Analysis of xx-top500-268-base.sdk
Contents
Original Sudoku
level: medium
position: ....924..7.1................5....2.....81.......7.....54.3...........6.93......2. initial
Autosolve
position: ....924..7.143895.....71....5.94.2..2..81.......72....542369......2546393..187524 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 6,8 => CTR => C1: 3,5 * PRF # A4: 6,8 => SOL * DIS # A4: 1 => CTR => A4: 6,8 * PRF # C1: 3,8 => SOL * DIS # C1: 5,6 => CTR => C1: 3,8 * DIS # B6: 3,8 => CTR => B6: 1 * PRF # B6: 1 => SOL * DIS # B3: 2,6 => CTR => B3: 9 * PRF # B3: 9 => SOL * DIS # C3: 4,9 => CTR => C3: 5,6 * PRF # C3: 5,6 => SOL * DIS # C1: 5,6 => CTR => C1: 3,8 * PRF # C1: 3,8 => SOL * PRF # C3: 5,6 => SOL * DIS # C3: 4,9 => CTR => C3: 5,6 * DIS # H4: 1,7 => CTR => H4: 6,8 * PRF # I3: 2,6 => SOL * DIS # I3: 3,8 => CTR => I3: 2,6 * DIS # I3: 3,8 => CTR => I3: 2,6 * PRF # I3: 2,6 => SOL * PRF # G6: 3,8 => SOL * DIS # G6: 1 => CTR => G6: 3,8 * DIS # I3: 6,8 => CTR => I3: 2,3 * DIS # H4: 1,7 => CTR => H4: 6,8 * DIS # C4: 6,8 => CTR => C4: 3,7 * DIS # C3: 4,9 => CTR => C3: 5,6 * PRF # C3: 5,6 => SOL * DIS # F6: 3,6 => CTR => F6: 5 * DIS # C4: 3,6 => CTR => C4: 7,8 * DIS # I4: 3,6 => CTR => I4: 1,7,8 * DIS # F6: 3 => CTR => F6: 5,6 * DIS # I6: 5,6 => CTR => I6: 1,3,8 * PRF # I6: 1,3,8 => SOL * DIS # B8: 1,8 => CTR => B8: 7 * PRF # B8: 7 => SOL * PRF # A4: 1,8 => SOL * DIS # A4: 6 => CTR => A4: 1,8 * PRF # B8: 7,8 => SOL * DIS # B8: 1 => CTR => B8: 7,8 * DIS # C4: 3,6 => CTR => C4: 7,8 * PRF # B3: 6,9 => SOL * DIS # B3: 2 => CTR => B3: 6,9 * DIS # C3: 6,9 => CTR => C3: 4,5 * CNT 43 HDP CHAINS / 59 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 6,8 => CTR => C1: 3,5 * PRF C1: 3,5 # A4: 6,8 => SOL * STA C1: 3,5 + A4: 6,8 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....924..7.1................5....2.....81.......7.....54.3...........6.93......2. | initial |
| ....924..7.143895.....71....5.94.2..2..81.......72....542369......2546393..187524 | autosolve |
| 683592417721438956495671382857943261234816795916725843542369178178254639369187524 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (24) A1: 6,8 B1: 3,8 B2: 2,6 A3: 4,9 D1: 5,6 D3: 5,6 H1: 1,7 I1: 1,7 I2: 2,6 G3: 3,8 H3: 6,8 B5: 3,7 C5: 4,9 A6: 4,9 F4: 3,6 F5: 5,6 G5: 3,7 H5: 4,9 I5: 5,6 H6: 4,9 A8: 1,8 C8: 7,8 B9: 6,9 C9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H1,I1: 1.. / H1 = 1 => 24 pairs (_) / I1 = 1 => 24 pairs (_) A4,B6: 1.. / A4 = 1 => 0 pairs (X) / B6 = 1 => 0 pairs (_) A8,B8: 1.. / A8 = 1 => 0 pairs (*) / B8 = 1 => 0 pairs (X) A4,A8: 1.. / A4 = 1 => 0 pairs (X) / A8 = 1 => 0 pairs (_) B6,B8: 1.. / B6 = 1 => 0 pairs (*) / B8 = 1 => 0 pairs (X) G6,G7: 1.. / G6 = 1 => 0 pairs (X) / G7 = 1 => 0 pairs (_) B2,B3: 2.. / B2 = 2 => 0 pairs (*) / B3 = 2 => 0 pairs (X) I2,I3: 2.. / I2 = 2 => 0 pairs (X) / I3 = 2 => 0 pairs (_) B2,I2: 2.. / B2 = 2 => 0 pairs (*) / I2 = 2 => 0 pairs (X) B3,I3: 2.. / B3 = 2 => 0 pairs (X) / I3 = 2 => 0 pairs (_) B1,C1: 3.. / B1 = 3 => 0 pairs (X) / C1 = 3 => 0 pairs (_) G3,I3: 3.. / G3 = 3 => 0 pairs (*) / I3 = 3 => 0 pairs (X) F4,F6: 3.. / F4 = 3 => 24 pairs (_) / F6 = 3 => 0 pairs (X) B5,G5: 3.. / B5 = 3 => 0 pairs (*) / G5 = 3 => 0 pairs (X) A3,C3: 4.. / A3 = 4 => 19 pairs (_) / C3 = 4 => 0 pairs (X) C5,A6: 4.. / C5 = 4 => 19 pairs (_) / A6 = 4 => 0 pairs (X) H5,H6: 4.. / H5 = 4 => 0 pairs (X) / H6 = 4 => 19 pairs (_) C5,H5: 4.. / C5 = 4 => 19 pairs (_) / H5 = 4 => 0 pairs (X) A6,H6: 4.. / A6 = 4 => 0 pairs (X) / H6 = 4 => 19 pairs (_) A3,A6: 4.. / A3 = 4 => 19 pairs (_) / A6 = 4 => 0 pairs (X) C3,C5: 4.. / C3 = 4 => 0 pairs (X) / C5 = 4 => 19 pairs (_) C1,C3: 5.. / C1 = 5 => 0 pairs (X) / C3 = 5 => 0 pairs (_) D1,D3: 5.. / D1 = 5 => 0 pairs (*) / D3 = 5 => 0 pairs (X) F5,F6: 5.. / F5 = 5 => 0 pairs (X) / F6 = 5 => 21 pairs (_) I5,I6: 5.. / I5 = 5 => 21 pairs (_) / I6 = 5 => 0 pairs (X) C1,D1: 5.. / C1 = 5 => 0 pairs (X) / D1 = 5 => 0 pairs (_) C3,D3: 5.. / C3 = 5 => 0 pairs (*) / D3 = 5 => 0 pairs (X) F5,I5: 5.. / F5 = 5 => 0 pairs (X) / I5 = 5 => 21 pairs (_) F6,I6: 5.. / F6 = 5 => 21 pairs (_) / I6 = 5 => 0 pairs (X) D1,D3: 6.. / D1 = 6 => 0 pairs (X) / D3 = 6 => 0 pairs (_) B9,C9: 6.. / B9 = 6 => 0 pairs (*) / C9 = 6 => 0 pairs (X) B2,I2: 6.. / B2 = 6 => 0 pairs (X) / I2 = 6 => 0 pairs (_) F5,I5: 6.. / F5 = 6 => 21 pairs (_) / I5 = 6 => 0 pairs (X) A1,A4: 6.. / A1 = 6 => 0 pairs (*) / A4 = 6 => 0 pairs (X) H3,H4: 6.. / H3 = 6 => 0 pairs (X) / H4 = 6 => 0 pairs (_) H1,I1: 7.. / H1 = 7 => 24 pairs (_) / I1 = 7 => 24 pairs (_) C4,B5: 7.. / C4 = 7 => 0 pairs (*) / B5 = 7 => 0 pairs (X) B8,C8: 7.. / B8 = 7 => 0 pairs (*) / C8 = 7 => 0 pairs (X) B5,G5: 7.. / B5 = 7 => 0 pairs (X) / G5 = 7 => 0 pairs (_) B5,B8: 7.. / B5 = 7 => 0 pairs (X) / B8 = 7 => 0 pairs (_) C4,C8: 7.. / C4 = 7 => 0 pairs (*) / C8 = 7 => 0 pairs (X) G5,G7: 7.. / G5 = 7 => 0 pairs (*) / G7 = 7 => 0 pairs (X) C5,A6: 9.. / C5 = 9 => 0 pairs (X) / A6 = 9 => 19 pairs (_) H5,H6: 9.. / H5 = 9 => 19 pairs (_) / H6 = 9 => 0 pairs (X) B9,C9: 9.. / B9 = 9 => 0 pairs (X) / C9 = 9 => 0 pairs (_) C5,H5: 9.. / C5 = 9 => 0 pairs (X) / H5 = 9 => 19 pairs (_) A6,H6: 9.. / A6 = 9 => 19 pairs (_) / H6 = 9 => 0 pairs (X) A3,A6: 9.. / A3 = 9 => 0 pairs (X) / A6 = 9 => 19 pairs (_) B3,B9: 9.. / B3 = 9 => 0 pairs (*) / B9 = 9 => 0 pairs (X) * DURATION: 0:01:48.652003 START: 12:02:20.819927 END: 12:04:09.471930 2017-05-04 * CP COUNT: (49) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A6,A8,B1,B2,B5,B9,C5,C8,C9,D1,D3,F4,F5,G3,G5,H1,H3,H5,H6,I1,I2,I5) * ....924..7.143895.....71....5.94.2..2..81.......72....542369......2546393..187524 * PAIR A1: 6,8 BLK 1 C1: 6,8,3,5 # reduction candidate for 6,8 C1: 6,8 => CTR * .3.5924..7.143895...5671.8..5.94.26.2748163.....72....542369......2546393..187524 C1: 3,5 # 25 pairs * PAIR A1: 6,8 COL A A4: 6,8,1 # reduction candidate for 6,8 A4: 6,8 => SOLVED * 683592417721438956495671382857943261234816795916725843542369178178254639369187524 A4: 1 => CTR * 6..5924..72143895649567138215.9432672.4816.959.6725.4.542369...817254639369187524 * PAIR B1: 3,8 BLK 1 C1: 3,8,5,6 # reduction candidate for 3,8 C1: 3,8 => SOLVED * 683592417721438956495671382857943261234816795916725843542369178178254639369187524 C1: 5,6 => CTR * 83..924..7.143895.....7186365.9432..27.81.3...1.72....5423697....72546393..187524 * PAIR B1: 3,8 COL B B6: 3,8,1 # reduction candidate for 3,8 B6: 3,8 => CTR * 6..5924..721438956.95671.8215.94.2672748163.....72....542369...8172546393..187524 B6: 1 => SOLVED * 683592417721438956495671382857943261234816795916725843542369178178254639369187524 * PAIR B2: 2,6 BLK 1 B3: 2,6,9 # reduction candidate for 2,6 B3: 2,6 => CTR * 8356924..7.143895....571.6.65.9432..27.81.....1.72....5423691..1..254639396187524 B3: 9 => SOLVED * 683592417721438956495671382857943261234816795916725843542369178178254639369187524 * PAIR A3: 4,9 BLK 1 C3: 4,9,5,6 # reduction candidate for 4,9 C3: 4,9 => CTR * ..56924..7.143895....571...65.9432..2..81.....1372.8..5423691..1..2546393.6187524 C3: 5,6 => SOLVED * 683592417721438956495671382857943261234816795916725843542369178178254639369187524 * PAIR D1: 5,6 ROW 1 C1: 5,6,3,8 # reduction candidate for 5,6 C1: 5,6 => CTR * 83..924..7.143895.....7186365.9432..27.81.3...1.72....5423697....72546393..187524 C1: 3,8 => SOLVED * 683592417721438956495671382857943261234816795916725843542369178178254639369187524 * PAIR D3: 5,6 ROW 3 C3: 5,6,4,9 # reduction candidate for 5,6 C3: 5,6 => SOLVED * 683592417721438956495671382857943261234816795916725843542369178178254639369187524 C3: 4,9 => CTR * ..56924..7.143895....571...65.9432..2..81.....1372.8..5423691..1..2546393.6187524 * PAIR H1: 1,7 COL H H4: 1,7,6,8 # reduction candidate for 1,7 H4: 1,7 => CTR * 835692471761438952.2.571.6.6579432..2..81.....1.72....5423691871..254639396187524 H4: 6,8 # 26 pairs H7: 1,7,8 # reduction candidate for 1,7 H7: 1,7 # 26 pairs * PAIR I1: 1,7 COL I I4: 1,7,3,6,8 # reduction candidate for 1,7 I4: 1,7 # 28 pairs I7: 1,7,8 # reduction candidate for 1,7 I7: 1,7 # 25 pairs * PAIR I2: 2,6 BLK 3 I3: 2,6,3,8 # reduction candidate for 2,6 I3: 2,6 => SOLVED * 683592417721438956495671382857943261234816795916725843542369178178254639369187524 I3: 3,8 => CTR * 8356924..761438952.2.571.6.65.9432..27.81.....1.72....5423691..1..254639396187524 * PAIR G3: 3,8 BLK 3 I3: 3,8,2,6 # reduction candidate for 3,8 I3: 3,8 => CTR * 8356924..761438952.2.571.6.65.9432..27.81.....1.72....5423691..1..254639396187524 I3: 2,6 => SOLVED * 683592417721438956495671382857943261234816795916725843542369178178254639369187524 * PAIR G3: 3,8 COL G G6: 3,8,1 # reduction candidate for 3,8 G6: 3,8 => SOLVED * 683592417721438956495671382857943261234816795916725843542369178178254639369187524 G6: 1 => CTR * 6..5924..721438956....71...15.94.2..27.81.3.....72.1..5423697..8172546393..187524 * PAIR H3: 6,8 BLK 3 I3: 6,8,2,3 # reduction candidate for 6,8 I3: 6,8 => CTR * ....924..7.1438952.2..713...5.94.2..23.81.7.....72....542369....78254639396187524 I3: 2,3 # 25 pairs * PAIR H3: 6,8 COL H H4: 6,8,1,7 # reduction candidate for 6,8 H4: 1,7 => CTR * 835692471761438952.2.571.6.6579432..2..81.....1.72....5423691871..254639396187524 H4: 6,8 # 26 pairs * PAIR B5: 3,7 BLK 4 C4: 3,7,6,8 # reduction candidate for 3,7 C4: 6,8 => CTR * ...6924..761438952.2.571863.5.9432..27.81.3.....72.1..5423697...172546393..187524 C4: 3,7 # 27 pairs * PAIR C5: 4,9 COL C C3: 4,9,5,6 # reduction candidate for 4,9 C3: 4,9 => CTR * ..56924..7.143895....571...65.9432..2..81.....1372.8..5423691..1..2546393.6187524 C3: 5,6 => SOLVED * 683592417721438956495671382857943261234816795916725843542369178178254639369187524 * PAIR F4: 3,6 BLK 5 F6: 3,6,5 # reduction candidate for 3,6 F6: 3,6 => CTR * 8356924..761438952.2.571.6365.9432..27.815..6.1.726..55423691..1..254639396187524 F6: 5 # 21 pairs * PAIR F4: 3,6 ROW 4 C4: 3,6,7,8 # reduction candidate for 3,6 C4: 3,6 => CTR * ...6924..761438952.2.571863.5.94.2..27.81.3.....72.1..5423697...172546393..187524 C4: 7,8 # 26 pairs I4: 3,6,1,7,8 # reduction candidate for 3,6 I4: 3,6 => CTR * 6835924..721438956.95671.82.5.9462.3234815......72....542369......2546393..187524 I4: 1,7,8 # 24 pairs * PAIR F5: 5,6 BLK 5 F6: 5,6,3 # reduction candidate for 5,6 F6: 3 => CTR * ....924..7.143895.....71....5.94.2..2..815..6..6723..5542369......254639369187524 F6: 5,6 # 24 pairs * PAIR G5: 3,7 BLK 6 I4: 3,7,1,6,8 # reduction candidate for 3,7 I4: 3,7 # 26 pairs I4: 1,6,8 # 24 pairs * PAIR I5: 5,6 BLK 6 I6: 5,6,1,3,8 # reduction candidate for 5,6 I6: 5,6 => CTR * 8356924..761438952.2.571.6365.9432..27.81.....1.72....5423691..1..254639396187524 I6: 1,3,8 => SOLVED * 683592417721438956495671382857943261234816795916725843542369178178254639369187524 * PAIR A8: 1,8 BLK 7 B8: 1,8,7 # reduction candidate for 1,8 B8: 1,8 => CTR * ...6924..761438952.2.571863.5.94.2..27.81.3.....72.1..5423697...172546393..187524 B8: 7 => SOLVED * 683592417721438956495671382857943261234816795916725843542369178178254639369187524 * PAIR A8: 1,8 COL A A4: 1,8,6 # reduction candidate for 1,8 A4: 1,8 => SOLVED * 683592417721438956495671382857943261234816795916725843542369178178254639369187524 A4: 6 => CTR * 83..924..7.143895.....71.6.65.9432..27.81.....1.72....5423691..1..2546393..187524 * PAIR C8: 7,8 BLK 7 B8: 7,8,1 # reduction candidate for 7,8 B8: 7,8 => SOLVED * 683592417721438956495671382857943261234816795916725843542369178178254639369187524 B8: 1 => CTR * 6..5924..7.143895.....7186315.94.2..27.81.3.....72.1..5423697..8172546393..187524 * PAIR C8: 7,8 COL C C4: 7,8,3,6 # reduction candidate for 7,8 C4: 3,6 => CTR * ...6924..761438952.2.571863.5.94.2..27.81.3.....72.1..5423697...172546393..187524 C4: 7,8 # 26 pairs * PAIR B9: 6,9 COL B B3: 6,9,2 # reduction candidate for 6,9 B3: 6,9 => SOLVED * 683592417721438956495671382857943261234816795916725843542369178178254639369187524 B3: 2 => CTR * 8356924..761438952.2.571.6.65.9432..27.81.....1.72....5423691..1..254639396187524 * PAIR C9: 6,9 COL C C3: 6,9,4,5 # reduction candidate for 6,9 C3: 6,9 => CTR * ..56924..7.143895.4..571...65.9432..2.481..9.91372.84.5423691..1..2546393..187524 C3: 4,5 # 25 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-268-base-pr-000.dot * REASONING * DIS # C1: 6,8 => CTR => C1: 3,5 * PRF # A4: 6,8 => SOL * DIS # A4: 1 => CTR => A4: 6,8 * PRF # C1: 3,8 => SOL * DIS # C1: 5,6 => CTR => C1: 3,8 * DIS # B6: 3,8 => CTR => B6: 1 * PRF # B6: 1 => SOL * DIS # B3: 2,6 => CTR => B3: 9 * PRF # B3: 9 => SOL * DIS # C3: 4,9 => CTR => C3: 5,6 * PRF # C3: 5,6 => SOL * DIS # C1: 5,6 => CTR => C1: 3,8 * PRF # C1: 3,8 => SOL * PRF # C3: 5,6 => SOL * DIS # C3: 4,9 => CTR => C3: 5,6 * DIS # H4: 1,7 => CTR => H4: 6,8 * PRF # I3: 2,6 => SOL * DIS # I3: 3,8 => CTR => I3: 2,6 * DIS # I3: 3,8 => CTR => I3: 2,6 * PRF # I3: 2,6 => SOL * PRF # G6: 3,8 => SOL * DIS # G6: 1 => CTR => G6: 3,8 * DIS # I3: 6,8 => CTR => I3: 2,3 * DIS # H4: 1,7 => CTR => H4: 6,8 * DIS # C4: 6,8 => CTR => C4: 3,7 * DIS # C3: 4,9 => CTR => C3: 5,6 * PRF # C3: 5,6 => SOL * DIS # F6: 3,6 => CTR => F6: 5 * DIS # C4: 3,6 => CTR => C4: 7,8 * DIS # I4: 3,6 => CTR => I4: 1,7,8 * DIS # F6: 3 => CTR => F6: 5,6 * DIS # I6: 5,6 => CTR => I6: 1,3,8 * PRF # I6: 1,3,8 => SOL * DIS # B8: 1,8 => CTR => B8: 7 * PRF # B8: 7 => SOL * PRF # A4: 1,8 => SOL * DIS # A4: 6 => CTR => A4: 1,8 * PRF # B8: 7,8 => SOL * DIS # B8: 1 => CTR => B8: 7,8 * DIS # C4: 3,6 => CTR => C4: 7,8 * PRF # B3: 6,9 => SOL * DIS # B3: 2 => CTR => B3: 6,9 * DIS # C3: 6,9 => CTR => C3: 4,5 * CNT 43 HDP CHAINS / 59 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A6,A8,B1,B2,B5,B9,C5,C8,C9,D1,D3,F4,F5,G3,G5,H1,H3,H5,H6,I1,I2,I5) * ....924..7.143895.....71....5.94.2..2..81.......72....542369......2546393..187524 * PAIR A1: 6,8 BLK 1 C1: 6,8,3,5 # reduction candidate for 6,8 C1: 6,8 => CTR * .3.5924..7.143895...5671.8..5.94.26.2748163.....72....542369......2546393..187524 * PAIR A1: 6,8 COL A A4: 6,8,1 # reduction candidate for 6,8 A4: 6,8 => SOLVED * 683592417721438956495671382857943261234816795916725843542369178178254639369187524 * DURATION: 0:00:04.850349 START: 12:05:26.923688 END: 12:05:31.774037 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-268-base-pr-001.dot * REASONING * DIS # C1: 6,8 => CTR => C1: 3,5 * PRF C1: 3,5 # A4: 6,8 => SOL * STA C1: 3,5 + A4: 6,8 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 268 solution: 683592417721438956495671382857943261234816795916725843542369178178254639369187524 info: 2142 FNBTHWY S8.f 6692 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 683592417721438956495671382857943261234816795916725843542369178178254639369187524 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:
* DIS # C1: 6,8 => CTR => C1: 3,5 * INC # C1: 3,5 => UNS * PRF # A4: 6,8 => SOL * DIS # A4: 1 => CTR => A4: 6,8 * PRF # C1: 3,8 => SOL * DIS # C1: 5,6 => CTR => C1: 3,8 * DIS # B6: 3,8 => CTR => B6: 1 * PRF # B6: 1 => SOL * DIS # B3: 2,6 => CTR => B3: 9 * PRF # B3: 9 => SOL * DIS # C3: 4,9 => CTR => C3: 5,6 * PRF # C3: 5,6 => SOL * DIS # C1: 5,6 => CTR => C1: 3,8 * PRF # C1: 3,8 => SOL * PRF # C3: 5,6 => SOL * DIS # C3: 4,9 => CTR => C3: 5,6 * DIS # H4: 1,7 => CTR => H4: 6,8 * INC # H4: 6,8 => UNS * INC # H7: 1,7 => UNS * INC # I4: 1,7 => UNS * INC # I7: 1,7 => UNS * PRF # I3: 2,6 => SOL * DIS # I3: 3,8 => CTR => I3: 2,6 * DIS # I3: 3,8 => CTR => I3: 2,6 * PRF # I3: 2,6 => SOL * PRF # G6: 3,8 => SOL * DIS # G6: 1 => CTR => G6: 3,8 * DIS # I3: 6,8 => CTR => I3: 2,3 * INC # I3: 2,3 => UNS * INC # H4: 6,8 => UNS * DIS # H4: 1,7 => CTR => H4: 6,8 * INC # C4: 3,7 => UNS * DIS # C4: 6,8 => CTR => C4: 3,7 * DIS # C3: 4,9 => CTR => C3: 5,6 * PRF # C3: 5,6 => SOL * DIS # F6: 3,6 => CTR => F6: 5 * INC # F6: 5 => UNS * DIS # C4: 3,6 => CTR => C4: 7,8 * INC # C4: 7,8 => UNS * DIS # I4: 3,6 => CTR => I4: 1,7,8 * INC # I4: 1,7,8 => UNS * INC # F6: 5,6 => UNS * DIS # F6: 3 => CTR => F6: 5,6 * INC # I4: 3,7 => UNS * INC # I4: 1,6,8 => UNS * DIS # I6: 5,6 => CTR => I6: 1,3,8 * PRF # I6: 1,3,8 => SOL * DIS # B8: 1,8 => CTR => B8: 7 * PRF # B8: 7 => SOL * PRF # A4: 1,8 => SOL * DIS # A4: 6 => CTR => A4: 1,8 * PRF # B8: 7,8 => SOL * DIS # B8: 1 => CTR => B8: 7,8 * INC # C4: 7,8 => UNS * DIS # C4: 3,6 => CTR => C4: 7,8 * PRF # B3: 6,9 => SOL * DIS # B3: 2 => CTR => B3: 6,9 * DIS # C3: 6,9 => CTR => C3: 4,5 * INC # C3: 4,5 => UNS * CNT 59 HDP CHAINS / 59 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C1: 6,8 => CTR => C1: 3,5 * PRF C1: 3,5 # A4: 6,8 => SOL * STA C1: 3,5 + A4: 6,8 * CNT 2 HDP CHAINS / 2 HYP OPENED