Analysis of xx-top500-353-base.sdk
Contents
Original Sudoku
level: medium
position: .2....7.54..3........6.....5.....1..6.3.........8......8..7...........46....5..3. initial
Autosolve
position: 32..487654673.5.8.85.6273.45.876.1236.35.2478.7.83.659.864735..735.8..46....56837 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D8: 1,9 => CTR => D8: 2 * PRF # D8: 2 => SOL * PRF # A9: 1,2 => SOL * DIS # A9: 9 => CTR => A9: 1,2 * PRF # A9: 2,9 => SOL * DIS # A9: 1 => CTR => A9: 2,9 * DIS # D8: 1,9 => CTR => D8: 2 * PRF # D8: 2 => SOL * PRF # D8: 2,9 => SOL * DIS # D8: 1 => CTR => D8: 2,9 * PRF # A9: 2,9 => SOL * DIS # A9: 1 => CTR => A9: 2,9 * PRF # D8: 2,9 => SOL * DIS # D8: 1 => CTR => D8: 2,9 * CNT 14 HDP CHAINS / 14 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D8: 1,9 => CTR => D8: 2 * PRF D8: 2 => SOL * STA D8: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2....7.54..3........6.....5.....1..6.3.........8......8..7...........46....5..3. | initial |
| 32..487654673.5.8.85.6273.45.876.1236.35.2478.7.83.659.864735..735.8..46....56837 | autosolve |
| 329148765467395281851627394548769123693512478172834659986473512735281946214956837 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (22) C1: 1,9 C3: 1,9 D1: 1,9 E2: 1,9 G2: 2,9 I2: 1,2 H3: 1,9 B4: 4,9 B5: 1,9 A6: 1,2 C6: 2,4 F4: 4,9 E5: 1,9 F6: 1,4 A7: 2,9 B9: 1,4 C9: 2,4 F8: 1,9 D9: 2,9 H7: 1,9 I7: 1,2 G8: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,C3: 1.. / C1 = 1 => 0 pairs (X) / C3 = 1 => 0 pairs (_) D1,E2: 1.. / D1 = 1 => 0 pairs (*) / E2 = 1 => 0 pairs (X) I2,H3: 1.. / I2 = 1 => 0 pairs (*) / H3 = 1 => 0 pairs (X) B5,A6: 1.. / B5 = 1 => 0 pairs (X) / A6 = 1 => 0 pairs (_) E5,F6: 1.. / E5 = 1 => 0 pairs (*) / F6 = 1 => 0 pairs (X) A9,B9: 1.. / A9 = 1 => 0 pairs (X) / B9 = 1 => 0 pairs (_) D8,F8: 1.. / D8 = 1 => 0 pairs (X) / F8 = 1 => 0 pairs (_) H7,I7: 1.. / H7 = 1 => 0 pairs (*) / I7 = 1 => 0 pairs (X) C1,D1: 1.. / C1 = 1 => 0 pairs (X) / D1 = 1 => 0 pairs (_) E2,I2: 1.. / E2 = 1 => 0 pairs (X) / I2 = 1 => 0 pairs (_) C3,H3: 1.. / C3 = 1 => 0 pairs (*) / H3 = 1 => 0 pairs (X) B5,E5: 1.. / B5 = 1 => 0 pairs (X) / E5 = 1 => 0 pairs (_) A6,F6: 1.. / A6 = 1 => 0 pairs (*) / F6 = 1 => 0 pairs (X) A6,A9: 1.. / A6 = 1 => 0 pairs (*) / A9 = 1 => 0 pairs (X) B5,B9: 1.. / B5 = 1 => 0 pairs (X) / B9 = 1 => 0 pairs (_) D1,D8: 1.. / D1 = 1 => 0 pairs (*) / D8 = 1 => 0 pairs (X) E2,E5: 1.. / E2 = 1 => 0 pairs (X) / E5 = 1 => 0 pairs (_) F6,F8: 1.. / F6 = 1 => 0 pairs (X) / F8 = 1 => 0 pairs (_) H3,H7: 1.. / H3 = 1 => 0 pairs (X) / H7 = 1 => 0 pairs (_) I2,I7: 1.. / I2 = 1 => 0 pairs (*) / I7 = 1 => 0 pairs (X) G2,I2: 2.. / G2 = 2 => 0 pairs (*) / I2 = 2 => 0 pairs (X) A6,C6: 2.. / A6 = 2 => 0 pairs (X) / C6 = 2 => 0 pairs (_) D8,D9: 2.. / D8 = 2 => 0 pairs (*) / D9 = 2 => 0 pairs (X) I7,G8: 2.. / I7 = 2 => 0 pairs (*) / G8 = 2 => 0 pairs (X) A7,I7: 2.. / A7 = 2 => 0 pairs (X) / I7 = 2 => 0 pairs (_) D8,G8: 2.. / D8 = 2 => 0 pairs (*) / G8 = 2 => 0 pairs (X) C6,C9: 2.. / C6 = 2 => 0 pairs (*) / C9 = 2 => 0 pairs (X) G2,G8: 2.. / G2 = 2 => 0 pairs (*) / G8 = 2 => 0 pairs (X) I2,I7: 2.. / I2 = 2 => 0 pairs (X) / I7 = 2 => 0 pairs (_) B4,C6: 4.. / B4 = 4 => 0 pairs (*) / C6 = 4 => 0 pairs (X) F4,F6: 4.. / F4 = 4 => 0 pairs (X) / F6 = 4 => 0 pairs (_) B9,C9: 4.. / B9 = 4 => 0 pairs (X) / C9 = 4 => 0 pairs (_) B4,F4: 4.. / B4 = 4 => 0 pairs (*) / F4 = 4 => 0 pairs (X) C6,F6: 4.. / C6 = 4 => 0 pairs (X) / F6 = 4 => 0 pairs (_) B4,B9: 4.. / B4 = 4 => 0 pairs (*) / B9 = 4 => 0 pairs (X) C6,C9: 4.. / C6 = 4 => 0 pairs (X) / C9 = 4 => 0 pairs (_) C1,C3: 9.. / C1 = 9 => 0 pairs (*) / C3 = 9 => 0 pairs (X) D1,E2: 9.. / D1 = 9 => 0 pairs (X) / E2 = 9 => 0 pairs (_) G2,H3: 9.. / G2 = 9 => 0 pairs (X) / H3 = 9 => 0 pairs (_) B4,B5: 9.. / B4 = 9 => 0 pairs (X) / B5 = 9 => 0 pairs (_) F4,E5: 9.. / F4 = 9 => 0 pairs (*) / E5 = 9 => 0 pairs (X) A7,A9: 9.. / A7 = 9 => 0 pairs (*) / A9 = 9 => 0 pairs (X) H7,G8: 9.. / H7 = 9 => 0 pairs (X) / G8 = 9 => 0 pairs (_) C1,D1: 9.. / C1 = 9 => 0 pairs (*) / D1 = 9 => 0 pairs (X) E2,G2: 9.. / E2 = 9 => 0 pairs (*) / G2 = 9 => 0 pairs (X) C3,H3: 9.. / C3 = 9 => 0 pairs (X) / H3 = 9 => 0 pairs (_) B4,F4: 9.. / B4 = 9 => 0 pairs (X) / F4 = 9 => 0 pairs (_) B5,E5: 9.. / B5 = 9 => 0 pairs (*) / E5 = 9 => 0 pairs (X) A7,H7: 9.. / A7 = 9 => 0 pairs (*) / H7 = 9 => 0 pairs (X) A9,D9: 9.. / A9 = 9 => 0 pairs (X) / D9 = 9 => 0 pairs (_) E2,E5: 9.. / E2 = 9 => 0 pairs (*) / E5 = 9 => 0 pairs (X) F4,F8: 9.. / F4 = 9 => 0 pairs (*) / F8 = 9 => 0 pairs (X) G2,G8: 9.. / G2 = 9 => 0 pairs (X) / G8 = 9 => 0 pairs (_) H3,H7: 9.. / H3 = 9 => 0 pairs (*) / H7 = 9 => 0 pairs (X) * DURATION: 0:01:36.514254 START: 14:48:42.841288 END: 14:50:19.355542 2017-05-04 * CP COUNT: (54) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A7,B4,B5,B9,C1,C3,C6,C9,D1,D9,E2,E5,F4,F6,F8,G2,G8,H3,H7,I2,I7) * 32..487654673.5.8.85.6273.45.876.1236.35.2478.7.83.659.864735..735.8..46....56837 * PAIR D1: 1,9 COL D D8: 1,9,2 # reduction candidate for 1,9 D8: 1,9 => CTR * 32..487654673.59828596273145.876.1236.3592478.7283.659.864735..735.8.246...256837 D8: 2 => SOLVED * 329148765467395281851627394548769123693512478172834659986473512735281946214956837 * PAIR A6: 1,2 COL A A9: 1,2,9 # reduction candidate for 1,2 A9: 1,2 => SOLVED * 329148765467395281851627394548769123693512478172834659986473512735281946214956837 A9: 9 => CTR * 32.148765467395.8.85.6273.45.876.1236.35.2478172834659286473591735.81246914256837 * PAIR A7: 2,9 BLK 7 A9: 2,9,1 # reduction candidate for 2,9 A9: 2,9 => SOLVED * 329148765467395281851627394548769123693512478172834659986473512735281946214956837 A9: 1 => CTR * 32..487654673.5.8.85.6273.45.876.1236.35.2478.7.83.6599864735127352819461...56837 * PAIR F8: 1,9 BLK 8 D8: 1,9,2 # reduction candidate for 1,9 D8: 1,9 => CTR * 32..487654673.59828596273145.876.1236.3592478.7283.659.864735..735.8.246...256837 D8: 2 => SOLVED * 329148765467395281851627394548769123693512478172834659986473512735281946214956837 * PAIR D9: 2,9 BLK 8 D8: 2,9,1 # reduction candidate for 2,9 D8: 2,9 => SOLVED * 329148765467395281851627394548769123693512478172834659986473512735281946214956837 D8: 1 => CTR * 32..487654673.5.8.85.6273.45.876.1236.35.2478.7.83.659.864735..735189246914256837 * PAIR D9: 2,9 ROW 9 A9: 2,9,1 # reduction candidate for 2,9 A9: 2,9 => SOLVED * 329148765467395281851627394548769123693512478172834659986473512735281946214956837 A9: 1 => CTR * 32..487654673.5.8.85.6273.45.876.1236.35.2478.7.83.6599864735127352819461...56837 * PAIR G8: 2,9 ROW 8 D8: 2,9,1 # reduction candidate for 2,9 D8: 2,9 => SOLVED * 329148765467395281851627394548769123693512478172834659986473512735281946214956837 D8: 1 => CTR * 32..487654673.5.8.85.6273.45.876.1236.35.2478.7.83.659.864735..735189246914256837 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-353-base-pr-000.dot * REASONING * DIS # D8: 1,9 => CTR => D8: 2 * PRF # D8: 2 => SOL * PRF # A9: 1,2 => SOL * DIS # A9: 9 => CTR => A9: 1,2 * PRF # A9: 2,9 => SOL * DIS # A9: 1 => CTR => A9: 2,9 * DIS # D8: 1,9 => CTR => D8: 2 * PRF # D8: 2 => SOL * PRF # D8: 2,9 => SOL * DIS # D8: 1 => CTR => D8: 2,9 * PRF # A9: 2,9 => SOL * DIS # A9: 1 => CTR => A9: 2,9 * PRF # D8: 2,9 => SOL * DIS # D8: 1 => CTR => D8: 2,9 * CNT 14 HDP CHAINS / 14 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A7,B4,B5,B9,C1,C3,C6,C9,D1,D9,E2,E5,F4,F6,F8,G2,G8,H3,H7,I2,I7) * 32..487654673.5.8.85.6273.45.876.1236.35.2478.7.83.659.864735..735.8..46....56837 * PAIR D1: 1,9 COL D D8: 1,9,2 # reduction candidate for 1,9 D8: 1,9 => CTR * 32..487654673.59828596273145.876.1236.3592478.7283.659.864735..735.8.246...256837 D8: 2 => SOLVED * 329148765467395281851627394548769123693512478172834659986473512735281946214956837 * DURATION: 0:00:03.136621 START: 14:50:37.492542 END: 14:50:40.629163 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-353-base-pr-001.dot * REASONING * DIS # D8: 1,9 => CTR => D8: 2 * PRF D8: 2 => SOL * STA D8: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 353 solution: 329148765467395281851627394548769123693512478172834659986473512735281946214956837 info: 4885 FNBWY S8.f 16394 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 329148765467395281851627394548769123693512478172834659986473512735281946214956837 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 # D8: 1,9 => CTR => D8: 2 * PRF # D8: 2 => SOL * PRF # A9: 1,2 => SOL * DIS # A9: 9 => CTR => A9: 1,2 * PRF # A9: 2,9 => SOL * DIS # A9: 1 => CTR => A9: 2,9 * DIS # D8: 1,9 => CTR => D8: 2 * PRF # D8: 2 => SOL * PRF # D8: 2,9 => SOL * DIS # D8: 1 => CTR => D8: 2,9 * PRF # A9: 2,9 => SOL * DIS # A9: 1 => CTR => A9: 2,9 * PRF # D8: 2,9 => SOL * DIS # D8: 1 => CTR => D8: 2,9 * CNT 14 HDP CHAINS / 14 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D8: 1,9 => CTR => D8: 2 * PRF D8: 2 => SOL * STA D8: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED