Analysis of xx-top500-380-base.sdk
Contents
Original Sudoku
level: medium
position: 4..6..5.783..............1...8.91...2.....4......8.......4..3....1.......9....... initial
Autosolve
position: 41263859783.1.92649...42813.48.91.3.2.93..4811.3.849...8.41.329.219...48.9482.1.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C3: 5,7 => SOL * PRF # C7: 6 => SOL * PRF # C3: 5,7 => SOL * PRF # B6: 5,7 => SOL * PRF # B3: 6 => SOL * DIS # A4: 5 => CTR => A4: 6,7 * PRF # B6: 5,7 => SOL * DIS # A8: 6,7 => CTR => A8: 3,5 * DIS # F8: 6,7 => CTR => F8: 3,5 * CNT 9 HDP CHAINS / 31 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C3: 5,7 => SOL * STA C3: 5,7 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 4..6..5.783..............1...8.91...2.....4......8.......4..3....1.......9....... | initial |
| 41263859783.1.92649...42813.48.91.3.2.93..4811.3.849...8.41.329.219...48.9482.1.. | autosolve |
| 412638597837159264965742813648591732259367481173284956786415329521973648394826175 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) C2: 5,7 E2: 5,7 D3: 5,7 B5: 5,7 G4: 6,7 H6: 5,7 G8: 6,7 H9: 5,7 I9: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D4,D6: 2.. / D4 = 2 => 14 pairs (_) / D6 = 2 => 12 pairs (_) I4,I6: 2.. / I4 = 2 => 12 pairs (_) / I6 = 2 => 14 pairs (_) D4,I4: 2.. / D4 = 2 => 14 pairs (_) / I4 = 2 => 12 pairs (_) D6,I6: 2.. / D6 = 2 => 12 pairs (_) / I6 = 2 => 14 pairs (_) A8,A9: 3.. / A8 = 3 => 11 pairs (_) / A9 = 3 => 10 pairs (_) F8,F9: 3.. / F8 = 3 => 10 pairs (_) / F9 = 3 => 11 pairs (_) A8,F8: 3.. / A8 = 3 => 11 pairs (_) / F8 = 3 => 10 pairs (_) A9,F9: 3.. / A9 = 3 => 10 pairs (_) / F9 = 3 => 11 pairs (_) E2,D3: 5.. / E2 = 5 => 0 pairs (*) / D3 = 5 => 0 pairs (X) H9,I9: 5.. / H9 = 5 => 14 pairs (_) / I9 = 5 => 16 pairs (_) C2,E2: 5.. / C2 = 5 => 0 pairs (X) / E2 = 5 => 0 pairs (_) H6,H9: 5.. / H6 = 5 => 16 pairs (_) / H9 = 5 => 14 pairs (_) B3,C3: 6.. / B3 = 6 => 0 pairs (*) / C3 = 6 => 0 pairs (X) A4,B6: 6.. / A4 = 6 => 0 pairs (*) / B6 = 6 => 0 pairs (X) E5,F5: 6.. / E5 = 6 => 11 pairs (_) / F5 = 6 => 16 pairs (_) G8,I9: 6.. / G8 = 6 => 16 pairs (_) / I9 = 6 => 14 pairs (_) B6,I6: 6.. / B6 = 6 => 13 pairs (_) / I6 = 6 => 0 pairs (*) B3,B6: 6.. / B3 = 6 => 0 pairs (*) / B6 = 6 => 0 pairs (X) C3,C7: 6.. / C3 = 6 => 13 pairs (_) / C7 = 6 => 0 pairs (*) E5,E8: 6.. / E5 = 6 => 11 pairs (_) / E8 = 6 => 16 pairs (_) G4,G8: 6.. / G4 = 6 => 14 pairs (_) / G8 = 6 => 16 pairs (_) E2,D3: 7.. / E2 = 7 => 0 pairs (X) / D3 = 7 => 0 pairs (_) G4,H6: 7.. / G4 = 7 => 16 pairs (_) / H6 = 7 => 14 pairs (_) G8,H9: 7.. / G8 = 7 => 14 pairs (_) / H9 = 7 => 16 pairs (_) C2,E2: 7.. / C2 = 7 => 0 pairs (*) / E2 = 7 => 0 pairs (X) G4,G8: 7.. / G4 = 7 => 16 pairs (_) / G8 = 7 => 14 pairs (_) H6,H9: 7.. / H6 = 7 => 14 pairs (_) / H9 = 7 => 16 pairs (_) * DURATION: 0:00:48.326246 START: 15:51:50.740170 END: 15:52:39.066416 2017-05-04 * CP COUNT: (27) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,C2,D3,E2,G4,G8,H6,H9,I9) * 41263859783.1.92649...42813.48.91.3.2.93..4811.3.849...8.41.329.219...48.9482.1.. * PAIR C2: 5,7 BLK 1 B3: 5,7,6 # reduction candidate for 5,7 B3: 5,7 # 13 pairs C3: 5,7,6 # reduction candidate for 5,7 C3: 5,7 => SOLVED * 412638597837159264965742813648591732259367481173284956786415329521973648394826175 C3: 6 # 13 pairs * PAIR C2: 5,7 COL C C7: 5,7,6 # reduction candidate for 5,7 C7: 6 => SOLVED * 412638597837159264965742813648591732259367481173284956786415329521973648394826175 C7: 5,7 # 13 pairs * PAIR E2: 5,7 COL E E5: 5,7,6 # reduction candidate for 5,7 E5: 5,7 # 16 pairs E8: 5,7,6 # reduction candidate for 5,7 E8: 5,7 # 11 pairs * PAIR D3: 5,7 ROW 3 B3: 5,7,6 # reduction candidate for 5,7 B3: 5,7 # 13 pairs C3: 5,7,6 # reduction candidate for 5,7 C3: 5,7 => SOLVED * 412638597837159264965742813648591732259367481173284956786415329521973648394826175 C3: 6 # 13 pairs * PAIR D3: 5,7 COL D D4: 5,7,2 # reduction candidate for 5,7 D4: 5,7 # 12 pairs D6: 5,7,2 # reduction candidate for 5,7 D6: 5,7 # 14 pairs * PAIR B5: 5,7 BLK 4 A4: 5,7,6 # reduction candidate for 5,7 A4: 5,7 # 13 pairs B6: 5,7,6 # reduction candidate for 5,7 B6: 5,7 => SOLVED * 412638597837159264965742813648591732259367481173284956786415329521973648394826175 B6: 6 # 13 pairs * PAIR B5: 5,7 ROW 5 E5: 5,7,6 # reduction candidate for 5,7 E5: 5,7 # 16 pairs F5: 5,7,6 # reduction candidate for 5,7 F5: 5,7 # 11 pairs * PAIR B5: 5,7 COL B B3: 5,7,6 # reduction candidate for 5,7 B3: 6 => SOLVED * 412638597837159264965742813648591732259367481173284956786415329521973648394826175 B3: 5,7 # 13 pairs * PAIR G4: 6,7 ROW 4 A4: 6,7,5 # reduction candidate for 6,7 A4: 5 => CTR * 412638597837159264956742813548291736279365481163.849...8541.329.219...48.9482.1.. A4: 6,7 # 14 pairs * PAIR H6: 5,7 ROW 6 B6: 5,7,6 # reduction candidate for 5,7 B6: 5,7 => SOLVED * 412638597837159264965742813648591732259367481173284956786415329521973648394826175 B6: 6 # 13 pairs D6: 5,7,2 # reduction candidate for 5,7 D6: 5,7 # 14 pairs * PAIR G8: 6,7 ROW 8 A8: 6,7,3,5 # reduction candidate for 6,7 A8: 6,7 => CTR * 4126385978351792649..542813.48.91.3.2.9365481153.84976.8.41.329.21953.4839482.1.. A8: 3,5 # 10 pairs E8: 6,7,5 # reduction candidate for 6,7 E8: 6,7 # 13 pairs F8: 6,7,3,5 # reduction candidate for 6,7 F8: 6,7 => CTR * 4126385978351792649..542813.48.91.3.2.9365481153.84976.8.41.32932195..48.948231.. F8: 3,5 # 10 pairs * PAIR I9: 5,6 COL I I4: 5,6,2 # reduction candidate for 5,6 I4: 5,6 # 14 pairs I6: 5,6,2 # reduction candidate for 5,6 I6: 5,6 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-380-base-pr-000.dot * REASONING * PRF # C3: 5,7 => SOL * PRF # C7: 6 => SOL * PRF # C3: 5,7 => SOL * PRF # B6: 5,7 => SOL * PRF # B3: 6 => SOL * DIS # A4: 5 => CTR => A4: 6,7 * PRF # B6: 5,7 => SOL * DIS # A8: 6,7 => CTR => A8: 3,5 * DIS # F8: 6,7 => CTR => F8: 3,5 * CNT 9 HDP CHAINS / 31 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,C2,D3,E2,G4,G8,H6,H9,I9) * 41263859783.1.92649...42813.48.91.3.2.93..4811.3.849...8.41.329.219...48.9482.1.. * PAIR C2: 5,7 BLK 1 B3: 5,7,6 # reduction candidate for 5,7 B3: 5,7 # 13 pairs C3: 5,7,6 # reduction candidate for 5,7 C3: 5,7 => SOLVED * 412638597837159264965742813648591732259367481173284956786415329521973648394826175 * DURATION: 0:00:02.968964 START: 15:53:10.725171 END: 15:53:13.694135 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-380-base-pr-001.dot * REASONING * PRF # C3: 5,7 => SOL * STA C3: 5,7 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 380 solution: 412638597837159264965742813648591732259367481173284956786415329521973648394826175 info: 32793 FNBO S8.f 39511 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 412638597837159264965742813648591732259367481173284956786415329521973648394826175 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: 5,7 => UNS * PRF # C3: 5,7 => SOL * INC # C3: 6 => UNS * INC # C7: 5,7 => UNS * PRF # C7: 6 => SOL * INC # E5: 5,7 => UNS * INC # E8: 5,7 => UNS * INC # B3: 5,7 => UNS * PRF # C3: 5,7 => SOL * INC # C3: 6 => UNS * INC # D4: 5,7 => UNS * INC # D6: 5,7 => UNS * INC # A4: 5,7 => UNS * PRF # B6: 5,7 => SOL * INC # B6: 6 => UNS * INC # E5: 5,7 => UNS * INC # F5: 5,7 => UNS * INC # B3: 5,7 => UNS * PRF # B3: 6 => SOL * INC # A4: 6,7 => UNS * DIS # A4: 5 => CTR => A4: 6,7 * PRF # B6: 5,7 => SOL * INC # B6: 6 => UNS * INC # D6: 5,7 => UNS * DIS # A8: 6,7 => CTR => A8: 3,5 * INC # A8: 3,5 => UNS * INC # E8: 6,7 => UNS * DIS # F8: 6,7 => CTR => F8: 3,5 * INC # F8: 3,5 => UNS * INC # I4: 5,6 => UNS * INC # I6: 5,6 => UNS * CNT 31 HDP CHAINS / 31 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B3: 5,7 => UNS * PRF # C3: 5,7 => SOL * STA C3: 5,7 * CNT 2 HDP CHAINS / 2 HYP OPENED