Analysis of xx-top500-363-base.sdk
Contents
Original Sudoku
level: medium
position: 9.....68.4...7..........2...8.....17...42..............7.8.1......9..4..3........ initial
Autosolve
position: 9.715.68.4.8.7.1..1...8.27.284.9..1771.4289...9.71.842.79841.2.8.29374.1341.6.798 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 6 => CTR => B2: 2,3 * DIS # F1: 4 => CTR => F1: 2,3 * DIS # B3: 3 => CTR => B3: 5,6 * PRF # C6: 5,6 => SOL * DIS # C6: 3 => CTR => C6: 5,6 * PRF # D2: 3,6 => SOL * DIS # F2: 3,6 => CTR => F2: 2,9 * PRF # B3: 3,6 => SOL * DIS # B3: 5 => CTR => B3: 3,6 * PRF # D4: 5 => SOL * PRF # F1: 2 => SOL * DIS # I2: 9 => CTR => I2: 3,5 * PRF # H5: 3,5 => SOL * DIS # H5: 6 => CTR => H5: 3,5 * DIS # C6: 3,5 => CTR => C6: 6 * PRF # C6: 6 => SOL * PRF # H5: 3,5 => SOL * DIS # H5: 6 => CTR => H5: 3,5 * DIS # I5: 3,5 => CTR => I5: 6 * PRF # I5: 6 => SOL * PRF # C6: 5,6 => SOL * DIS # C6: 3 => CTR => C6: 5,6 * DIS # F4: 3,5 => CTR => F4: 6 * DIS # C6: 3,5 => CTR => C6: 6 * PRF # C6: 6 => SOL * PRF # H5: 3,5 => SOL * DIS # H5: 6 => CTR => H5: 3,5 * DIS # I5: 3,5 => CTR => I5: 6 * PRF # I5: 6 => SOL * DIS # F4: 3,5 => CTR => F4: 6 * DIS # I7: 5,6 => CTR => I7: 3 * PRF # I7: 3 => SOL * DIS # B3: 3 => CTR => B3: 5,6 * PRF # I7: 3,5 => SOL * DIS # I7: 6 => CTR => I7: 3,5 * DIS # I7: 5,6 => CTR => I7: 3 * PRF # I7: 3 => SOL * DIS # H5: 3 => CTR => H5: 5,6 * CNT 38 HDP CHAINS / 52 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 6 => CTR => B2: 2,3 * PRF B2: 2,3 # C6: 5,6 => SOL * STA B2: 2,3 + C6: 5,6 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 9.....68.4...7..........2...8.....17...42..............7.8.1......9..4..3........ | initial |
| 9.715.68.4.8.7.1..1...8.27.284.9..1771.4289...9.71.842.79841.2.8.29374.1341.6.798 | autosolve |
| 937152684428679135165384279284596317713428956596713842679841523852937461341265798 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) B1: 2,3 C3: 5,6 D3: 3,6 F3: 4,9 I1: 3,4 H2: 3,5 I3: 4,9 C5: 3,5 A6: 5,6 F6: 3,5 G4: 3,5 A7: 5,6 B8: 5,6 D9: 2,5 F9: 2,5 G7: 3,5 H8: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,B2: 2.. / B1 = 2 => 18 pairs (_) / B2 = 2 => 0 pairs (*) D9,F9: 2.. / D9 = 2 => 0 pairs (*) / F9 = 2 => 0 pairs (X) B1,F1: 2.. / B1 = 2 => 18 pairs (_) / F1 = 2 => 0 pairs (*) D2,D9: 2.. / D2 = 2 => 17 pairs (_) / D9 = 2 => 0 pairs (*) C5,C6: 3.. / C5 = 3 => 0 pairs (*) / C6 = 3 => 0 pairs (X) G7,I7: 3.. / G7 = 3 => 0 pairs (X) / I7 = 3 => 0 pairs (_) B3,D3: 3.. / B3 = 3 => 0 pairs (X) / D3 = 3 => 21 pairs (_) C6,F6: 3.. / C6 = 3 => 0 pairs (X) / F6 = 3 => 0 pairs (_) G4,G7: 3.. / G4 = 3 => 0 pairs (*) / G7 = 3 => 0 pairs (X) H2,H5: 3.. / H2 = 3 => 20 pairs (_) / H5 = 3 => 0 pairs (X) F1,F3: 4.. / F1 = 4 => 0 pairs (X) / F3 = 4 => 19 pairs (_) I1,I3: 4.. / I1 = 4 => 19 pairs (_) / I3 = 4 => 0 pairs (X) F1,I1: 4.. / F1 = 4 => 0 pairs (X) / I1 = 4 => 19 pairs (_) F3,I3: 4.. / F3 = 4 => 19 pairs (_) / I3 = 4 => 0 pairs (X) B3,C3: 5.. / B3 = 5 => 0 pairs (X) / C3 = 5 => 0 pairs (_) H2,I2: 5.. / H2 = 5 => 0 pairs (X) / I2 = 5 => 20 pairs (_) A7,B8: 5.. / A7 = 5 => 0 pairs (X) / B8 = 5 => 0 pairs (_) D9,F9: 5.. / D9 = 5 => 17 pairs (_) / F9 = 5 => 0 pairs (*) B8,H8: 5.. / B8 = 5 => 0 pairs (*) / H8 = 5 => 0 pairs (X) A6,A7: 5.. / A6 = 5 => 0 pairs (*) / A7 = 5 => 0 pairs (X) B3,B8: 5.. / B3 = 5 => 0 pairs (X) / B8 = 5 => 0 pairs (_) D4,D9: 5.. / D4 = 5 => 0 pairs (*) / D9 = 5 => 0 pairs (X) G4,G7: 5.. / G4 = 5 => 0 pairs (X) / G7 = 5 => 0 pairs (_) A6,C6: 6.. / A6 = 6 => 0 pairs (X) / C6 = 6 => 0 pairs (_) D4,F4: 6.. / D4 = 6 => 0 pairs (X) / F4 = 6 => 18 pairs (_) H5,I5: 6.. / H5 = 6 => 0 pairs (X) / I5 = 6 => 0 pairs (_) A7,B8: 6.. / A7 = 6 => 0 pairs (*) / B8 = 6 => 0 pairs (X) I7,H8: 6.. / I7 = 6 => 0 pairs (X) / H8 = 6 => 0 pairs (_) A7,I7: 6.. / A7 = 6 => 0 pairs (*) / I7 = 6 => 0 pairs (X) B8,H8: 6.. / B8 = 6 => 0 pairs (X) / H8 = 6 => 0 pairs (_) A6,A7: 6.. / A6 = 6 => 0 pairs (X) / A7 = 6 => 0 pairs (_) C3,C6: 6.. / C3 = 6 => 0 pairs (X) / C6 = 6 => 0 pairs (_) F2,F4: 6.. / F2 = 6 => 0 pairs (X) / F4 = 6 => 18 pairs (_) H5,H8: 6.. / H5 = 6 => 0 pairs (X) / H8 = 6 => 0 pairs (_) I5,I7: 6.. / I5 = 6 => 0 pairs (*) / I7 = 6 => 0 pairs (X) F2,F3: 9.. / F2 = 9 => 19 pairs (_) / F3 = 9 => 0 pairs (X) I2,I3: 9.. / I2 = 9 => 0 pairs (X) / I3 = 9 => 19 pairs (_) F2,I2: 9.. / F2 = 9 => 19 pairs (_) / I2 = 9 => 0 pairs (X) F3,I3: 9.. / F3 = 9 => 0 pairs (X) / I3 = 9 => 19 pairs (_) * DURATION: 0:01:14.049336 START: 15:12:32.282468 END: 15:13:46.331804 2017-05-04 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A7,B1,B8,C3,C5,D3,D9,F3,F6,F9,G4,G7,H2,H8,I1,I3) * 9.715.68.4.8.7.1..1...8.27.284.9..1771.4289...9.71.842.79841.2.8.29374.1341.6.798 * PAIR B1: 2,3 BLK 1 B2: 2,3,6 # reduction candidate for 2,3 B2: 6 => CTR * 92715468346837215.13568.27.284.96.177134289..596713842679841.2.852937461341.65798 B2: 2,3 # 21 pairs * PAIR B1: 2,3 ROW 1 F1: 2,3,4 # reduction candidate for 2,3 F1: 4 => CTR * 9271546834.8.7.1591...89274284.9..1771.428936.93715842.79841.2.8.29374.1341.6.798 F1: 2,3 # 19 pairs * PAIR C3: 5,6 BLK 1 B3: 5,6,3 # reduction candidate for 5,6 B3: 3 => CTR * 92715468346837215.13568.27.284.96.177134289..596713842679841.2.852937461341.65798 B3: 5,6 # 21 pairs * PAIR C3: 5,6 COL C C6: 5,6,3 # reduction candidate for 5,6 C6: 5,6 => SOLVED * 937152684428679135165384279284596317713428956596713842679841523852937461341265798 C6: 3 => CTR * 9271546834.8.7.1..1.638.27.284.9..177154289..693715842579841326862937451341562798 * PAIR D3: 3,6 BLK 2 D2: 3,6,2 # reduction candidate for 3,6 D2: 3,6 => SOLVED * 937152684428679135165384279284596317713428956596713842679841523852937461341265798 D2: 2 # 17 pairs F2: 3,6,2,9 # reduction candidate for 3,6 F2: 3,6 => CTR * 9.71546834.827.1591...89274284.9..1771.428936.93715842.79841.2.8.29374.1341.6.798 F2: 2,9 # 19 pairs * PAIR D3: 3,6 ROW 3 B3: 3,6,5 # reduction candidate for 3,6 B3: 3,6 => SOLVED * 937152684428679135165384279284596317713428956596713842679841523852937461341265798 B3: 5 => CTR * 9.715.68.4.8.7.13515638.279284.93517715428963693715842579841326862937451341.6.798 * PAIR D3: 3,6 COL D D4: 3,6,5 # reduction candidate for 3,6 D4: 5 => SOLVED * 937152684428679135165384279284596317713428956596713842679841523852937461341265798 D4: 3,6 # 17 pairs * PAIR I1: 3,4 ROW 1 F1: 3,4,2 # reduction candidate for 3,4 F1: 2 => SOLVED * 937152684428679135165384279284596317713428956596713842679841523852937461341265798 F1: 3,4 # 18 pairs * PAIR H2: 3,5 BLK 3 I2: 3,5,9 # reduction candidate for 3,5 I2: 9 => CTR * 9.715.68.4.8.7.1591...89274284.9..1771.428936.93715842.79841.2.8.29374.1341.6.798 I2: 3,5 # 19 pairs * PAIR H2: 3,5 COL H H5: 3,5,6 # reduction candidate for 3,5 H5: 3,5 => SOLVED * 937152684428679135165384279284596317713428956596713842679841523852937461341265798 H5: 6 => CTR * 92715.68.4.8.7.1351...8.279284.9.517715428963693715842579841326862937451341562798 * PAIR C5: 3,5 BLK 4 C6: 3,5,6 # reduction candidate for 3,5 C6: 3,5 => CTR * 9.715.68.4.8.7.13515638.279284.93517715428963693715842579841326862937451341.6.798 C6: 6 => SOLVED * 937152684428679135165384279284596317713428956596713842679841523852937461341265798 * PAIR C5: 3,5 ROW 5 H5: 3,5,6 # reduction candidate for 3,5 H5: 3,5 => SOLVED * 937152684428679135165384279284596317713428956596713842679841523852937461341265798 H5: 6 => CTR * 92715.68.4.8.7.1351...8.279284.9.517715428963693715842579841326862937451341562798 I5: 3,5,6 # reduction candidate for 3,5 I5: 3,5 => CTR * 9.715.68.4.8.7.13515638.279284.9.517715428963693715842579841326862937451341562798 I5: 6 => SOLVED * 937152684428679135165384279284596317713428956596713842679841523852937461341265798 * PAIR A6: 5,6 BLK 4 C6: 5,6,3 # reduction candidate for 5,6 C6: 5,6 => SOLVED * 937152684428679135165384279284596317713428956596713842679841523852937461341265798 C6: 3 => CTR * 9271546834.8.7.1..1.638.27.284.9..177154289..693715842579841326862937451341562798 * PAIR F6: 3,5 BLK 5 D4: 3,5,6 # reduction candidate for 3,5 D4: 3,5 # 18 pairs F4: 3,5,6 # reduction candidate for 3,5 F4: 3,5 => CTR * 9271546834382761591..38927428469..1771.428936.93715842.79841.2.8.29374.1341562798 F4: 6 # 18 pairs * PAIR F6: 3,5 ROW 6 C6: 3,5,6 # reduction candidate for 3,5 C6: 3,5 => CTR * 9.715.68.4.8.7.13515638.279284.93517715428963693715842579841326862937451341.6.798 C6: 6 => SOLVED * 937152684428679135165384279284596317713428956596713842679841523852937461341265798 * PAIR G4: 3,5 BLK 6 H5: 3,5,6 # reduction candidate for 3,5 H5: 3,5 => SOLVED * 937152684428679135165384279284596317713428956596713842679841523852937461341265798 H5: 6 => CTR * 92715.68.4.8.7.1351...8.279284.9.517715428963693715842579841326862937451341562798 I5: 3,5,6 # reduction candidate for 3,5 I5: 3,5 => CTR * 9.715.68.4.8.7.13515638.279284.9.517715428963693715842579841326862937451341562798 I5: 6 => SOLVED * 937152684428679135165384279284596317713428956596713842679841523852937461341265798 * PAIR G4: 3,5 ROW 4 D4: 3,5,6 # reduction candidate for 3,5 D4: 3,5 # 18 pairs F4: 3,5,6 # reduction candidate for 3,5 F4: 3,5 => CTR * 9271546834382761591..38927428469..1771.428936.93715842.79841.2.8.29374.1341562798 F4: 6 # 18 pairs * PAIR A7: 5,6 ROW 7 I7: 5,6,3 # reduction candidate for 5,6 I7: 5,6 => CTR * 92715.68.438.7.1..1...8.27.284.9.5177154289..693715842579841326862937451341562798 I7: 3 => SOLVED * 937152684428679135165384279284596317713428956596713842679841523852937461341265798 * PAIR B8: 5,6 COL B B3: 5,6,3 # reduction candidate for 5,6 B3: 3 => CTR * 92715468346837215.13568.27.284.96.177134289..596713842679841.2.852937461341.65798 B3: 5,6 # 21 pairs * PAIR G7: 3,5 BLK 9 I7: 3,5,6 # reduction candidate for 3,5 I7: 3,5 => SOLVED * 937152684428679135165384279284596317713428956596713842679841523852937461341265798 I7: 6 => CTR * 9.715.68.4.8.7.13515638.279284.93517715428963693715842.79841326862937451341.6.798 * PAIR H8: 5,6 BLK 9 I7: 5,6,3 # reduction candidate for 5,6 I7: 5,6 => CTR * 92715.68.438.7.1..1...8.27.284.9.5177154289..693715842579841326862937451341562798 I7: 3 => SOLVED * 937152684428679135165384279284596317713428956596713842679841523852937461341265798 * PAIR H8: 5,6 COL H H5: 5,6,3 # reduction candidate for 5,6 H5: 3 => CTR * 9.715.68.4.8.7.1..1...8.27.284.9..1771.428936.93715842.79841.2.8.29374.1341.6.798 H5: 5,6 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-363-base-pr-000.dot * REASONING * DIS # B2: 6 => CTR => B2: 2,3 * DIS # F1: 4 => CTR => F1: 2,3 * DIS # B3: 3 => CTR => B3: 5,6 * PRF # C6: 5,6 => SOL * DIS # C6: 3 => CTR => C6: 5,6 * PRF # D2: 3,6 => SOL * DIS # F2: 3,6 => CTR => F2: 2,9 * PRF # B3: 3,6 => SOL * DIS # B3: 5 => CTR => B3: 3,6 * PRF # D4: 5 => SOL * PRF # F1: 2 => SOL * DIS # I2: 9 => CTR => I2: 3,5 * PRF # H5: 3,5 => SOL * DIS # H5: 6 => CTR => H5: 3,5 * DIS # C6: 3,5 => CTR => C6: 6 * PRF # C6: 6 => SOL * PRF # H5: 3,5 => SOL * DIS # H5: 6 => CTR => H5: 3,5 * DIS # I5: 3,5 => CTR => I5: 6 * PRF # I5: 6 => SOL * PRF # C6: 5,6 => SOL * DIS # C6: 3 => CTR => C6: 5,6 * DIS # F4: 3,5 => CTR => F4: 6 * DIS # C6: 3,5 => CTR => C6: 6 * PRF # C6: 6 => SOL * PRF # H5: 3,5 => SOL * DIS # H5: 6 => CTR => H5: 3,5 * DIS # I5: 3,5 => CTR => I5: 6 * PRF # I5: 6 => SOL * DIS # F4: 3,5 => CTR => F4: 6 * DIS # I7: 5,6 => CTR => I7: 3 * PRF # I7: 3 => SOL * DIS # B3: 3 => CTR => B3: 5,6 * PRF # I7: 3,5 => SOL * DIS # I7: 6 => CTR => I7: 3,5 * DIS # I7: 5,6 => CTR => I7: 3 * PRF # I7: 3 => SOL * DIS # H5: 3 => CTR => H5: 5,6 * CNT 38 HDP CHAINS / 52 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A7,B1,B8,C3,C5,D3,D9,F3,F6,F9,G4,G7,H2,H8,I1,I3) * 9.715.68.4.8.7.1..1...8.27.284.9..1771.4289...9.71.842.79841.2.8.29374.1341.6.798 * PAIR B1: 2,3 BLK 1 B2: 2,3,6 # reduction candidate for 2,3 B2: 6 => CTR * 92715468346837215.13568.27.284.96.177134289..596713842679841.2.852937461341.65798 * PAIR C3: 5,6 COL C C6: 5,6,3 # reduction candidate for 5,6 C6: 5,6 => SOLVED * 937152684428679135165384279284596317713428956596713842679841523852937461341265798 * DURATION: 0:00:04.317630 START: 15:14:44.684793 END: 15:14:49.002423 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-363-base-pr-001.dot * REASONING * DIS # B2: 6 => CTR => B2: 2,3 * PRF B2: 2,3 # C6: 5,6 => SOL * STA B2: 2,3 + C6: 5,6 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 363 solution: 937152684428679135165384279284596317713428956596713842679841523852937461341265798 info: 4950 FNBHWY S8.f 43452 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 937152684428679135165384279284596317713428956596713842679841523852937461341265798 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 # B2: 2,3 => UNS * DIS # B2: 6 => CTR => B2: 2,3 * INC # F1: 2,3 => UNS * DIS # F1: 4 => CTR => F1: 2,3 * INC # B3: 5,6 => UNS * DIS # B3: 3 => CTR => B3: 5,6 * PRF # C6: 5,6 => SOL * DIS # C6: 3 => CTR => C6: 5,6 * PRF # D2: 3,6 => SOL * INC # D2: 2 => UNS * DIS # F2: 3,6 => CTR => F2: 2,9 * INC # F2: 2,9 => UNS * PRF # B3: 3,6 => SOL * DIS # B3: 5 => CTR => B3: 3,6 * INC # D4: 3,6 => UNS * PRF # D4: 5 => SOL * INC # F1: 3,4 => UNS * PRF # F1: 2 => SOL * INC # I2: 3,5 => UNS * DIS # I2: 9 => CTR => I2: 3,5 * PRF # H5: 3,5 => SOL * DIS # H5: 6 => CTR => H5: 3,5 * DIS # C6: 3,5 => CTR => C6: 6 * PRF # C6: 6 => SOL * PRF # H5: 3,5 => SOL * DIS # H5: 6 => CTR => H5: 3,5 * DIS # I5: 3,5 => CTR => I5: 6 * PRF # I5: 6 => SOL * PRF # C6: 5,6 => SOL * DIS # C6: 3 => CTR => C6: 5,6 * INC # D4: 3,5 => UNS * DIS # F4: 3,5 => CTR => F4: 6 * INC # F4: 6 => UNS * DIS # C6: 3,5 => CTR => C6: 6 * PRF # C6: 6 => SOL * PRF # H5: 3,5 => SOL * DIS # H5: 6 => CTR => H5: 3,5 * DIS # I5: 3,5 => CTR => I5: 6 * PRF # I5: 6 => SOL * INC # D4: 3,5 => UNS * DIS # F4: 3,5 => CTR => F4: 6 * INC # F4: 6 => UNS * DIS # I7: 5,6 => CTR => I7: 3 * PRF # I7: 3 => SOL * INC # B3: 5,6 => UNS * DIS # B3: 3 => CTR => B3: 5,6 * PRF # I7: 3,5 => SOL * DIS # I7: 6 => CTR => I7: 3,5 * DIS # I7: 5,6 => CTR => I7: 3 * PRF # I7: 3 => SOL * INC # H5: 5,6 => UNS * DIS # H5: 3 => CTR => H5: 5,6 * CNT 52 HDP CHAINS / 52 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 2,3 => UNS * DIS # B2: 6 => CTR => B2: 2,3 * PRF B2: 2,3 # C6: 5,6 => SOL * STA B2: 2,3 + C6: 5,6 * CNT 3 HDP CHAINS / 3 HYP OPENED