Analysis of xx-top500-120-base.sdk
Contents
Original Sudoku
level: medium
position: 3...26.........4.15........2......6......5.3..4.1........41.7.....8.....6........ initial
Autosolve
position: 314526....623.84515...41623253..416.1..6.5234.46132..5.254137.643.86.5126.125.34. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A6: 8 => SOL * PRF # E4: 7,9 => SOL * PRF # H1: 8,9 => SOL * DIS # H1: 7 => CTR => H1: 8,9 * DIS # I1: 8,9 => CTR => I1: 7 * PRF # I1: 7 => SOL * PRF # E4: 7,9 => SOL * PRF # I4: 8 => SOL * PRF # I4: 8,9 => SOL * DIS # I4: 7 => CTR => I4: 8,9 * DIS # H6: 8,9 => CTR => H6: 7 * PRF # H6: 7 => SOL * PRF # A6: 8,9 => SOL * DIS # A6: 7 => CTR => A6: 8,9 * PRF # A6: 8,9 => SOL * DIS # A6: 7 => CTR => A6: 8,9 * PRF # B9: 8 => SOL * PRF # B9: 8 => SOL * PRF # H1: 8,9 => SOL * DIS # H1: 7 => CTR => H1: 8,9 * DIS # H6: 8,9 => CTR => H6: 7 * PRF # H6: 7 => SOL * DIS # I1: 8,9 => CTR => I1: 7 * PRF # I1: 7 => SOL * PRF # I4: 8,9 => SOL * DIS # I4: 7 => CTR => I4: 8,9 * CNT 26 HDP CHAINS / 44 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A6: 8 => SOL * STA A6: 8 * CNT 1 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 3...26.........4.15........2......6......5.3..4.1........41.7.....8.....6........ | initial |
| 314526....623.84515...41623253..416.1..6.5234.46132..5.254137.643.86.5126.125.34. | autosolve |
| 314526897762398451598741623253974168179685234846132975925413786437869512681257349 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) A2: 7,9 E2: 7,9 D3: 7,9 G1: 8,9 D4: 7,9 G6: 8,9 A7: 8,9 C8: 7,9 F8: 7,9 F9: 7,9 H7: 8,9 I9: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,D3: 7.. / E2 = 7 => 0 pairs (X) / D3 = 7 => 0 pairs (_) H1,I1: 7.. / H1 = 7 => 0 pairs (X) / I1 = 7 => 0 pairs (_) I4,H6: 7.. / I4 = 7 => 0 pairs (X) / H6 = 7 => 0 pairs (_) C8,B9: 7.. / C8 = 7 => 12 pairs (_) / B9 = 7 => 16 pairs (_) F8,F9: 7.. / F8 = 7 => 16 pairs (_) / F9 = 7 => 12 pairs (_) A2,E2: 7.. / A2 = 7 => 0 pairs (*) / E2 = 7 => 0 pairs (X) A6,H6: 7.. / A6 = 7 => 0 pairs (X) / H6 = 7 => 0 pairs (_) C8,F8: 7.. / C8 = 7 => 12 pairs (_) / F8 = 7 => 16 pairs (_) B9,F9: 7.. / B9 = 7 => 16 pairs (_) / F9 = 7 => 12 pairs (_) A2,A6: 7.. / A2 = 7 => 0 pairs (*) / A6 = 7 => 0 pairs (X) D3,D4: 7.. / D3 = 7 => 0 pairs (*) / D4 = 7 => 0 pairs (X) H1,H6: 7.. / H1 = 7 => 0 pairs (X) / H6 = 7 => 0 pairs (_) I1,I4: 7.. / I1 = 7 => 0 pairs (*) / I4 = 7 => 0 pairs (X) B3,C3: 8.. / B3 = 8 => 18 pairs (_) / C3 = 8 => 14 pairs (_) E4,E5: 8.. / E4 = 8 => 16 pairs (_) / E5 = 8 => 0 pairs (*) A7,B9: 8.. / A7 = 8 => 16 pairs (_) / B9 = 8 => 0 pairs (*) H7,I9: 8.. / H7 = 8 => 0 pairs (*) / I9 = 8 => 0 pairs (X) E4,I4: 8.. / E4 = 8 => 16 pairs (_) / I4 = 8 => 0 pairs (*) A7,H7: 8.. / A7 = 8 => 16 pairs (_) / H7 = 8 => 0 pairs (*) B9,I9: 8.. / B9 = 8 => 0 pairs (*) / I9 = 8 => 0 pairs (X) A6,A7: 8.. / A6 = 8 => 0 pairs (*) / A7 = 8 => 0 pairs (X) C3,C5: 8.. / C3 = 8 => 14 pairs (_) / C5 = 8 => 18 pairs (_) G1,G6: 8.. / G1 = 8 => 16 pairs (_) / G6 = 8 => 0 pairs (X) E2,D3: 9.. / E2 = 9 => 0 pairs (*) / D3 = 9 => 0 pairs (X) F8,F9: 9.. / F8 = 9 => 12 pairs (_) / F9 = 9 => 16 pairs (_) H7,I9: 9.. / H7 = 9 => 16 pairs (_) / I9 = 9 => 0 pairs (*) A2,E2: 9.. / A2 = 9 => 0 pairs (X) / E2 = 9 => 0 pairs (_) A7,H7: 9.. / A7 = 9 => 0 pairs (*) / H7 = 9 => 0 pairs (X) C8,F8: 9.. / C8 = 9 => 16 pairs (_) / F8 = 9 => 12 pairs (_) D3,D4: 9.. / D3 = 9 => 0 pairs (X) / D4 = 9 => 0 pairs (_) G1,G6: 9.. / G1 = 9 => 0 pairs (X) / G6 = 9 => 16 pairs (_) * DURATION: 0:00:51.556454 START: 06:53:05.069792 END: 06:53:56.626246 2017-05-04 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,C8,D3,D4,E2,F8,F9,G1,G6,H7,I9) * 314526....623.84515...41623253..416.1..6.5234.46132..5.254137.643.86.5126.125.34. * PAIR A2: 7,9 BLK 1 B3: 7,9,8 # reduction candidate for 7,9 B3: 7,9 # 14 pairs C3: 7,9,8 # reduction candidate for 7,9 C3: 7,9 # 18 pairs * PAIR A2: 7,9 COL A A6: 7,9,8 # reduction candidate for 7,9 A6: 8 => SOLVED * 314526897762398451598741623253974168179685234846132975925413786437869512681257349 A6: 7,9 # 16 pairs * PAIR E2: 7,9 COL E E4: 7,9,8 # reduction candidate for 7,9 E4: 7,9 => SOLVED * 314526897762398451598741623253974168179685234846132975925413786437869512681257349 E4: 8 # 16 pairs E5: 7,9,8 # reduction candidate for 7,9 E5: 7,9 # 16 pairs * PAIR D3: 7,9 ROW 3 B3: 7,9,8 # reduction candidate for 7,9 B3: 7,9 # 14 pairs C3: 7,9,8 # reduction candidate for 7,9 C3: 7,9 # 18 pairs * PAIR G1: 8,9 BLK 3 H1: 8,9,7 # reduction candidate for 8,9 H1: 8,9 => SOLVED * 314526897762398451598741623253974168179685234846132975925413786437869512681257349 H1: 7 => CTR * 314526.7..623.84515...41623253..41671..675234746132..582541379643.86.5126.125.348 I1: 8,9,7 # reduction candidate for 8,9 I1: 8,9 => CTR * 314526.7..623.84515...41623253..41671..675234746132..582541379643.86.5126.125.348 I1: 7 => SOLVED * 314526897762398451598741623253974168179685234846132975925413786437869512681257349 * PAIR D4: 7,9 BLK 5 E4: 7,9,8 # reduction candidate for 7,9 E4: 7,9 => SOLVED * 314526897762398451598741623253974168179685234846132975925413786437869512681257349 E4: 8 # 16 pairs E5: 7,9,8 # reduction candidate for 7,9 E5: 7,9 # 16 pairs * PAIR D4: 7,9 ROW 4 I4: 7,9,8 # reduction candidate for 7,9 I4: 8 => SOLVED * 314526897762398451598741623253974168179685234846132975925413786437869512681257349 I4: 7,9 # 16 pairs * PAIR G6: 8,9 BLK 6 I4: 8,9,7 # reduction candidate for 8,9 I4: 8,9 => SOLVED * 314526897762398451598741623253974168179685234846132975925413786437869512681257349 I4: 7 => CTR * 314526....623.84515...41623253.841671..675234746132..582541379643.86.5126.125.348 H6: 8,9,7 # reduction candidate for 8,9 H6: 8,9 => CTR * 314526.7..623.84515...41623253..41671..675234746132..582541379643.86.5126.125.348 H6: 7 => SOLVED * 314526897762398451598741623253974168179685234846132975925413786437869512681257349 * PAIR G6: 8,9 ROW 6 A6: 8,9,7 # reduction candidate for 8,9 A6: 8,9 => SOLVED * 314526897762398451598741623253974168179685234846132975925413786437869512681257349 A6: 7 => CTR * 314526.799623784515..9416232537.416.1..6.5234746132..582541379643.86.5126.125.348 * PAIR A7: 8,9 BLK 7 B9: 8,9,7 # reduction candidate for 8,9 B9: 7 # 16 pairs B9: 8,9 # 12 pairs * PAIR A7: 8,9 COL A A6: 8,9,7 # reduction candidate for 8,9 A6: 8,9 => SOLVED * 314526897762398451598741623253974168179685234846132975925413786437869512681257349 A6: 7 => CTR * 314526.799623784515..9416232537.416.1..6.5234746132..582541379643.86.5126.125.348 * PAIR C8: 7,9 BLK 7 B9: 7,9,8 # reduction candidate for 7,9 B9: 8 => SOLVED * 314526897762398451598741623253974168179685234846132975925413786437869512681257349 B9: 7,9 # 16 pairs * PAIR C8: 7,9 COL C C3: 7,9,8 # reduction candidate for 7,9 C3: 7,9 # 18 pairs C5: 7,9,8 # reduction candidate for 7,9 C5: 7,9 # 14 pairs * PAIR F9: 7,9 ROW 9 B9: 7,9,8 # reduction candidate for 7,9 B9: 8 => SOLVED * 314526897762398451598741623253974168179685234846132975925413786437869512681257349 B9: 7,9 # 16 pairs * PAIR H7: 8,9 COL H H1: 8,9,7 # reduction candidate for 8,9 H1: 8,9 => SOLVED * 314526897762398451598741623253974168179685234846132975925413786437869512681257349 H1: 7 => CTR * 314526.7..623.84515...41623253..41671..675234746132..582541379643.86.5126.125.348 H6: 8,9,7 # reduction candidate for 8,9 H6: 8,9 => CTR * 314526.7..623.84515...41623253..41671..675234746132..582541379643.86.5126.125.348 H6: 7 => SOLVED * 314526897762398451598741623253974168179685234846132975925413786437869512681257349 * PAIR I9: 8,9 ROW 9 B9: 8,9,7 # reduction candidate for 8,9 B9: 7 # 16 pairs B9: 8,9 # 12 pairs * PAIR I9: 8,9 COL I I1: 8,9,7 # reduction candidate for 8,9 I1: 8,9 => CTR * 314526.7..623.84515...41623253..41671..675234746132..582541379643.86.5126.125.348 I1: 7 => SOLVED * 314526897762398451598741623253974168179685234846132975925413786437869512681257349 I4: 8,9,7 # reduction candidate for 8,9 I4: 8,9 => SOLVED * 314526897762398451598741623253974168179685234846132975925413786437869512681257349 I4: 7 => CTR * 314526....623.84515...41623253.841671..675234746132..582541379643.86.5126.125.348 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-120-base-pr-000.dot * REASONING * PRF # A6: 8 => SOL * PRF # E4: 7,9 => SOL * PRF # H1: 8,9 => SOL * DIS # H1: 7 => CTR => H1: 8,9 * DIS # I1: 8,9 => CTR => I1: 7 * PRF # I1: 7 => SOL * PRF # E4: 7,9 => SOL * PRF # I4: 8 => SOL * PRF # I4: 8,9 => SOL * DIS # I4: 7 => CTR => I4: 8,9 * DIS # H6: 8,9 => CTR => H6: 7 * PRF # H6: 7 => SOL * PRF # A6: 8,9 => SOL * DIS # A6: 7 => CTR => A6: 8,9 * PRF # A6: 8,9 => SOL * DIS # A6: 7 => CTR => A6: 8,9 * PRF # B9: 8 => SOL * PRF # B9: 8 => SOL * PRF # H1: 8,9 => SOL * DIS # H1: 7 => CTR => H1: 8,9 * DIS # H6: 8,9 => CTR => H6: 7 * PRF # H6: 7 => SOL * DIS # I1: 8,9 => CTR => I1: 7 * PRF # I1: 7 => SOL * PRF # I4: 8,9 => SOL * DIS # I4: 7 => CTR => I4: 8,9 * CNT 26 HDP CHAINS / 44 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,C8,D3,D4,E2,F8,F9,G1,G6,H7,I9) * 314526....623.84515...41623253..416.1..6.5234.46132..5.254137.643.86.5126.125.34. * PAIR A2: 7,9 BLK 1 B3: 7,9,8 # reduction candidate for 7,9 B3: 7,9 # 14 pairs C3: 7,9,8 # reduction candidate for 7,9 C3: 7,9 # 18 pairs * PAIR A2: 7,9 COL A A6: 7,9,8 # reduction candidate for 7,9 A6: 8 => SOLVED * 314526897762398451598741623253974168179685234846132975925413786437869512681257349 * DURATION: 0:00:04.556573 START: 06:54:41.513627 END: 06:54:46.070200 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-120-base-pr-001.dot * REASONING * PRF # A6: 8 => SOL * STA A6: 8 * CNT 1 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 120 solution: 314526897762398451598741623253974168179685234846132975925413786437869512681257349 info: 1802 FNWX S8.f 29127 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 314526897762398451598741623253974168179685234846132975925413786437869512681257349 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 # B3: 7,9 => UNS * INC # C3: 7,9 => UNS * INC # A6: 7,9 => UNS * PRF # A6: 8 => SOL * PRF # E4: 7,9 => SOL * INC # E4: 8 => UNS * INC # E5: 7,9 => UNS * INC # B3: 7,9 => UNS * INC # C3: 7,9 => UNS * PRF # H1: 8,9 => SOL * DIS # H1: 7 => CTR => H1: 8,9 * DIS # I1: 8,9 => CTR => I1: 7 * PRF # I1: 7 => SOL * PRF # E4: 7,9 => SOL * INC # E4: 8 => UNS * INC # E5: 7,9 => UNS * INC # I4: 7,9 => UNS * PRF # I4: 8 => SOL * PRF # I4: 8,9 => SOL * DIS # I4: 7 => CTR => I4: 8,9 * DIS # H6: 8,9 => CTR => H6: 7 * PRF # H6: 7 => SOL * PRF # A6: 8,9 => SOL * DIS # A6: 7 => CTR => A6: 8,9 * INC # B9: 8,9 => UNS * INC # B9: 7 => UNS * PRF # A6: 8,9 => SOL * DIS # A6: 7 => CTR => A6: 8,9 * INC # B9: 7,9 => UNS * PRF # B9: 8 => SOL * INC # C3: 7,9 => UNS * INC # C5: 7,9 => UNS * INC # B9: 7,9 => UNS * PRF # B9: 8 => SOL * PRF # H1: 8,9 => SOL * DIS # H1: 7 => CTR => H1: 8,9 * DIS # H6: 8,9 => CTR => H6: 7 * PRF # H6: 7 => SOL * INC # B9: 8,9 => UNS * INC # B9: 7 => UNS * DIS # I1: 8,9 => CTR => I1: 7 * PRF # I1: 7 => SOL * PRF # I4: 8,9 => SOL * DIS # I4: 7 => CTR => I4: 8,9 * CNT 44 HDP CHAINS / 44 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B3: 7,9 => UNS * INC # C3: 7,9 => UNS * INC # A6: 7,9 => UNS * PRF # A6: 8 => SOL * STA A6: 8 * CNT 4 HDP CHAINS / 4 HYP OPENED