D5 = 9 => 0 pairs (_) I7,I9: 9.. / I7 = 9 => 27 pairs (_) / I9 = 9 => 20 pairs (_) A1,G1: 9.. / A1 = 9 => 0 pairs (X) / G1 = 9 => 19 pairs (_) C5,D5: 9.. / C5 = 9 => 0 pairs (X) / D5 = 9 => 0 pairs (_) A7,I7: 9.. / A7 = 9 => 20 pairs (_) / I7 = 9 => 27 pairs (_) B3,B4: 9.. / B3 = 9 => 0 pairs (X) / B4 = 9 => 0 pairs (_) * DURATION: 0:01:07.879550 START: 01:52:10.675904 END: 01:53:18.555454 2019-05-01 * CP COUNT: (49) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B8,C5,C9,D5,D8,E7,F1,F4,F5,G1,G2,G5,G6,G9,H5,H9,I7,I9) * .71....322.8.39.57...2.7.86..7.8...482......5..5.23.98.823.657.7.6.92843.3..7.... * PAIR B2: 4,6 BLK 1 A1: 4,6,5,9 # reduction candidate for 4,6 A1: 5,9 # 24 pairs A1: 4,6 # 22 pairs * PAIR B2: 4,6 ROW 2 D2: 4,6,1 # reduction candidate for 4,6 D2: 1 => CTR * .71.5.932268139457.5.247186.97685..4823.....5..5.23.98.823.657.71659284353..7.... D2: 4,6 # 21 pairs * PAIR B2: 4,6 COL B B6: 4,6,1 # reduction candidate for 4,6 B6: 1 => CTR * .71.58.322.8.391575.3217.863.7.8...482..64.15415723698.8234657.756192843.34.7.26. B6: 4,6 # 22 pairs * PAIR F1: 4,8 BLK 2 D1: 4,8,6 # reduction candidate for 4,8 D1: 4,8 # 25 pairs D1: 6 # 22 pairs * PAIR F1: 4,8 COL F F9: 4,8,1,5 # reduction candidate for 4,8 F9: 4,8 => CTR * .71.6..32268.39.57...257186..7.8521482.741365..56237984823.657.7.6.92843.3..7.62. F9: 1,5 # 22 pairs * PAIR G1: 4,9 BLK 3 G3: 4,9,1 # reduction candidate for 4,9 G3: 1 => CTR * 471.58932268139457.5.247186.9768...482......5..5.23.98.823.657.71659284353..7.... G3: 4,9 # 21 pairs * PAIR G1: 4,9 ROW 1 A1: 4,9,5,6 # reduction candidate for 4,9 A1: 5,6 # 25 pairs A1: 4,9 # 22 pairs * PAIR G2: 1,4 BLK 3 G3: 1,4,9 # reduction candidate for 1,4 G3: 9 => CTR * 971.5.432268439157354217986697.8...48239..7.5..5723698.8234657.7.6.92843.39.7.261 G3: 1,4 # 19 pairs * PAIR G2: 1,4 ROW 2 D2: 1,4,6 # reduction candidate for 1,4 D2: 1,4 # 21 pairs D2: 6 # 20 pairs * PAIR C5: 3,9 BLK 4 A4: 3,9,1,6 # reduction candidate for 3,9 A4: 3,9 => CTR * .71.5.9322.8.391575932174863.7985..4829.....5..5.23.98.8234657.756192843.34.7.... A4: 1,6 => SOLVED * 471658932268439157359217486697185324823964715145723698982346571716592843534871269 * PAIR C5: 3,9 COL C C3: 3,9,4 # reduction candidate for 3,9 C3: 4 => CTR * .71....32268.39.573.42.7.86697.81324823964715145723698482316579716592843.39.7.261 C3: 3,9 # 22 pairs * PAIR F4: 1,5 BLK 5 D4: 1,5,6,9 # reduction candidate for 1,5 D4: 1,5 => SOLVED * 471658932268439157359217486697185324823964715145723698982346571716592843534871269 D4: 6,9 # 19 pairs * PAIR F4: 1,5 COL F F9: 1,5,4,8 # reduction candidate for 1,5 F9: 4,8 => CTR * .71.6..32268.39.57...257186..7.8521482.741365..56237984823.657.7.6.92843.3..7.62. F9: 1,5 # 22 pairs * PAIR F5: 1,4 BLK 5 E5: 1,4,6 # reduction candidate for 1,4 E5: 1,4 => CTR * .71.6..32268.39.57...257186..7.8...482.....65..5.23798.823.657.756192843.3..7.62. E5: 6 # 21 pairs * PAIR F5: 1,4 COL F F9: 1,4,5,8 # reduction candidate for 1,4 F9: 1,4 => SOLVED * 471658932268439157359217486697185324823964715145723698982346571716592843534871269 F9: 5,8 # 28 pairs * PAIR H5: 1,6 BLK 6 H4: 1,6,2 # reduction candidate for 1,6 H4: 1,6 => CTR * .71....322.8.39.57.932.7.863.79852.48297..3.5..5.23798.8234657.756192843.3457862. H4: 2 # 19 pairs * PAIR H5: 1,6 ROW 5 E5: 1,6,4 # reduction candidate for 1,6 E5: 4 => CTR * .71.6..32268.39.57...257186..7.8...482..41.65..5.237984823165797.6.92843.3..7.... E5: 1,6 # 22 pairs * PAIR G6: 6,7 ROW 6 D6: 6,7,1 # reduction candidate for 6,7 D6: 1 => CTR * .71....322.8.39.57...2.7.86..7.8...482.7..3.5..5123798.823.657.71659284353..7.... D6: 6,7 # 25 pairs * PAIR B8: 1,5 BLK 7 A9: 1,5,4,9 # reduction candidate for 1,5 A9: 4,9 => CTR * .71.5..322.8.391575.3217.863.7.8...482976...5..5.23.98182346579756192843.3..7...1 A9: 1,5 # 21 pairs * PAIR C9: 4,9 BLK 7 A7: 4,9,1 # reduction candidate for 4,9 A7: 4,9 # 21 pairs A9: 4,9,1,5 # reduction candidate for 4,9 A9: 4,9 => CTR * .71.5..322.8.391575.3217.863.7.8...482976...5..5.23.98182346579756192843.3..7...1 A9: 1,5 # 21 pairs * PAIR C9: 4,9 COL C C3: 4,9,3 # reduction candidate for 4,9 C3: 4,9 => SOLVED * 471658932268439157359217486697185324823964715145723698982346571716592843534871269 C3: 3 => CTR * .71....322.8.39.57.932.7.863.7985..48297..3.5..5.23798.8234657.756192843.34578... * PAIR E7: 1,4 BLK 8 D9: 1,4,5,8 # reduction candidate for 1,4 D9: 1,4 => CTR * .718.49322.8.39.57...2.7.86..7.8...482..41.65..5.2379848231657971659284353947.... D9: 5,8 # 21 pairs F9: 1,4,5,8 # reduction candidate for 1,4 F9: 1,4 => SOLVED * 471658932268439157359217486697185324823964715145723698982346571716592843534871269 F9: 5,8 # 28 pairs * PAIR E7: 1,4 ROW 7 A7: 1,4,9 # reduction candidate for 1,4 A7: 1,4 # 27 pairs A7: 9 # 20 pairs * PAIR E7: 1,4 COL E E3: 1,4,5 # reduction candidate for 1,4 E3: 1,4 # 21 pairs E5: 1,4,6 # reduction candidate for 1,4 E5: 1,4 => CTR * .71.6..32268.39.57...257186..7.8...482.....65..5.23798.823.657.756192843.3..7.62. E5: 6 # 21 pairs * PAIR D8: 1,5 BLK 8 D9: 1,5,4,8 # reduction candidate for 1,5 D9: 1,5 => CTR * .718.49322.8.39.57...2.7.86..7.8...482..41.65..5.23798482316579716592843.3..7.... D9: 4,8 # 20 pairs F9: 1,5,4,8 # reduction candidate for 1,5 F9: 1,5 # 22 pairs * PAIR D8: 1,5 COL D D4: 1,5,6,9 # reduction candidate for 1,5 D4: 1,5 => SOLVED * 471658932268439157359217486697185324823964715145723698982346571716592843534871269 D4: 6,9 # 19 pairs * PAIR I7: 1,9 ROW 7 A7: 1,9,4 # reduction candidate for 1,9 A7: 4 => CTR * .71.5..322.8139457.542.7.86..7.8...482......5..5.23.98482316579716592843539.7...1 A7: 1,9 # 22 pairs * PAIR G9: 2,6 COL G G4: 2,6,3 # reduction candidate for 2,6 G4: 2,6 => CTR * .71....322.8.39.57.932.7.863.7985..48297..3.5..5.23798.8234657.756192843.34578... G4: 3 => SOLVED * 471658932268439157359217486697185324823964715145723698982346571716592843534871269 * PAIR H9: 2,6 COL H H4: 2,6,1 # reduction candidate for 2,6 H4: 1 => CTR * .71.6..32268.39.57..3257186397.8.21482....365..5.23798.823.657.7.6.92843.3..7.62. H4: 2,6 # 21 pairs * PAIR I9: 1,9 ROW 9 A9: 1,9,4,5 # reduction candidate for 1,9 A9: 1,9 => CTR * .71.5..322.8.391575.3217.863.7.8...482976...5..5.23.98.8234657.756192843.34.7.... A9: 4,5 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060818-absurd-base-pr-000.dot * REASONING * DIS # D2: 1 => CTR => D2: 4,6 * DIS # B6: 1 => CTR => B6: 4,6 * DIS # F9: 4,8 => CTR => F9: 1,5 * DIS # G3: 1 => CTR => G3: 4,9 * DIS # G3: 9 => CTR => G3: 1,4 * DIS # A4: 3,9 => CTR => A4: 1,6 * PRF # A4: 1,6 => SOL * DIS # C3: 4 => CTR => C3: 3,9 * PRF # D4: 1,5 => SOL * DIS # F9: 4,8 => CTR => F9: 1,5 * DIS # E5: 1,4 => CTR => E5: 6 * PRF # F9: 1,4 => SOL * DIS # H4: 1,6 => CTR => H4: 2 * DIS # E5: 4 => CTR => E5: 1,6 * DIS # D6: 1 => CTR => D6: 6,7 * DIS # A9: 4,9 => CTR => A9: 1,5 * DIS # A9: 4,9 => CTR => A9: 1,5 * PRF # C3: 4,9 => SOL * DIS # C3: 3 => CTR => C3: 4,9 * DIS # D9: 1,4 => CTR => D9: 5,8 * PRF # F9: 1,4 => SOL * DIS # E5: 1,4 => CTR => E5: 6 * DIS # D9: 1,5 => CTR => D9: 4,8 * PRF # D4: 1,5 => SOL * DIS # A7: 4 => CTR => A7: 1,9 * DIS # G4: 2,6 => CTR => G4: 3 * PRF # G4: 3 => SOL * DIS # H4: 1 => CTR => H4: 2,6 * DIS # A9: 1,9 => CTR => A9: 4,5 * CNT 29 HDP CHAINS / 65 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B8,C5,C9,D5,D8,E7,F1,F4,F5,G1,G2,G5,G6,G9,H5,H9,I7,I9) * .71....322.8.39.57...2.7.86..7.8...482......5..5.23.98.823.657.7.6.92843.3..7.... * PAIR B2: 4,6 BLK 1 A1: 4,6,5,9 # reduction candidate for 4,6 A1: 5,9 # 24 pairs A1: 4,6 # 22 pairs * PAIR B2: 4,6 ROW 2 D2: 4,6,1 # reduction candidate for 4,6 D2: 1 => CTR * .71.5.932268139457.5.247186.97685..4823.....5..5.23.98.823.657.71659284353..7.... * PAIR B2: 4,6 COL B B6: 4,6,1 # reduction candidate for 4,6 B6: 1 => CTR * .71.58.322.8.391575.3217.863.7.8...482..64.15415723698.8234657.756192843.3487526. * PAIR RESTART * PAIR B2: 4,6 BLK 1 A1: 4,6,9 # reduction candidate for 4,6 A1: 9 => CTR * 971658432268439157.5.217986.97.8...48239647151.5.23.98.8234657.7.6.92843.3.87.... * PAIR F4: 1,5 BLK 5 D4: 1,5,9 # reduction candidate for 1,5 D4: 1,5 => SOLVED * 471658932268439157359217486697185324823964715145723698982346571716592843534871269 * DURATION: 0:00:08.113070 START: 01:54:07.538617 END: 01:54:15.651687 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060818-absurd-base-pr-001.dot * REASONING * DIS # D2: 1 => CTR => D2: 4,6 * DIS D2: 4,6 # B6: 1 => CTR => B6: 4,6 * DIS D2: 4,6 + B6: 4,6 # A1: 9 => CTR => A1: 4,6 * PRF D2: 4,6 + B6: 4,6 + A1: 4,6 # D4: 1,5 => SOL * STA D2: 4,6 + B6: 4,6 + A1: 4,6 + D4: 1,5 * CNT 4 HDP CHAINS / 9 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060818, absurd
Solution
position: 471658932268439157359217486697185324823964715145723698982346571716592843534871269 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 # A1: 4,6 => UNS * INC # A1: 5,9 => UNS * INC # D2: 4,6 => UNS * DIS # D2: 1 => CTR => D2: 4,6 * INC # B6: 4,6 => UNS * DIS # B6: 1 => CTR => B6: 4,6 * INC # D1: 4,8 => UNS * INC # D1: 6 => UNS * DIS # F9: 4,8 => CTR => F9: 1,5 * INC # F9: 1,5 => UNS * INC # G3: 4,9 => UNS * DIS # G3: 1 => CTR => G3: 4,9 * INC # A1: 4,9 => UNS * INC # A1: 5,6 => UNS * INC # G3: 1,4 => UNS * DIS # G3: 9 => CTR => G3: 1,4 * INC # D2: 1,4 => UNS * INC # D2: 6 => UNS * DIS # A4: 3,9 => CTR => A4: 1,6 * PRF # A4: 1,6 => SOL * INC # C3: 3,9 => UNS * DIS # C3: 4 => CTR => C3: 3,9 * PRF # D4: 1,5 => SOL * INC # D4: 6,9 => UNS * INC # F9: 1,5 => UNS * DIS # F9: 4,8 => CTR => F9: 1,5 * DIS # E5: 1,4 => CTR => E5: 6 * INC # E5: 6 => UNS * PRF # F9: 1,4 => SOL * INC # F9: 5,8 => UNS * DIS # H4: 1,6 => CTR => H4: 2 * INC # H4: 2 => UNS * INC # E5: 1,6 => UNS * DIS # E5: 4 => CTR => E5: 1,6 * INC # D6: 6,7 => UNS * DIS # D6: 1 => CTR => D6: 6,7 * INC # A9: 1,5 => UNS * DIS # A9: 4,9 => CTR => A9: 1,5 * INC # A7: 4,9 => UNS * DIS # A9: 4,9 => CTR => A9: 1,5 * INC # A9: 1,5 => UNS * PRF # C3: 4,9 => SOL * DIS # C3: 3 => CTR => C3: 4,9 * DIS # D9: 1,4 => CTR => D9: 5,8 * INC # D9: 5,8 => UNS * PRF # F9: 1,4 => SOL * INC # F9: 5,8 => UNS * INC # A7: 1,4 => UNS * INC # A7: 9 => UNS * INC # E3: 1,4 => UNS * DIS # E5: 1,4 => CTR => E5: 6 * INC # E5: 6 => UNS * DIS # D9: 1,5 => CTR => D9: 4,8 * INC # D9: 4,8 => UNS * INC # F9: 1,5 => UNS * PRF # D4: 1,5 => SOL * INC # D4: 6,9 => UNS * INC # A7: 1,9 => UNS * DIS # A7: 4 => CTR => A7: 1,9 * DIS # G4: 2,6 => CTR => G4: 3 * PRF # G4: 3 => SOL * INC # H4: 2,6 => UNS * DIS # H4: 1 => CTR => H4: 2,6 * DIS # A9: 1,9 => CTR => A9: 4,5 * INC # A9: 4,5 => UNS * CNT 65 HDP CHAINS / 65 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 4,6 => UNS * INC # A1: 5,9 => UNS * INC # D2: 4,6 => UNS * DIS # D2: 1 => CTR => D2: 4,6 * INC D2: 4,6 # B6: 4,6 => UNS * DIS D2: 4,6 # B6: 1 => CTR => B6: 4,6 * INC D2: 4,6 + B6: 4,6 # A1: 4,6 => UNS * DIS D2: 4,6 + B6: 4,6 # A1: 9 => CTR => A1: 4,6 * PRF D2: 4,6 + B6: 4,6 + A1: 4,6 # D4: 1,5 => SOL * STA D2: 4,6 + B6: 4,6 + A1: 4,6 + D4: 1,5 * CNT 9 HDP CHAINS / 9 HYP OPENED