Analysis of xx-top95-083-base.sdk
Contents
Original Sudoku
level: medium
position: ....75....1..2.....4...3...5.....3.2...8...1.......6.....1..48.2........7........ initial
Autosolve
position: ....75....1..28....4..13...5.87.13.24..8...1.1..2..6.8.5.1.24872....7...7........ autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 6,9 => CTR => C1: 2,3 * DIS # B5: 7 => CTR => B5: 2,3 * DIS # D1: 6,9 => CTR => D1: 4 * DIS # A3: 6,9 => CTR => A3: 8 * DIS # H3: 6,9 => CTR => H3: 2,5,7 * DIS # C5: 2,3 => CTR => C5: 6,9 * PRF # E4: 4 => SOL * DIS # B5: 3,7 => CTR => B5: 2 * PRF # C5: 3,9 => SOL * DIS # C1: 3,9 => CTR => C1: 2,6 * PRF # E4: 4 => SOL * DIS # C5: 2,3 => CTR => C5: 6,9 * PRF # F9: 4 => SOL * PRF # E4: 4,9 => SOL * DIS # E4: 6 => CTR => E4: 4,9 * DIS # H6: 5,7 => CTR => H6: 4,9 * PRF # F9: 4,9 => SOL * DIS # F9: 6 => CTR => F9: 4,9 * DIS # H6: 5,7 => CTR => H6: 4,9 * PRF # E4: 4,9 => SOL * DIS # E4: 6 => CTR => E4: 4,9 * DIS # G5: 5,9 => CTR => G5: 7 * DIS # I2: 5,9 => CTR => I2: 3,4,6 * DIS # E8: 6,9 => CTR => E8: 4,8 * PRF # E9: 6,9 => SOL * DIS # A7: 6,9 => CTR => A7: 3 * PRF # E4: 4 => SOL * CNT 27 HDP CHAINS / 67 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 6,9 => CTR => C1: 2,3 * DIS C1: 2,3 # B5: 7 => CTR => B5: 2,3 * DIS C1: 2,3 + B5: 2,3 # H2: 5,7 => CTR => H2: 3,6,9 * DIS C1: 2,3 + B5: 2,3 + H2: 3,6,9 # C5: 2,3 => CTR => C5: 6,9 * PRF C1: 2,3 + B5: 2,3 + H2: 3,6,9 + C5: 6,9 # E4: 4 => SOL * STA C1: 2,3 + B5: 2,3 + H2: 3,6,9 + C5: 6,9 + E4: 4 * CNT 5 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....75....1..2.....4...3...5.....3.2...8...1.......6.....1..48.2........7........ | initial |
| ....75....1..28....4..13...5.87.13.24..8...1.1..2..6.8.5.1.24872....7...7........ | autosolve |
| 932475861617928534845613279568741392429836715173259648356192487294387156781564923 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) B1: 2,3 C2: 5,7 C3: 5,7 D3: 6,9 B4: 6,9 B6: 3,7 C6: 3,9 E5: 3,5 F5: 6,9 E6: 3,5 F6: 4,9 H4: 4,9 I5: 5,9 C8: 1,4 C9: 1,4 E7: 6,9 D8: 3,5 D9: 3,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G1,I1: 1.. / G1 = 1 => 0 pairs (X) / I1 = 1 => 20 pairs (_) C8,C9: 1.. / C8 = 1 => 21 pairs (_) / C9 = 1 => 16 pairs (_) B1,C1: 2.. / B1 = 2 => 0 pairs (X) / C1 = 2 => 20 pairs (_) G3,H3: 2.. / G3 = 2 => 19 pairs (_) / H3 = 2 => 18 pairs (_) B5,C5: 2.. / B5 = 2 => 20 pairs (_) / C5 = 2 => 0 pairs (X) G9,H9: 2.. / G9 = 2 => 18 pairs (_) / H9 = 2 => 19 pairs (_) B1,B5: 2.. / B1 = 2 => 0 pairs (X) / B5 = 2 => 20 pairs (_) C1,C5: 2.. / C1 = 2 => 20 pairs (_) / C5 = 2 => 0 pairs (X) G3,G9: 2.. / G3 = 2 => 19 pairs (_) / G9 = 2 => 18 pairs (_) H3,H9: 2.. / H3 = 2 => 18 pairs (_) / H9 = 2 => 19 pairs (_) E5,E6: 3.. / E5 = 3 => 17 pairs (_) / E6 = 3 => 0 pairs (X) A7,C7: 3.. / A7 = 3 => 22 pairs (_) / C7 = 3 => 0 pairs (X) D8,D9: 3.. / D8 = 3 => 16 pairs (_) / D9 = 3 => 17 pairs (_) D1,D2: 4.. / D1 = 4 => 19 pairs (_) / D2 = 4 => 0 pairs (X) I1,I2: 4.. / I1 = 4 => 0 pairs (X) / I2 = 4 => 19 pairs (_) E4,F6: 4.. / E4 = 4 => 0 pairs (*) / F6 = 4 => 0 pairs (X) H4,H6: 4.. / H4 = 4 => 20 pairs (_) / H6 = 4 => 0 pairs (*) C8,C9: 4.. / C8 = 4 => 16 pairs (_) / C9 = 4 => 21 pairs (_) D1,I1: 4.. / D1 = 4 => 19 pairs (_) / I1 = 4 => 0 pairs (X) D2,I2: 4.. / D2 = 4 => 0 pairs (X) / I2 = 4 => 19 pairs (_) E4,H4: 4.. / E4 = 4 => 0 pairs (*) / H4 = 4 => 0 pairs (X) F6,H6: 4.. / F6 = 4 => 20 pairs (_) / H6 = 4 => 0 pairs (*) C8,E8: 4.. / C8 = 4 => 16 pairs (_) / E8 = 4 => 21 pairs (_) F6,F9: 4.. / F6 = 4 => 20 pairs (_) / F9 = 4 => 0 pairs (*) C2,C3: 5.. / C2 = 5 => 17 pairs (_) / C3 = 5 => 21 pairs (_) E5,E6: 5.. / E5 = 5 => 0 pairs (X) / E6 = 5 => 17 pairs (_) D8,D9: 5.. / D8 = 5 => 17 pairs (_) / D9 = 5 => 16 pairs (_) E6,H6: 5.. / E6 = 5 => 17 pairs (_) / H6 = 5 => 0 pairs (X) B4,C5: 6.. / B4 = 6 => 0 pairs (*) / C5 = 6 => 0 pairs (X) E4,F5: 6.. / E4 = 6 => 0 pairs (X) / F5 = 6 => 0 pairs (_) B4,E4: 6.. / B4 = 6 => 0 pairs (*) / E4 = 6 => 0 pairs (X) C5,F5: 6.. / C5 = 6 => 0 pairs (X) / F5 = 6 => 0 pairs (_) F5,F9: 6.. / F5 = 6 => 0 pairs (*) / F9 = 6 => 0 pairs (X) C2,C3: 7.. / C2 = 7 => 21 pairs (_) / C3 = 7 => 17 pairs (_) B5,B6: 7.. / B5 = 7 => 0 pairs (X) / B6 = 7 => 19 pairs (_) G5,H6: 7.. / G5 = 7 => 19 pairs (_) / H6 = 7 => 0 pairs (X) B5,G5: 7.. / B5 = 7 => 0 pairs (X) / G5 = 7 => 19 pairs (_) B6,H6: 7.. / B6 = 7 => 19 pairs (_) / H6 = 7 => 0 pairs (X) A1,A3: 8.. / A1 = 8 => 0 pairs (X) / A3 = 8 => 19 pairs (_) G1,G3: 8.. / G1 = 8 => 19 pairs (_) / G3 = 8 => 0 pairs (X) B8,B9: 8.. / B8 = 8 => 19 pairs (_) / B9 = 8 => 17 pairs (_) E8,E9: 8.. / E8 = 8 => 17 pairs (_) / E9 = 8 => 19 pairs (_) A1,G1: 8.. / A1 = 8 => 0 pairs (X) / G1 = 8 => 19 pairs (_) A3,G3: 8.. / A3 = 8 => 19 pairs (_) / G3 = 8 => 0 pairs (X) B8,E8: 8.. / B8 = 8 => 19 pairs (_) / E8 = 8 => 17 pairs (_) B9,E9: 8.. / B9 = 8 => 17 pairs (_) / E9 = 8 => 19 pairs (_) * DURATION: 0:01:36.106270 START: 00:51:16.669103 END: 00:52:52.775373 2017-05-04 * CP COUNT: (46) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B4,B6,C2,C3,C6,C8,C9,D3,D8,D9,E5,E6,E7,F5,F6,H4,I5) * ....75....1..28....4..13...5.87.13.24..8...1.1..2..6.8.5.1.24872....7...7........ * PAIR B1: 2,3 BLK 1 C1: 2,3,6,9 # reduction candidate for 2,3 C1: 6,9 => CTR * .2..75....1..28....4..13...5687.13.24.28.6.1.1.92.46.8.531.24872....7...7....9... C1: 2,3 # 22 pairs * PAIR B1: 2,3 COL B B5: 2,3,7 # reduction candidate for 2,3 B5: 7 => CTR * .2..75....1..28....4..13...568791342472836.1.13925467895.1.24872....7...7....9... B5: 2,3 # 19 pairs * PAIR C2: 5,7 ROW 2 G2: 5,7,9 # reduction candidate for 5,7 G2: 5,7 # 19 pairs H2: 5,7,3,6,9 # reduction candidate for 5,7 H2: 5,7 # 26 pairs * PAIR C3: 5,7 ROW 3 G3: 5,7,2,8,9 # reduction candidate for 5,7 G3: 5,7 # 19 pairs H3: 5,7,2,6,9 # reduction candidate for 5,7 H3: 5,7 # 21 pairs * PAIR D3: 6,9 BLK 2 D1: 6,9,4 # reduction candidate for 6,9 D1: 6,9 => CTR * 8...751.4.15428....47.138255687913424..8.6.191.92.46.895.1.24872....7...7....92.. D1: 4 # 19 pairs D2: 6,9,4 # reduction candidate for 6,9 D2: 6,9 # 19 pairs * PAIR D3: 6,9 ROW 3 A3: 6,9,8 # reduction candidate for 6,9 A3: 6,9 => CTR * 8...75....15.28....47.138255687913424..8.6.191.92.46.895.1.24872....7...7....92.. A3: 8 # 19 pairs H3: 6,9,2,5,7 # reduction candidate for 6,9 H3: 6,9 => CTR * ...4758.1.15.28..4847.132.55687913424..8.6.191.92.46.895.1.24872....7...7....9.2. H3: 2,5,7 # 18 pairs I3: 6,9,5 # reduction candidate for 6,9 I3: 6,9 # 20 pairs * PAIR B4: 6,9 BLK 4 C5: 6,9,2,3 # reduction candidate for 6,9 C5: 2,3 => CTR * ....75....1..28....4..13...5687913424..8.6.1.1.92.46.895.1.24872....7...7....9... C5: 6,9 # 13 pairs * PAIR B4: 6,9 ROW 4 E4: 6,9,4 # reduction candidate for 6,9 E4: 4 => SOLVED * 932475861617928534845613279568741392429836715173259648356192487294387156781564923 E4: 6,9 # 20 pairs * PAIR B4: 6,9 COL B B8: 6,9,8 # reduction candidate for 6,9 B8: 6,9 # 17 pairs B9: 6,9,8 # reduction candidate for 6,9 B9: 6,9 # 19 pairs * PAIR B6: 3,7 BLK 4 B5: 3,7,2 # reduction candidate for 3,7 B5: 3,7 => CTR * .2..75....1..28....4..13...5687913424.28.6.1.1.92.46.895.1.24872....7...7....9... B5: 2 # 20 pairs * PAIR C6: 3,9 BLK 4 C5: 3,9,2,6 # reduction candidate for 3,9 C5: 3,9 => SOLVED * 932475861617928534845613279568741392429836715173259648356192487294387156781564923 C5: 2,6 # 19 pairs * PAIR C6: 3,9 COL C C1: 3,9,2,6 # reduction candidate for 3,9 C1: 3,9 => CTR * .2..75....1..28....4..13...5687413924.28.6.151.92..6.8.561924872....7...7....4... C1: 2,6 # 20 pairs C7: 3,9,6 # reduction candidate for 3,9 C7: 3,9 # 22 pairs * PAIR F5: 6,9 BLK 5 E4: 6,9,4 # reduction candidate for 6,9 E4: 4 => SOLVED * 932475861617928534845613279568741392429836715173259648356192487294387156781564923 E4: 6,9 # 20 pairs * PAIR F5: 6,9 ROW 5 C5: 6,9,2,3 # reduction candidate for 6,9 C5: 2,3 => CTR * ....75....1..28....4..13...5687913424..8.6.1.1.92.46.895.1.24872....7...7....9... C5: 6,9 # 13 pairs * PAIR F5: 6,9 COL F F9: 6,9,4 # reduction candidate for 6,9 F9: 4 => SOLVED * 932475861617928534845613279568741392429836715173259648356192487294387156781564923 F9: 6,9 # 20 pairs * PAIR F6: 4,9 BLK 5 E4: 4,9,6 # reduction candidate for 4,9 E4: 4,9 => SOLVED * 932475861617928534845613279568741392429836715173259648356192487294387156781564923 E4: 6 => CTR * ....75....1..28....4..13...5.87613424.68.9.151..2546986531.24872....7...7........ * PAIR F6: 4,9 ROW 6 H6: 4,9,5,7 # reduction candidate for 4,9 H6: 5,7 => CTR * ....75....1..28....4..13...5687913424..8.6.1.1.92.46.895.1.24872....7...7........ H6: 4,9 # 13 pairs * PAIR F6: 4,9 COL F F9: 4,9,6 # reduction candidate for 4,9 F9: 4,9 => SOLVED * 932475861617928534845613279568741392429836715173259648356192487294387156781564923 F9: 6 => CTR * ....75....1..28....4..13...5.87613424.68.9.151..2546986531.24872....7...7....6... * PAIR H4: 4,9 BLK 6 H6: 4,9,5,7 # reduction candidate for 4,9 H6: 5,7 => CTR * ....75....1..28....4..13...5687913424..8.6.1.1.92.46.895.1.24872....7...7........ H6: 4,9 # 13 pairs * PAIR H4: 4,9 ROW 4 E4: 4,9,6 # reduction candidate for 4,9 E4: 4,9 => SOLVED * 932475861617928534845613279568741392429836715173259648356192487294387156781564923 E4: 6 => CTR * ....75....1..28....4..13...5.87613424.68.9.151..2546986531.24872....7...7........ * PAIR I5: 5,9 BLK 6 G5: 5,9,7 # reduction candidate for 5,9 G5: 5,9 => CTR * .2..75....1..28....4..13...568791342472836.1.13925467895.1.24872....7...7....9... G5: 7 # 19 pairs H6: 5,9,4,7 # reduction candidate for 5,9 H6: 5,9 # 22 pairs * PAIR I5: 5,9 COL I I2: 5,9,3,4,6 # reduction candidate for 5,9 I2: 5,9 => CTR * 8...751.4.1.428....47.138255.87.13.24..8...191..2..6.8.5.1.24872....7...7.....2.. I2: 3,4,6 # 18 pairs I3: 5,9,6 # reduction candidate for 5,9 I3: 5,9 # 19 pairs I8: 5,9,1,3,6 # reduction candidate for 5,9 I8: 5,9 # 18 pairs I9: 5,9,1,3,6 # reduction candidate for 5,9 I9: 5,9 # 20 pairs * PAIR E7: 6,9 BLK 8 E8: 6,9,4,8 # reduction candidate for 6,9 E8: 6,9 => CTR * .32.75164.1.4285...4..13..9568741392429836715173259648356192487284.679.1791.84..6 E8: 4,8 # 19 pairs E9: 6,9,4,8 # reduction candidate for 6,9 E9: 6,9 => SOLVED * 932475861617928534845613279568741392429836715173259648356192487294387156781564923 E9: 4,8 # 19 pairs F9: 6,9,4 # reduction candidate for 6,9 F9: 6,9 # 20 pairs * PAIR E7: 6,9 ROW 7 A7: 6,9,3 # reduction candidate for 6,9 A7: 6,9 => CTR * ....75....1..28....4..13...5687913424.28.6.1.1.92.46.8.531.24872....7...7........ A7: 3 # 22 pairs C7: 6,9,3 # reduction candidate for 6,9 C7: 6,9 # 22 pairs * PAIR E7: 6,9 COL E E4: 6,9,4 # reduction candidate for 6,9 E4: 4 => SOLVED * 932475861617928534845613279568741392429836715173259648356192487294387156781564923 E4: 6,9 # 20 pairs * PAIR D8: 3,5 ROW 8 H8: 3,5,6,9 # reduction candidate for 3,5 H8: 3,5 # 20 pairs I8: 3,5,1,6,9 # reduction candidate for 3,5 I8: 3,5 # 21 pairs * PAIR D9: 3,5 ROW 9 H9: 3,5,2,6,9 # reduction candidate for 3,5 H9: 3,5 # 19 pairs I9: 3,5,1,6,9 # reduction candidate for 3,5 I9: 3,5 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-083-base-pr-000.dot * REASONING * DIS # C1: 6,9 => CTR => C1: 2,3 * DIS # B5: 7 => CTR => B5: 2,3 * DIS # D1: 6,9 => CTR => D1: 4 * DIS # A3: 6,9 => CTR => A3: 8 * DIS # H3: 6,9 => CTR => H3: 2,5,7 * DIS # C5: 2,3 => CTR => C5: 6,9 * PRF # E4: 4 => SOL * DIS # B5: 3,7 => CTR => B5: 2 * PRF # C5: 3,9 => SOL * DIS # C1: 3,9 => CTR => C1: 2,6 * PRF # E4: 4 => SOL * DIS # C5: 2,3 => CTR => C5: 6,9 * PRF # F9: 4 => SOL * PRF # E4: 4,9 => SOL * DIS # E4: 6 => CTR => E4: 4,9 * DIS # H6: 5,7 => CTR => H6: 4,9 * PRF # F9: 4,9 => SOL * DIS # F9: 6 => CTR => F9: 4,9 * DIS # H6: 5,7 => CTR => H6: 4,9 * PRF # E4: 4,9 => SOL * DIS # E4: 6 => CTR => E4: 4,9 * DIS # G5: 5,9 => CTR => G5: 7 * DIS # I2: 5,9 => CTR => I2: 3,4,6 * DIS # E8: 6,9 => CTR => E8: 4,8 * PRF # E9: 6,9 => SOL * DIS # A7: 6,9 => CTR => A7: 3 * PRF # E4: 4 => SOL * CNT 27 HDP CHAINS / 67 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B4,B6,C2,C3,C6,C8,C9,D3,D8,D9,E5,E6,E7,F5,F6,H4,I5) * ....75....1..28....4..13...5.87.13.24..8...1.1..2..6.8.5.1.24872....7...7........ * PAIR B1: 2,3 BLK 1 C1: 2,3,6,9 # reduction candidate for 2,3 C1: 6,9 => CTR * .2..75....1..28....4..13...5687.13.24.28.6.1.1.92.46.8.531.24872....7...7....9... * PAIR B1: 2,3 COL B B5: 2,3,7 # reduction candidate for 2,3 B5: 7 => CTR * .23.75....1..28....4..13...5.87.13.2472836.1.1392546783561924872....7...7........ * PAIR RESTART * PAIR C2: 5,7 ROW 2 H2: 5,7,3,6,9 # reduction candidate for 5,7 H2: 5,7 => CTR * 8..9751646154289739476138255.87.13424..8567191792346583561924872..3.759.7..5..23. * PAIR RESTART * PAIR B4: 6,9 BLK 4 C5: 6,9,2,3 # reduction candidate for 6,9 C5: 2,3 => CTR * ...4758.1.17.28534845.1327.5687.13.24..8.67191792346583561924872....7...7......2. * PAIR B4: 6,9 ROW 4 E4: 6,9,4 # reduction candidate for 6,9 E4: 4 => SOLVED * 932475861617928534845613279568741392429836715173259648356192487294387156781564923 * DURATION: 0:00:16.172231 START: 00:54:13.423289 END: 00:54:29.595520 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-083-base-pr-001.dot * REASONING * DIS # C1: 6,9 => CTR => C1: 2,3 * DIS C1: 2,3 # B5: 7 => CTR => B5: 2,3 * DIS C1: 2,3 + B5: 2,3 # H2: 5,7 => CTR => H2: 3,6,9 * DIS C1: 2,3 + B5: 2,3 + H2: 3,6,9 # C5: 2,3 => CTR => C5: 6,9 * PRF C1: 2,3 + B5: 2,3 + H2: 3,6,9 + C5: 6,9 # E4: 4 => SOL * STA C1: 2,3 + B5: 2,3 + H2: 3,6,9 + C5: 6,9 + E4: 4 * CNT 5 HDP CHAINS / 9 HYP OPENED
Header Info
Top 95 Sudokus 083 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 932475861617928534845613279568741392429836715173259648356192487294387156781564923 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: 2,3 => UNS * DIS # C1: 6,9 => CTR => C1: 2,3 * INC # B5: 2,3 => UNS * DIS # B5: 7 => CTR => B5: 2,3 * INC # G2: 5,7 => UNS * INC # H2: 5,7 => UNS * INC # G3: 5,7 => UNS * INC # H3: 5,7 => UNS * DIS # D1: 6,9 => CTR => D1: 4 * INC # D1: 4 => UNS * INC # D2: 6,9 => UNS * DIS # A3: 6,9 => CTR => A3: 8 * INC # A3: 8 => UNS * DIS # H3: 6,9 => CTR => H3: 2,5,7 * INC # H3: 2,5,7 => UNS * INC # I3: 6,9 => UNS * INC # C5: 6,9 => UNS * DIS # C5: 2,3 => CTR => C5: 6,9 * INC # E4: 6,9 => UNS * PRF # E4: 4 => SOL * INC # B8: 6,9 => UNS * INC # B9: 6,9 => UNS * DIS # B5: 3,7 => CTR => B5: 2 * INC # B5: 2 => UNS * PRF # C5: 3,9 => SOL * INC # C5: 2,6 => UNS * DIS # C1: 3,9 => CTR => C1: 2,6 * INC # C1: 2,6 => UNS * INC # C7: 3,9 => UNS * INC # E4: 6,9 => UNS * PRF # E4: 4 => SOL * INC # C5: 6,9 => UNS * DIS # C5: 2,3 => CTR => C5: 6,9 * INC # F9: 6,9 => UNS * PRF # F9: 4 => SOL * PRF # E4: 4,9 => SOL * DIS # E4: 6 => CTR => E4: 4,9 * INC # H6: 4,9 => UNS * DIS # H6: 5,7 => CTR => H6: 4,9 * PRF # F9: 4,9 => SOL * DIS # F9: 6 => CTR => F9: 4,9 * INC # H6: 4,9 => UNS * DIS # H6: 5,7 => CTR => H6: 4,9 * PRF # E4: 4,9 => SOL * DIS # E4: 6 => CTR => E4: 4,9 * DIS # G5: 5,9 => CTR => G5: 7 * INC # G5: 7 => UNS * INC # H6: 5,9 => UNS * DIS # I2: 5,9 => CTR => I2: 3,4,6 * INC # I2: 3,4,6 => UNS * INC # I3: 5,9 => UNS * INC # I8: 5,9 => UNS * INC # I9: 5,9 => UNS * DIS # E8: 6,9 => CTR => E8: 4,8 * INC # E8: 4,8 => UNS * PRF # E9: 6,9 => SOL * INC # E9: 4,8 => UNS * INC # F9: 6,9 => UNS * DIS # A7: 6,9 => CTR => A7: 3 * INC # A7: 3 => UNS * INC # C7: 6,9 => UNS * INC # E4: 6,9 => UNS * PRF # E4: 4 => SOL * INC # H8: 3,5 => UNS * INC # I8: 3,5 => UNS * INC # H9: 3,5 => UNS * INC # I9: 3,5 => UNS * CNT 67 HDP CHAINS / 67 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 2,3 => UNS * DIS # C1: 6,9 => CTR => C1: 2,3 * INC C1: 2,3 # B5: 2,3 => UNS * DIS C1: 2,3 # B5: 7 => CTR => B5: 2,3 * DIS C1: 2,3 + B5: 2,3 # H2: 5,7 => CTR => H2: 3,6,9 * INC C1: 2,3 + B5: 2,3 + H2: 3,6,9 # C5: 6,9 => UNS * DIS C1: 2,3 + B5: 2,3 + H2: 3,6,9 # C5: 2,3 => CTR => C5: 6,9 * INC C1: 2,3 + B5: 2,3 + H2: 3,6,9 + C5: 6,9 # E4: 6,9 => UNS * PRF C1: 2,3 + B5: 2,3 + H2: 3,6,9 + C5: 6,9 # E4: 4 => SOL * STA C1: 2,3 + B5: 2,3 + H2: 3,6,9 + C5: 6,9 + E4: 4 * CNT 9 HDP CHAINS / 9 HYP OPENED