Analysis of zz-www.sudokuoftheday.co.uk-20060326-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006
level: medium
position: ......6......67.23...1.2..4.57.......2..3...569....2..5.6...1..2...8695...95.13.. initial
Autosolve
position: ..2...6..9...67.23.6.192..4.57.......2..3...569.7..2..5.6...1..2...86957..95.13.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 5 => CTR => C3: 3,8 * DIS # A4: 1,4 => CTR => A4: 3,8 * DIS # F1: 4,5 => CTR => F1: 3 * DIS # E6: 1 => CTR => E6: 4,5 * DIS # D1: 3 => CTR => D1: 4,8 * DIS # B2: 4,8 => CTR => B2: 1 * DIS # C2: 4,8 => CTR => C2: 1,5 * DIS # I4: 1,9 => CTR => I4: 6,8 * DIS # G3: 7 => CTR => G3: 5,8 * DIS # C2: 1,4 => CTR => C2: 5,8 * DIS # G3: 7,8 => CTR => G3: 5 * DIS # H5: 7,8 => CTR => H5: 1,6,9 * DIS # A4: 4,8 => CTR => A4: 1,3 * DIS # A5: 4,8 => CTR => A5: 1 * DIS # G5: 4,8 => CTR => G5: 7 * DIS # C2: 4,8 => CTR => C2: 1,5 * DIS # D4: 6,9 => CTR => D4: 2 * DIS # H5: 1,7,8 => CTR => H5: 6,9 * DIS # G5: 4,8 => CTR => G5: 7 * DIS # A4: 4,8 => CTR => A4: 1,3 * PRF # I4: 1,8 => SOL * DIS # H5: 1,8 => CTR => H5: 6,7,9 * DIS # H6: 1,8 => CTR => H6: 3 * DIS # B8: 3 => CTR => B8: 1,4 * DIS # C2: 1,4 => CTR => C2: 5,8 * DIS # D4: 6 => CTR => D4: 2,9 * DIS # F7: 9 => CTR => F7: 3,4 * DIS # B8: 1 => CTR => B8: 3,4 * DIS # D1: 3,4 => CTR => D1: 8 * PRF # H9: 4,8 => SOL * DIS # H9: 6 => CTR => H9: 4,8 * DIS # B7: 4,8 => CTR => B7: 3,7 * DIS # I9: 2,8 => CTR => I9: 6 * PRF # I9: 6 => SOL * CNT 34 HDP CHAINS / 70 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 5 => CTR => C3: 3,8 * DIS C3: 3,8 # A4: 1 => CTR => A4: 3,8 * DIS C3: 3,8 + A4: 3,8 # I4: 1,9 => CTR => I4: 6,8 * PRF C3: 3,8 + A4: 3,8 + I4: 6,8 => SOL * STA C3: 3,8 + A4: 3,8 + I4: 6,8 * CNT 4 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ......6......67.23...1.2..4.57.......2..3...569....2..5.6...1..2...8695...95.13.. | initial |
| ..2...6..9...67.23.6.192..4.57.......2..3...569.7..2..5.6...1..2...86957..95.13.. | autosolve |
| 472853619915467823863192574357219468124638795698745231536974182241386957789521346 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) A3: 3,8 E1: 4,5 D2: 4,8 H1: 1,9 I1: 1,9 G2: 5,8 H3: 7,8 C5: 4,8 D5: 6,9 G4: 4,8 I6: 1,8 C8: 1,4 D7: 2,9 D8: 3,4 H7: 4,8 I7: 2,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,C2: 1.. / B2 = 1 => 16 pairs (_) / C2 = 1 => 0 pairs (X) H1,I1: 1.. / H1 = 1 => 15 pairs (_) / I1 = 1 => 0 pairs (X) A4,A5: 1.. / A4 = 1 => 0 pairs (X) / A5 = 1 => 16 pairs (_) E4,E6: 1.. / E4 = 1 => 18 pairs (_) / E6 = 1 => 0 pairs (X) B8,C8: 1.. / B8 = 1 => 0 pairs (X) / C8 = 1 => 16 pairs (_) A5,H5: 1.. / A5 = 1 => 16 pairs (_) / H5 = 1 => 0 pairs (X) B2,B8: 1.. / B2 = 1 => 16 pairs (_) / B8 = 1 => 0 pairs (X) C2,C8: 1.. / C2 = 1 => 0 pairs (X) / C8 = 1 => 16 pairs (_) D4,E4: 2.. / D4 = 2 => 18 pairs (_) / E4 = 2 => 0 pairs (X) I7,I9: 2.. / I7 = 2 => 16 pairs (_) / I9 = 2 => 0 pairs (X) E9,I9: 2.. / E9 = 2 => 16 pairs (_) / I9 = 2 => 0 pairs (X) D4,D7: 2.. / D4 = 2 => 18 pairs (_) / D7 = 2 => 0 pairs (X) A3,C3: 3.. / A3 = 3 => 0 pairs (X) / C3 = 3 => 16 pairs (_) D1,F1: 3.. / D1 = 3 => 0 pairs (X) / F1 = 3 => 23 pairs (_) A4,C6: 3.. / A4 = 3 => 16 pairs (_) / C6 = 3 => 0 pairs (X) H4,H6: 3.. / H4 = 3 => 0 pairs (X) / H6 = 3 => 16 pairs (_) B7,B8: 3.. / B7 = 3 => 23 pairs (_) / B8 = 3 => 0 pairs (X) F7,D8: 3.. / F7 = 3 => 0 pairs (X) / D8 = 3 => 23 pairs (_) A4,H4: 3.. / A4 = 3 => 16 pairs (_) / H4 = 3 => 0 pairs (X) C6,H6: 3.. / C6 = 3 => 0 pairs (X) / H6 = 3 => 16 pairs (_) B7,F7: 3.. / B7 = 3 => 23 pairs (_) / F7 = 3 => 0 pairs (X) B8,D8: 3.. / B8 = 3 => 0 pairs (X) / D8 = 3 => 23 pairs (_) A3,A4: 3.. / A3 = 3 => 0 pairs (X) / A4 = 3 => 16 pairs (_) C3,C6: 3.. / C3 = 3 => 16 pairs (_) / C6 = 3 => 0 pairs (X) D1,D8: 3.. / D1 = 3 => 0 pairs (X) / D8 = 3 => 23 pairs (_) F1,F7: 3.. / F1 = 3 => 23 pairs (_) / F7 = 3 => 0 pairs (X) G4,G5: 4.. / G4 = 4 => 18 pairs (_) / G5 = 4 => 0 pairs (X) H7,H9: 4.. / H7 = 4 => 18 pairs (_) / H9 = 4 => 0 pairs (*) C2,C3: 5.. / C2 = 5 => 18 pairs (_) / C3 = 5 => 0 pairs (X) E1,F1: 5.. / E1 = 5 => 17 pairs (_) / F1 = 5 => 0 pairs (X) G2,G3: 5.. / G2 = 5 => 0 pairs (X) / G3 = 5 => 18 pairs (_) E6,F6: 5.. / E6 = 5 => 0 pairs (X) / F6 = 5 => 17 pairs (_) C2,G2: 5.. / C2 = 5 => 18 pairs (_) / G2 = 5 => 0 pairs (X) C3,G3: 5.. / C3 = 5 => 0 pairs (X) / G3 = 5 => 18 pairs (_) E1,E6: 5.. / E1 = 5 => 17 pairs (_) / E6 = 5 => 0 pairs (X) F1,F6: 5.. / F1 = 5 => 0 pairs (X) / F6 = 5 => 17 pairs (_) D4,D5: 6.. / D4 = 6 => 0 pairs (X) / D5 = 6 => 16 pairs (_) H9,I9: 6.. / H9 = 6 => 0 pairs (X) / I9 = 6 => 0 pairs (_) D5,H5: 6.. / D5 = 6 => 16 pairs (_) / H5 = 6 => 0 pairs (X) I4,I9: 6.. / I4 = 6 => 0 pairs (X) / I9 = 6 => 0 pairs (_) A1,B1: 7.. / A1 = 7 => 18 pairs (_) / B1 = 7 => 20 pairs (_) G3,H3: 7.. / G3 = 7 => 0 pairs (X) / H3 = 7 => 17 pairs (_) G5,H5: 7.. / G5 = 7 => 17 pairs (_) / H5 = 7 => 0 pairs (X) E7,E9: 7.. / E7 = 7 => 17 pairs (_) / E9 = 7 => 0 pairs (X) B7,E7: 7.. / B7 = 7 => 0 pairs (X) / E7 = 7 => 17 pairs (_) A1,A9: 7.. / A1 = 7 => 18 pairs (_) / A9 = 7 => 20 pairs (_) G3,G5: 7.. / G3 = 7 => 0 pairs (X) / G5 = 7 => 17 pairs (_) H3,H5: 7.. / H3 = 7 => 17 pairs (_) / H5 = 7 => 0 pairs (X) D1,D2: 8.. / D1 = 8 => 24 pairs (_) / D2 = 8 => 0 pairs (X) H1,I1: 9.. / H1 = 9 => 0 pairs (X) / I1 = 9 => 15 pairs (_) D7,F7: 9.. / D7 = 9 => 18 pairs (_) / F7 = 9 => 0 pairs (X) I1,I4: 9.. / I1 = 9 => 15 pairs (_) / I4 = 9 => 0 pairs (X) * DURATION: 0:01:11.365666 START: 21:54:15.744375 END: 21:55:27.110041 2019-04-30 * CP COUNT: (52) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,C5,C8,D2,D5,D7,D8,E1,G2,G4,H1,H3,H7,I1,I6,I7) * ..2...6..9...67.23.6.192..4.57.......2..3...569.7..2..5.6...1..2...86957..95.13.. * PAIR A3: 3,8 BLK 1 C3: 3,8,5 # reduction candidate for 3,8 C3: 5 => CTR * ..2...6199184675233651928748572194361246387956937452815.69.41..2.1.86957..95.136. C3: 3,8 # 18 pairs * PAIR A3: 3,8 COL A A4: 3,8,1,4 # reduction candidate for 3,8 A4: 1,4 => CTR * ..2...6919...67.2336.192..4.5721..3..2..39..56937..2..5.69..1..2...86957..95.13.. A4: 3,8 # 19 pairs * PAIR E1: 4,5 BLK 2 F1: 4,5,3 # reduction candidate for 4,5 F1: 4,5 => CTR * ..23..619914867523365192.74.572.9836.2863..956937..2..5.69.31..231486957..95.136. F1: 3 # 23 pairs * PAIR E1: 4,5 COL E E6: 4,5,1 # reduction candidate for 4,5 E6: 1 => CTR * ..2.5.6..9...67.23.6.192..4.57.......2..3...569.7152.85.6...1.22...86957..95213.6 E6: 4,5 # 18 pairs * PAIR D2: 4,8 BLK 2 D1: 4,8,3 # reduction candidate for 4,8 D1: 3 => CTR * ..23..619914867523365192.74.572.9836.2863..956937..2..5.69.31..231486957..95.136. D1: 4,8 # 23 pairs * PAIR D2: 4,8 ROW 2 B2: 4,8,1 # reduction candidate for 4,8 B2: 4,8 => CTR * ..2.536..9.1.67523365192..4.57..843.428.397156937.52..536.7.1..214386957..95.13.. B2: 1 # 16 pairs C2: 4,8,1,5 # reduction candidate for 4,8 C2: 4,8 => CTR * ..2...6199184675233651928748572194361246387956937452815.69.41..2.1.86957..95.136. C2: 1,5 # 17 pairs * PAIR H1: 1,9 COL H H4: 1,9,3,6,8 # reduction candidate for 1,9 H4: 1,9 # 19 pairs H5: 1,9,6,7,8 # reduction candidate for 1,9 H5: 1,9 # 19 pairs * PAIR I1: 1,9 COL I I4: 1,9,6,8 # reduction candidate for 1,9 I4: 1,9 => CTR * ..2...6..9...67.23.631925743572.846912.63...569.7..2385.697.1.22...86957..95213.6 I4: 6,8 # 17 pairs * PAIR G2: 5,8 BLK 3 G3: 5,8,7 # reduction candidate for 5,8 G3: 7 => CTR * ..2...6..9...67523.65192784.57.......2..3..756937..218586.73142231486957..952136. G3: 5,8 # 17 pairs * PAIR G2: 5,8 ROW 2 C2: 5,8,1,4 # reduction candidate for 5,8 C2: 1,4 => CTR * ..2...6919...67523365192..4.5721..3..28.39..56937..2..5.69..1..2...86957..95.13.. C2: 5,8 # 19 pairs * PAIR H3: 7,8 BLK 3 G3: 7,8,5 # reduction candidate for 7,8 G3: 7,8 => CTR * ..2...6199184675233651928748572194361246387956937452815.69.41..2.1.86957..95.136. G3: 5 # 18 pairs * PAIR H3: 7,8 COL H H5: 7,8,1,6,9 # reduction candidate for 7,8 H5: 7,8 => CTR * ..2...6199...67.2386319257435721..9612.6397856987..2315.69..14.2..486957..95.136. H5: 1,6,9 # 17 pairs * PAIR C5: 4,8 BLK 4 A4: 4,8,1,3 # reduction candidate for 4,8 A4: 4,8 => CTR * ..2...61991.467.2336.192.748572194361246387956937452815.69.41..2.1.86957..95.136. A4: 1,3 # 17 pairs A5: 4,8,1 # reduction candidate for 4,8 A5: 4,8 => CTR * ..2...6..9...67.23.6.192..4157....3..2..3..1569371.2..5.6...1..2...86957..95.13.. A5: 1 # 16 pairs C6: 4,8,3 # reduction candidate for 4,8 C6: 4,8 # 16 pairs * PAIR C5: 4,8 ROW 5 F5: 4,8,9 # reduction candidate for 4,8 F5: 4,8 # 22 pairs G5: 4,8,7 # reduction candidate for 4,8 G5: 4,8 => CTR * ..2...6..9...67523365192784.57....3..2..3..7569.7..2..5.6...14.2...86957..95.136. G5: 7 # 17 pairs * PAIR C5: 4,8 COL C C2: 4,8,1,5 # reduction candidate for 4,8 C2: 4,8 => CTR * ..2...6199184675233651928748572194361246387956937452815.69.41..2.1.86957..95.136. C2: 1,5 # 17 pairs * PAIR D5: 6,9 BLK 5 D4: 6,9,2 # reduction candidate for 6,9 D4: 6,9 => CTR * ..2...6..9...67.23.6.192..4.57.2.....2..3...569.7152.85.62..1..2...86957..95.13.. D4: 2 # 18 pairs * PAIR D5: 6,9 ROW 5 H5: 6,9,1,7,8 # reduction candidate for 6,9 H5: 1,7,8 => CTR * ..2...6199...67.2386319257435721..9612.6397856987..2315.69..14.2..486957..95.136. H5: 6,9 # 22 pairs * PAIR G4: 4,8 BLK 6 G5: 4,8,7 # reduction candidate for 4,8 G5: 4,8 => CTR * ..2...6..9...67523365192784.57....3..2..3..7569.7..2..5.6...14.2...86957..95.136. G5: 7 # 17 pairs * PAIR G4: 4,8 ROW 4 A4: 4,8,1,3 # reduction candidate for 4,8 A4: 4,8 => CTR * ..2...61991.467.2336.192.748572194361246387956937452815.69.41..2.1.86957..95.136. A4: 1,3 # 17 pairs F4: 4,8,9 # reduction candidate for 4,8 F4: 4,8 # 19 pairs * PAIR I6: 1,8 BLK 6 H4: 1,8,3,6,9 # reduction candidate for 1,8 H4: 1,8 # 20 pairs I4: 1,8,6,9 # reduction candidate for 1,8 I4: 1,8 => SOLVED * 472853619915467823863192574357219468124638795698745231536974182241386957789521346 I4: 6,9 # 17 pairs H5: 1,8,6,7,9 # reduction candidate for 1,8 H5: 1,8 => CTR * ..2...6199154678238631925743572184961246397856987.42315.69.314.2.1.86957..95.136. H5: 6,7,9 # 16 pairs H6: 1,8,3 # reduction candidate for 1,8 H6: 1,8 => CTR * ..2...61991.467.2336.192.748572194361246387956937452815.69.41..2.1.86957..95.136. H6: 3 # 16 pairs * PAIR C8: 1,4 BLK 7 B8: 1,4,3 # reduction candidate for 1,4 B8: 3 => CTR * ..23..619914867523365192.74.572.9836.2863..956937..2..5.69.31..231486957..95.136. B8: 1,4 # 23 pairs * PAIR C8: 1,4 COL C C2: 1,4,5,8 # reduction candidate for 1,4 C2: 1,4 => CTR * ..2...6919...67523365192..4.5721..3..28.39..56937..2..5.69..1..2...86957..95.13.. C2: 5,8 # 19 pairs * PAIR D7: 2,9 COL D D4: 2,9,6 # reduction candidate for 2,9 D4: 6 => CTR * ..2...6..9...67.23.6.192..4.5762.....2.93..6569.7152.85.6...1..2...86957..95.13.. D4: 2,9 # 16 pairs * PAIR D8: 3,4 BLK 8 F7: 3,4,9 # reduction candidate for 3,4 F7: 9 => CTR * ..2..36..9...67.23.6.192..4.57.......2..3...569.7.52..536.791482..386957..9541362 F7: 3,4 # 18 pairs * PAIR D8: 3,4 ROW 8 B8: 3,4,1 # reduction candidate for 3,4 B8: 1 => CTR * ..2.536..9.1.67523365192..4.57..843.428.397156937.52..536.7.1..214386957..95.13.. B8: 3,4 # 16 pairs * PAIR D8: 3,4 COL D D1: 3,4,8 # reduction candidate for 3,4 D1: 3,4 => CTR * ..2...6919..867523365192..4.5721..3..28.39..56937..2..5.69..1..2...86957..95.13.. D1: 8 # 24 pairs * PAIR H7: 4,8 BLK 9 H9: 4,8,6 # reduction candidate for 4,8 H9: 4,8 => SOLVED * 472853619915467823863192574357219468124638795698745231536974182241386957789521346 H9: 6 => CTR * ..23..619914867523.65192..445721.83612.63...569.7..2.15.69.314.231486957..95.136. * PAIR H7: 4,8 ROW 7 B7: 4,8,3,7 # reduction candidate for 4,8 B7: 4,8 => CTR * 8723..619914867523365192.74.572.9836.2863..956937..2..5.69731.2231486957..9521368 B7: 3,7 # 19 pairs * PAIR I7: 2,8 BLK 9 I9: 2,8,6 # reduction candidate for 2,8 I9: 2,8 => CTR * ..23..619914867523.65192..445721.83612.63...569.7..2.15.69.314.231486957..95.136. I9: 6 => SOLVED * 472853619915467823863192574357219468124638795698745231536974182241386957789521346 * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060326-absurd-base-pr-000.dot * REASONING * DIS # C3: 5 => CTR => C3: 3,8 * DIS # A4: 1,4 => CTR => A4: 3,8 * DIS # F1: 4,5 => CTR => F1: 3 * DIS # E6: 1 => CTR => E6: 4,5 * DIS # D1: 3 => CTR => D1: 4,8 * DIS # B2: 4,8 => CTR => B2: 1 * DIS # C2: 4,8 => CTR => C2: 1,5 * DIS # I4: 1,9 => CTR => I4: 6,8 * DIS # G3: 7 => CTR => G3: 5,8 * DIS # C2: 1,4 => CTR => C2: 5,8 * DIS # G3: 7,8 => CTR => G3: 5 * DIS # H5: 7,8 => CTR => H5: 1,6,9 * DIS # A4: 4,8 => CTR => A4: 1,3 * DIS # A5: 4,8 => CTR => A5: 1 * DIS # G5: 4,8 => CTR => G5: 7 * DIS # C2: 4,8 => CTR => C2: 1,5 * DIS # D4: 6,9 => CTR => D4: 2 * DIS # H5: 1,7,8 => CTR => H5: 6,9 * DIS # G5: 4,8 => CTR => G5: 7 * DIS # A4: 4,8 => CTR => A4: 1,3 * PRF # I4: 1,8 => SOL * DIS # H5: 1,8 => CTR => H5: 6,7,9 * DIS # H6: 1,8 => CTR => H6: 3 * DIS # B8: 3 => CTR => B8: 1,4 * DIS # C2: 1,4 => CTR => C2: 5,8 * DIS # D4: 6 => CTR => D4: 2,9 * DIS # F7: 9 => CTR => F7: 3,4 * DIS # B8: 1 => CTR => B8: 3,4 * DIS # D1: 3,4 => CTR => D1: 8 * PRF # H9: 4,8 => SOL * DIS # H9: 6 => CTR => H9: 4,8 * DIS # B7: 4,8 => CTR => B7: 3,7 * DIS # I9: 2,8 => CTR => I9: 6 * PRF # I9: 6 => SOL * CNT 34 HDP CHAINS / 70 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,C5,C8,D2,D5,D7,D8,E1,G2,G4,H1,H3,H7,I1,I6,I7) * ..2...6..9...67.23.6.192..4.57.......2..3...569.7..2..5.6...1..2...86957..95.13.. * PAIR A3: 3,8 BLK 1 C3: 3,8,5 # reduction candidate for 3,8 C3: 5 => CTR * ..2...6199184675233651928748572194361246387956937452815.69.41..2.1.86957..95.136. * PAIR A3: 3,8 COL A A4: 3,8,1 # reduction candidate for 3,8 A4: 1 => CTR * 4728536..915467823368192574157.2.43.824.397.569.7.52..536.7.1..2413869577895.13.. * PAIR RESTART * PAIR H1: 1,9 COL H H4: 1,9,3,6,8 # reduction candidate for 1,9 H4: 1,9 # 19 pairs H4: 3,6,8 # 18 pairs * PAIR I1: 1,9 COL I I4: 1,9,6,8 # reduction candidate for 1,9 I4: 1,9 => CTR * 4728536..915467823.6.192574.5721.46912.63978569.7.52..536.7.1.2241386957789521346 I4: 6,8 => SOLVED * 472853619915467823863192574357219468124638795698745231536974182241386957789521346 * DURATION: 0:00:08.248875 START: 21:56:19.200585 END: 21:56:27.449460 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060326-absurd-base-pr-001.dot * REASONING * DIS # C3: 5 => CTR => C3: 3,8 * DIS C3: 3,8 # A4: 1 => CTR => A4: 3,8 * DIS C3: 3,8 + A4: 3,8 # I4: 1,9 => CTR => I4: 6,8 * PRF C3: 3,8 + A4: 3,8 + I4: 6,8 => SOL * STA C3: 3,8 + A4: 3,8 + I4: 6,8 * CNT 4 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060326, absurd
Solution
position: 472853619915467823863192574357219468124638795698745231536974182241386957789521346 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 # C3: 3,8 => UNS * DIS # C3: 5 => CTR => C3: 3,8 * INC # A4: 3,8 => UNS * DIS # A4: 1,4 => CTR => A4: 3,8 * DIS # F1: 4,5 => CTR => F1: 3 * INC # F1: 3 => UNS * INC # E6: 4,5 => UNS * DIS # E6: 1 => CTR => E6: 4,5 * INC # D1: 4,8 => UNS * DIS # D1: 3 => CTR => D1: 4,8 * DIS # B2: 4,8 => CTR => B2: 1 * INC # B2: 1 => UNS * DIS # C2: 4,8 => CTR => C2: 1,5 * INC # C2: 1,5 => UNS * INC # H4: 1,9 => UNS * INC # H5: 1,9 => UNS * DIS # I4: 1,9 => CTR => I4: 6,8 * INC # I4: 6,8 => UNS * INC # G3: 5,8 => UNS * DIS # G3: 7 => CTR => G3: 5,8 * INC # C2: 5,8 => UNS * DIS # C2: 1,4 => CTR => C2: 5,8 * DIS # G3: 7,8 => CTR => G3: 5 * INC # G3: 5 => UNS * DIS # H5: 7,8 => CTR => H5: 1,6,9 * INC # H5: 1,6,9 => UNS * DIS # A4: 4,8 => CTR => A4: 1,3 * INC # A4: 1,3 => UNS * DIS # A5: 4,8 => CTR => A5: 1 * INC # A5: 1 => UNS * INC # C6: 4,8 => UNS * INC # F5: 4,8 => UNS * DIS # G5: 4,8 => CTR => G5: 7 * INC # G5: 7 => UNS * DIS # C2: 4,8 => CTR => C2: 1,5 * INC # C2: 1,5 => UNS * DIS # D4: 6,9 => CTR => D4: 2 * INC # D4: 2 => UNS * INC # H5: 6,9 => UNS * DIS # H5: 1,7,8 => CTR => H5: 6,9 * DIS # G5: 4,8 => CTR => G5: 7 * INC # G5: 7 => UNS * DIS # A4: 4,8 => CTR => A4: 1,3 * INC # A4: 1,3 => UNS * INC # F4: 4,8 => UNS * INC # H4: 1,8 => UNS * PRF # I4: 1,8 => SOL * INC # I4: 6,9 => UNS * DIS # H5: 1,8 => CTR => H5: 6,7,9 * INC # H5: 6,7,9 => UNS * DIS # H6: 1,8 => CTR => H6: 3 * INC # H6: 3 => UNS * INC # B8: 1,4 => UNS * DIS # B8: 3 => CTR => B8: 1,4 * DIS # C2: 1,4 => CTR => C2: 5,8 * INC # C2: 5,8 => UNS * INC # D4: 2,9 => UNS * DIS # D4: 6 => CTR => D4: 2,9 * INC # F7: 3,4 => UNS * DIS # F7: 9 => CTR => F7: 3,4 * INC # B8: 3,4 => UNS * DIS # B8: 1 => CTR => B8: 3,4 * DIS # D1: 3,4 => CTR => D1: 8 * INC # D1: 8 => UNS * PRF # H9: 4,8 => SOL * DIS # H9: 6 => CTR => H9: 4,8 * DIS # B7: 4,8 => CTR => B7: 3,7 * INC # B7: 3,7 => UNS * DIS # I9: 2,8 => CTR => I9: 6 * PRF # I9: 6 => SOL * CNT 70 HDP CHAINS / 70 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C3: 3,8 => UNS * DIS # C3: 5 => CTR => C3: 3,8 * INC C3: 3,8 # A4: 3,8 => UNS * DIS C3: 3,8 # A4: 1 => CTR => A4: 3,8 * INC C3: 3,8 + A4: 3,8 # H4: 1,9 => UNS * INC C3: 3,8 + A4: 3,8 # H4: 3,6,8 => UNS * DIS C3: 3,8 + A4: 3,8 # I4: 1,9 => CTR => I4: 6,8 * PRF C3: 3,8 + A4: 3,8 + I4: 6,8 => SOL * STA C3: 3,8 + A4: 3,8 + I4: 6,8 * CNT 8 HDP CHAINS / 7 HYP OPENED