Analysis of zz-www.sudokuoftheday.co.uk-20190129-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019
level: medium
position: .......6...5..4.92.2..5..8..8...2..39....1.46..7..9..1...9....545..........71.... initial
Autosolve
position: ...29.567..5..4.92.29.57.84.8...29.39325.1.46..7..9..1...94...545..2...9.9.7154.8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 3,8 => CTR => C1: 1,4 * PRF # A2: 6,7 => SOL * DIS # A2: 3,8 => CTR => A2: 6,7 * DIS # A2: 3,6 => CTR => A2: 7,8 * DIS # D3: 1 => CTR => D3: 3,6 * DIS # A9: 3,6 => CTR => A9: 2 * DIS # D2: 3,8 => CTR => D2: 1,6 * PRF # E2: 3,8 => SOL * DIS # E2: 6 => CTR => E2: 3,8 * DIS # C1: 3,8 => CTR => C1: 1,4 * PRF # F7: 3,8 => SOL * DIS # F7: 6 => CTR => F7: 3,8 * DIS # F8: 3,8 => CTR => F8: 6 * PRF # F8: 6 => SOL * DIS # D2: 6,8 => CTR => D2: 1,3 * DIS # D3: 1,3 => CTR => D3: 6 * PRF # D3: 6 => SOL * PRF # A4: 5,6 => SOL * DIS # A4: 1 => CTR => A4: 5,6 * DIS # C4: 4,6 => CTR => C4: 1 * PRF # C4: 1 => SOL * DIS # D6: 4,6 => CTR => D6: 3,8 * PRF # D6: 3,8 => SOL * DIS # D6: 4,6 => CTR => D6: 3,8 * PRF # D6: 3,8 => SOL * DIS # C4: 4,6 => CTR => C4: 1 * PRF # C4: 1 => SOL * PRF # A7: 1,7 => SOL * DIS # A7: 2,3,8 => CTR => A7: 1,7 * DIS # A9: 3,6 => CTR => A9: 2 * PRF # F7: 3,8 => SOL * DIS # F7: 6 => CTR => F7: 3,8 * DIS # F8: 3,8 => CTR => F8: 6 * PRF # F8: 6 => SOL * PRF # C8: 3,8 => SOL * DIS # C8: 1 => CTR => C8: 3,8 * DIS # D2: 3,8 => CTR => D2: 1,6 * PRF # D6: 3,8 => SOL * DIS # D6: 4,6 => CTR => D6: 3,8 * PRF # H7: 2,3 => SOL * DIS # H7: 1 => CTR => H7: 2,3 * DIS # A9: 6 => CTR => A9: 2,3 * CNT 42 HDP CHAINS / 53 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 3,8 => CTR => C1: 1,4 * PRF C1: 1,4 # A2: 6,7 => SOL * STA C1: 1,4 + A2: 6,7 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .......6...5..4.92.2..5..8..8...2..39....1.46..7..9..1...9....545..........71.... | initial |
| ...29.567..5..4.92.29.57.84.8...29.39325.1.46..7..9..1...94...545..2...9.9.7154.8 | autosolve |
| 814293567765184392329657184581462973932571846647839251173948625458326719296715438 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (21) B1: 1,4 B2: 6,7 A3: 3,6 F1: 3,8 G2: 1,3 G3: 1,3 A6: 5,6 B6: 4,6 D4: 4,6 E4: 6,7 E5: 7,8 H4: 5,7 G5: 7,8 G6: 2,8 H6: 2,5 B7: 1,7 C9: 3,6 D8: 3,8 G7: 2,6 G8: 6,7 H9: 2,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,D3: 1.. / D2 = 1 => 21 pairs (_) / D3 = 1 => 0 pairs (X) G2,G3: 1.. / G2 = 1 => 0 pairs (X) / G3 = 1 => 21 pairs (_) A4,C4: 1.. / A4 = 1 => 0 pairs (X) / C4 = 1 => 0 pairs (_) H7,H8: 1.. / H7 = 1 => 0 pairs (X) / H8 = 1 => 0 pairs (_) D2,G2: 1.. / D2 = 1 => 21 pairs (_) / G2 = 1 => 0 pairs (X) D3,G3: 1.. / D3 = 1 => 0 pairs (X) / G3 = 1 => 21 pairs (_) C8,H8: 1.. / C8 = 1 => 0 pairs (X) / H8 = 1 => 0 pairs (_) B1,B7: 1.. / B1 = 1 => 0 pairs (*) / B7 = 1 => 0 pairs (X) G6,H6: 2.. / G6 = 2 => 0 pairs (*) / H6 = 2 => 0 pairs (X) A7,A9: 2.. / A7 = 2 => 0 pairs (X) / A9 = 2 => 22 pairs (_) A9,H9: 2.. / A9 = 2 => 22 pairs (_) / H9 = 2 => 0 pairs (X) G6,G7: 2.. / G6 = 2 => 0 pairs (*) / G7 = 2 => 0 pairs (X) G2,G3: 3.. / G2 = 3 => 21 pairs (_) / G3 = 3 => 0 pairs (X) D6,E6: 3.. / D6 = 3 => 0 pairs (X) / E6 = 3 => 22 pairs (_) E2,E6: 3.. / E2 = 3 => 0 pairs (X) / E6 = 3 => 22 pairs (_) B1,C1: 4.. / B1 = 4 => 0 pairs (X) / C1 = 4 => 0 pairs (_) C4,B6: 4.. / C4 = 4 => 0 pairs (X) / B6 = 4 => 0 pairs (_) D4,D6: 4.. / D4 = 4 => 0 pairs (*) / D6 = 4 => 0 pairs (X) C4,D4: 4.. / C4 = 4 => 0 pairs (X) / D4 = 4 => 0 pairs (_) B6,D6: 4.. / B6 = 4 => 0 pairs (*) / D6 = 4 => 0 pairs (X) B1,B6: 4.. / B1 = 4 => 0 pairs (X) / B6 = 4 => 0 pairs (_) C1,C4: 4.. / C1 = 4 => 0 pairs (*) / C4 = 4 => 0 pairs (X) A4,A6: 5.. / A4 = 5 => 0 pairs (*) / A6 = 5 => 0 pairs (X) H4,H6: 5.. / H4 = 5 => 0 pairs (X) / H6 = 5 => 0 pairs (_) A4,H4: 5.. / A4 = 5 => 0 pairs (*) / H4 = 5 => 0 pairs (X) A6,H6: 5.. / A6 = 5 => 0 pairs (X) / H6 = 5 => 0 pairs (_) A9,C9: 6.. / A9 = 6 => 0 pairs (X) / C9 = 6 => 22 pairs (_) F7,F8: 6.. / F7 = 6 => 0 pairs (X) / F8 = 6 => 0 pairs (_) G7,G8: 6.. / G7 = 6 => 0 pairs (*) / G8 = 6 => 0 pairs (X) A3,D3: 6.. / A3 = 6 => 0 pairs (X) / D3 = 6 => 0 pairs (_) F7,G7: 6.. / F7 = 6 => 0 pairs (X) / G7 = 6 => 0 pairs (_) F8,G8: 6.. / F8 = 6 => 0 pairs (*) / G8 = 6 => 0 pairs (X) B2,B6: 6.. / B2 = 6 => 0 pairs (*) / B6 = 6 => 0 pairs (X) C4,C9: 6.. / C4 = 6 => 0 pairs (X) / C9 = 6 => 22 pairs (_) A2,B2: 7.. / A2 = 7 => 0 pairs (*) / B2 = 7 => 0 pairs (X) E4,E5: 7.. / E4 = 7 => 0 pairs (X) / E5 = 7 => 0 pairs (_) H4,G5: 7.. / H4 = 7 => 0 pairs (*) / G5 = 7 => 0 pairs (X) A7,B7: 7.. / A7 = 7 => 0 pairs (X) / B7 = 7 => 0 pairs (_) G8,H8: 7.. / G8 = 7 => 0 pairs (*) / H8 = 7 => 0 pairs (X) E4,H4: 7.. / E4 = 7 => 0 pairs (X) / H4 = 7 => 0 pairs (_) E5,G5: 7.. / E5 = 7 => 0 pairs (*) / G5 = 7 => 0 pairs (X) A2,A7: 7.. / A2 = 7 => 0 pairs (*) / A7 = 7 => 0 pairs (X) B2,B7: 7.. / B2 = 7 => 0 pairs (X) / B7 = 7 => 0 pairs (_) G5,G8: 7.. / G5 = 7 => 0 pairs (X) / G8 = 7 => 0 pairs (_) H4,H8: 7.. / H4 = 7 => 0 pairs (*) / H8 = 7 => 0 pairs (X) G5,G6: 8.. / G5 = 8 => 0 pairs (*) / G6 = 8 => 0 pairs (X) E5,G5: 8.. / E5 = 8 => 0 pairs (X) / G5 = 8 => 0 pairs (_) * DURATION: 0:01:02.072677 START: 03:17:46.899481 END: 03:18:48.972158 2019-05-01 * CP COUNT: (47) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A6,B1,B2,B6,B7,C9,D4,D8,E4,E5,F1,G2,G3,G5,G6,G7,G8,H4,H6,H9) * ...29.567..5..4.92.29.57.84.8...29.39325.1.46..7..9..1...94...545..2...9.9.7154.8 * PAIR B1: 1,4 BLK 1 C1: 1,4,3,8 # reduction candidate for 1,4 C1: 3,8 => CTR * .4.29.567..5..4.92.29.57.84.84672953932581746567439821.1.94.2.545..2...9.9.7154.8 C1: 1,4 # 24 pairs * PAIR B2: 6,7 BLK 1 A2: 6,7,3,8 # reduction candidate for 6,7 A2: 6,7 => SOLVED * 814293567765184392329657184581462973932571846647839251173948625458326719296715438 A2: 3,8 => CTR * ...29.567.75..4.92629.57.84.8...29.39325.1.4656743982171.94.23545..2...9.9.7154.8 * PAIR A3: 3,6 BLK 1 A2: 3,6,7,8 # reduction candidate for 3,6 A2: 3,6 => CTR * ...29.567.75..4.92.29.57.84.8...29.39325.1.46.6743982171.94.23545..2...9.9.7154.8 A2: 7,8 # 22 pairs * PAIR A3: 3,6 ROW 3 D3: 3,6,1 # reduction candidate for 3,6 D3: 1 => CTR * .4.29.567.75..419262915738418467295393258174656743982171.94.2.545..2.679296715438 D3: 3,6 # 21 pairs * PAIR A3: 3,6 COL A A9: 3,6,2 # reduction candidate for 3,6 A9: 3,6 => CTR * .1429.567765..4.92329657184186..29.39325.1.46..7..9..127.94.6.545..267.9.9.715428 A9: 2 # 22 pairs * PAIR F1: 3,8 BLK 2 D2: 3,8,1,6 # reduction candidate for 3,8 D2: 3,8 => CTR * .4.29.567.75.6419262915738418467295393258174656743982171.94.2.545..2.679296715438 D2: 1,6 # 22 pairs E2: 3,8,6 # reduction candidate for 3,8 E2: 3,8 => SOLVED * 814293567765184392329657184581462973932571846647839251173948625458326719296715438 E2: 6 => CTR * .4.29.567.75.64.92629.57.8418467295393258174656743982171.94.2.545..2.679296715438 * PAIR F1: 3,8 ROW 1 A1: 3,8,1 # reduction candidate for 3,8 A1: 3,8 # 24 pairs C1: 3,8,1,4 # reduction candidate for 3,8 C1: 3,8 => CTR * .4.29.567..5..4.92.29.57.84.84672953932581746567439821.1.94.2.545..2...9.9.7154.8 C1: 1,4 # 24 pairs * PAIR F1: 3,8 COL F F7: 3,8,6 # reduction candidate for 3,8 F7: 3,8 => SOLVED * 814293567765184392329657184581462973932571846647839251173948625458326719296715438 F7: 6 => CTR * .1429.567..5..4.92.29.57.84.8..729539325817465.7..9821...946215451.2.679296715438 F8: 3,8,6 # reduction candidate for 3,8 F8: 3,8 => CTR * .1429.567..5..4.92.29.57.84.8..729539325817465.7..9821...946215451.2.679296715438 F8: 6 => SOLVED * 814293567765184392329657184581462973932571846647839251173948625458326719296715438 * PAIR G2: 1,3 ROW 2 D2: 1,3,6,8 # reduction candidate for 1,3 D2: 6,8 => CTR * .4.29356737586419262915738418467295393258174656743982171.94.2.545.32.679296715438 D2: 1,3 # 23 pairs * PAIR G3: 1,3 ROW 3 D3: 1,3,6 # reduction candidate for 1,3 D3: 1,3 => CTR * .4.29.567.75..4.92629.57.8418467295393258174656743982171.94.2.545..2.679296715438 D3: 6 => SOLVED * 814293567765184392329657184581462973932571846647839251173948625458326719296715438 * PAIR A6: 5,6 BLK 4 A4: 5,6,1 # reduction candidate for 5,6 A4: 5,6 => SOLVED * 814293567765184392329657184581462973932571846647839251173948625458326719296715438 A4: 1 => CTR * ...29.567..5..4.92.29.57.84184672953932581746567439821...946215451.2.679296715438 * PAIR B6: 4,6 BLK 4 C4: 4,6,1 # reduction candidate for 4,6 C4: 4,6 => CTR * ...29.567..5..4.92.29.57.84184672953932581746567439821...946215451.2.679296715438 C4: 1 => SOLVED * 814293567765184392329657184581462973932571846647839251173948625458326719296715438 * PAIR B6: 4,6 ROW 6 D6: 4,6,3,8 # reduction candidate for 4,6 D6: 4,6 => CTR * .1429.567..5..4.92.29.57.84.8..729539325817465.7.39821...946215451.2.679296715438 D6: 3,8 => SOLVED * 814293567765184392329657184581462973932571846647839251173948625458326719296715438 * PAIR D4: 4,6 BLK 5 D6: 4,6,3,8 # reduction candidate for 4,6 D6: 4,6 => CTR * .1429.567..5..4.92.29.57.84.8..729539325817465.7.39821...946215451.2.679296715438 D6: 3,8 => SOLVED * 814293567765184392329657184581462973932571846647839251173948625458326719296715438 * PAIR D4: 4,6 ROW 4 C4: 4,6,1 # reduction candidate for 4,6 C4: 4,6 => CTR * ...29.567..5..4.92.29.57.84184672953932581746567439821...946215451.2.679296715438 C4: 1 => SOLVED * 814293567765184392329657184581462973932571846647839251173948625458326719296715438 * PAIR B7: 1,7 BLK 7 A7: 1,7,2,3,8 # reduction candidate for 1,7 A7: 1,7 => SOLVED * 814293567765184392329657184581462973932571846647839251173948625458326719296715438 A7: 2,3,8 => CTR * .142935677651843923296571841864729.39325.1.46.47..9..1.7.94...545..2...9.9.7154.8 * PAIR C9: 3,6 BLK 7 A9: 3,6,2 # reduction candidate for 3,6 A9: 3,6 => CTR * .1429.567765..4.92329657184186..29.39325.1.46..7..9..127.94.6.545..267.9.9.715428 A9: 2 # 22 pairs * PAIR D8: 3,8 BLK 8 F7: 3,8,6 # reduction candidate for 3,8 F7: 3,8 => SOLVED * 814293567765184392329657184581462973932571846647839251173948625458326719296715438 F7: 6 => CTR * .1429.567..5..4.92.29.57.84.8..729539325817465.7..9821...946215451.2.679296715438 F8: 3,8,6 # reduction candidate for 3,8 F8: 3,8 => CTR * .1429.567..5..4.92.29.57.84.8..729539325817465.7..9821...946215451.2.679296715438 F8: 6 => SOLVED * 814293567765184392329657184581462973932571846647839251173948625458326719296715438 * PAIR D8: 3,8 ROW 8 C8: 3,8,1 # reduction candidate for 3,8 C8: 3,8 => SOLVED * 814293567765184392329657184581462973932571846647839251173948625458326719296715438 C8: 1 => CTR * .1429.567..5..4.92.29.57.84186472953932581746547..9821.7.94...5451.2...9.9.7154.8 * PAIR D8: 3,8 COL D D2: 3,8,1,6 # reduction candidate for 3,8 D2: 3,8 => CTR * .4.29.567.75.6419262915738418467295393258174656743982171.94.2.545..2.679296715438 D2: 1,6 # 22 pairs D6: 3,8,4,6 # reduction candidate for 3,8 D6: 3,8 => SOLVED * 814293567765184392329657184581462973932571846647839251173948625458326719296715438 D6: 4,6 => CTR * .1429.567..5..4.92.29.57.84.8..729539325817465.7.39821...946215451.2.679296715438 * PAIR H9: 2,3 BLK 9 H7: 2,3,1 # reduction candidate for 2,3 H7: 2,3 => SOLVED * 814293567765184392329657184581462973932571846647839251173948625458326719296715438 H7: 1 => CTR * .1429.567..5..4.92.29.57.84186472953932581746547..9821.7.94..15451.2...9.9.7154.8 * PAIR H9: 2,3 ROW 9 A9: 2,3,6 # reduction candidate for 2,3 A9: 6 => CTR * ...29.567..5..4.92.29.57.84.8...29.39325.1.46..7..9..127.94.6.545..267.9693715428 A9: 2,3 # 22 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190129-absurd-base-pr-000.dot * REASONING * DIS # C1: 3,8 => CTR => C1: 1,4 * PRF # A2: 6,7 => SOL * DIS # A2: 3,8 => CTR => A2: 6,7 * DIS # A2: 3,6 => CTR => A2: 7,8 * DIS # D3: 1 => CTR => D3: 3,6 * DIS # A9: 3,6 => CTR => A9: 2 * DIS # D2: 3,8 => CTR => D2: 1,6 * PRF # E2: 3,8 => SOL * DIS # E2: 6 => CTR => E2: 3,8 * DIS # C1: 3,8 => CTR => C1: 1,4 * PRF # F7: 3,8 => SOL * DIS # F7: 6 => CTR => F7: 3,8 * DIS # F8: 3,8 => CTR => F8: 6 * PRF # F8: 6 => SOL * DIS # D2: 6,8 => CTR => D2: 1,3 * DIS # D3: 1,3 => CTR => D3: 6 * PRF # D3: 6 => SOL * PRF # A4: 5,6 => SOL * DIS # A4: 1 => CTR => A4: 5,6 * DIS # C4: 4,6 => CTR => C4: 1 * PRF # C4: 1 => SOL * DIS # D6: 4,6 => CTR => D6: 3,8 * PRF # D6: 3,8 => SOL * DIS # D6: 4,6 => CTR => D6: 3,8 * PRF # D6: 3,8 => SOL * DIS # C4: 4,6 => CTR => C4: 1 * PRF # C4: 1 => SOL * PRF # A7: 1,7 => SOL * DIS # A7: 2,3,8 => CTR => A7: 1,7 * DIS # A9: 3,6 => CTR => A9: 2 * PRF # F7: 3,8 => SOL * DIS # F7: 6 => CTR => F7: 3,8 * DIS # F8: 3,8 => CTR => F8: 6 * PRF # F8: 6 => SOL * PRF # C8: 3,8 => SOL * DIS # C8: 1 => CTR => C8: 3,8 * DIS # D2: 3,8 => CTR => D2: 1,6 * PRF # D6: 3,8 => SOL * DIS # D6: 4,6 => CTR => D6: 3,8 * PRF # H7: 2,3 => SOL * DIS # H7: 1 => CTR => H7: 2,3 * DIS # A9: 6 => CTR => A9: 2,3 * CNT 42 HDP CHAINS / 53 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A6,B1,B2,B6,B7,C9,D4,D8,E4,E5,F1,G2,G3,G5,G6,G7,G8,H4,H6,H9) * ...29.567..5..4.92.29.57.84.8...29.39325.1.46..7..9..1...94...545..2...9.9.7154.8 * PAIR B1: 1,4 BLK 1 C1: 1,4,3,8 # reduction candidate for 1,4 C1: 3,8 => CTR * .4.29.567..5..4.92.29.57.84.84672953932581746567439821.1.94.2.545..2...9.9.7154.8 * PAIR B2: 6,7 BLK 1 A2: 6,7,3,8 # reduction candidate for 6,7 A2: 6,7 => SOLVED * 814293567765184392329657184581462973932571846647839251173948625458326719296715438 * DURATION: 0:00:03.351359 START: 03:19:32.340466 END: 03:19:35.691825 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190129-absurd-base-pr-001.dot * REASONING * DIS # C1: 3,8 => CTR => C1: 1,4 * PRF C1: 1,4 # A2: 6,7 => SOL * STA C1: 1,4 + A2: 6,7 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190129, absurd
Solution
position: 814293567765184392329657184581462973932571846647839251173948625458326719296715438 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 # C1: 1,4 => UNS * DIS # C1: 3,8 => CTR => C1: 1,4 * PRF # A2: 6,7 => SOL * DIS # A2: 3,8 => CTR => A2: 6,7 * DIS # A2: 3,6 => CTR => A2: 7,8 * INC # A2: 7,8 => UNS * INC # D3: 3,6 => UNS * DIS # D3: 1 => CTR => D3: 3,6 * DIS # A9: 3,6 => CTR => A9: 2 * INC # A9: 2 => UNS * DIS # D2: 3,8 => CTR => D2: 1,6 * INC # D2: 1,6 => UNS * PRF # E2: 3,8 => SOL * DIS # E2: 6 => CTR => E2: 3,8 * INC # A1: 3,8 => UNS * DIS # C1: 3,8 => CTR => C1: 1,4 * INC # C1: 1,4 => UNS * PRF # F7: 3,8 => SOL * DIS # F7: 6 => CTR => F7: 3,8 * DIS # F8: 3,8 => CTR => F8: 6 * PRF # F8: 6 => SOL * INC # D2: 1,3 => UNS * DIS # D2: 6,8 => CTR => D2: 1,3 * DIS # D3: 1,3 => CTR => D3: 6 * PRF # D3: 6 => SOL * PRF # A4: 5,6 => SOL * DIS # A4: 1 => CTR => A4: 5,6 * DIS # C4: 4,6 => CTR => C4: 1 * PRF # C4: 1 => SOL * DIS # D6: 4,6 => CTR => D6: 3,8 * PRF # D6: 3,8 => SOL * DIS # D6: 4,6 => CTR => D6: 3,8 * PRF # D6: 3,8 => SOL * DIS # C4: 4,6 => CTR => C4: 1 * PRF # C4: 1 => SOL * PRF # A7: 1,7 => SOL * DIS # A7: 2,3,8 => CTR => A7: 1,7 * DIS # A9: 3,6 => CTR => A9: 2 * INC # A9: 2 => UNS * PRF # F7: 3,8 => SOL * DIS # F7: 6 => CTR => F7: 3,8 * DIS # F8: 3,8 => CTR => F8: 6 * PRF # F8: 6 => SOL * PRF # C8: 3,8 => SOL * DIS # C8: 1 => CTR => C8: 3,8 * DIS # D2: 3,8 => CTR => D2: 1,6 * INC # D2: 1,6 => UNS * PRF # D6: 3,8 => SOL * DIS # D6: 4,6 => CTR => D6: 3,8 * PRF # H7: 2,3 => SOL * DIS # H7: 1 => CTR => H7: 2,3 * INC # A9: 2,3 => UNS * DIS # A9: 6 => CTR => A9: 2,3 * CNT 53 HDP CHAINS / 53 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 1,4 => UNS * DIS # C1: 3,8 => CTR => C1: 1,4 * PRF C1: 1,4 # A2: 6,7 => SOL * STA C1: 1,4 + A2: 6,7 * CNT 3 HDP CHAINS / 3 HYP OPENED