Analysis of xx-top500-161-base.sdk
Contents
Original Sudoku
level: medium
position: ....8.2...5...3.........4......4.6...8.....3...57.....3......576..9........1..... initial
Autosolve
position: .7348.2652546.378.86.5724.3..23456787862..534435768...34.826.576.895734.5.71348.6 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I6: 1,9 => CTR => I6: 2 * PRF # I6: 2 => SOL * PRF # H6: 1,9 => SOL * DIS # H6: 2 => CTR => H6: 1,9 * PRF # H6: 1,9 => SOL * DIS # H6: 2 => CTR => H6: 1,9 * DIS # I6: 1,9 => CTR => I6: 2 * PRF # I6: 2 => SOL * PRF # I6: 1,2 => SOL * DIS # I6: 9 => CTR => I6: 1,2 * PRF # H6: 2,9 => SOL * DIS # H6: 1 => CTR => H6: 2,9 * CNT 12 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I6: 1,9 => CTR => I6: 2 * PRF I6: 2 => SOL * STA I6: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....8.2...5...3.........4......4.6...8.....3...57.....3......576..9........1..... | initial |
| .7348.2652546.378.86.5724.3..23456787862..534435768...34.826.576.895734.5.71348.6 | autosolve |
| 173489265254613789869572413912345678786291534435768192341826957628957341597134826 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) A1: 1,9 C3: 1,9 F1: 1,9 E2: 1,9 I2: 1,9 H3: 1,9 A4: 1,9 B4: 1,9 E5: 1,9 F5: 1,9 G6: 1,9 C7: 1,9 B8: 1,2 B9: 2,9 G7: 1,9 I8: 1,2 H9: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,C3: 1.. / A1 = 1 => 0 pairs (*) / C3 = 1 => 0 pairs (X) F1,E2: 1.. / F1 = 1 => 0 pairs (X) / E2 = 1 => 0 pairs (_) I2,H3: 1.. / I2 = 1 => 0 pairs (X) / H3 = 1 => 0 pairs (_) A4,B4: 1.. / A4 = 1 => 0 pairs (X) / B4 = 1 => 0 pairs (_) E5,F5: 1.. / E5 = 1 => 0 pairs (X) / F5 = 1 => 0 pairs (_) C7,B8: 1.. / C7 = 1 => 0 pairs (*) / B8 = 1 => 0 pairs (X) G7,I8: 1.. / G7 = 1 => 0 pairs (X) / I8 = 1 => 0 pairs (_) A1,F1: 1.. / A1 = 1 => 0 pairs (*) / F1 = 1 => 0 pairs (X) E2,I2: 1.. / E2 = 1 => 0 pairs (*) / I2 = 1 => 0 pairs (X) C3,H3: 1.. / C3 = 1 => 0 pairs (X) / H3 = 1 => 0 pairs (_) C7,G7: 1.. / C7 = 1 => 0 pairs (*) / G7 = 1 => 0 pairs (X) B8,I8: 1.. / B8 = 1 => 0 pairs (X) / I8 = 1 => 0 pairs (_) A1,A4: 1.. / A1 = 1 => 0 pairs (*) / A4 = 1 => 0 pairs (X) B4,B8: 1.. / B4 = 1 => 0 pairs (*) / B8 = 1 => 0 pairs (X) C3,C7: 1.. / C3 = 1 => 0 pairs (X) / C7 = 1 => 0 pairs (_) E2,E5: 1.. / E2 = 1 => 0 pairs (*) / E5 = 1 => 0 pairs (X) F1,F5: 1.. / F1 = 1 => 0 pairs (X) / F5 = 1 => 0 pairs (_) G6,G7: 1.. / G6 = 1 => 0 pairs (*) / G7 = 1 => 0 pairs (X) H3,H6: 1.. / H3 = 1 => 0 pairs (*) / H6 = 1 => 0 pairs (X) H6,I6: 2.. / H6 = 2 => 0 pairs (X) / I6 = 2 => 0 pairs (_) B8,B9: 2.. / B8 = 2 => 0 pairs (*) / B9 = 2 => 0 pairs (X) I8,H9: 2.. / I8 = 2 => 0 pairs (X) / H9 = 2 => 0 pairs (_) B8,I8: 2.. / B8 = 2 => 0 pairs (*) / I8 = 2 => 0 pairs (X) B9,H9: 2.. / B9 = 2 => 0 pairs (X) / H9 = 2 => 0 pairs (_) H6,H9: 2.. / H6 = 2 => 0 pairs (X) / H9 = 2 => 0 pairs (_) I6,I8: 2.. / I6 = 2 => 0 pairs (*) / I8 = 2 => 0 pairs (X) A1,C3: 9.. / A1 = 9 => 0 pairs (X) / C3 = 9 => 0 pairs (_) F1,E2: 9.. / F1 = 9 => 0 pairs (*) / E2 = 9 => 0 pairs (X) I2,H3: 9.. / I2 = 9 => 0 pairs (*) / H3 = 9 => 0 pairs (X) A4,B4: 9.. / A4 = 9 => 0 pairs (*) / B4 = 9 => 0 pairs (X) E5,F5: 9.. / E5 = 9 => 0 pairs (*) / F5 = 9 => 0 pairs (X) C7,B9: 9.. / C7 = 9 => 0 pairs (X) / B9 = 9 => 0 pairs (_) G7,H9: 9.. / G7 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) A1,F1: 9.. / A1 = 9 => 0 pairs (X) / F1 = 9 => 0 pairs (_) E2,I2: 9.. / E2 = 9 => 0 pairs (X) / I2 = 9 => 0 pairs (_) C3,H3: 9.. / C3 = 9 => 0 pairs (*) / H3 = 9 => 0 pairs (X) C7,G7: 9.. / C7 = 9 => 0 pairs (X) / G7 = 9 => 0 pairs (_) B9,H9: 9.. / B9 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) A1,A4: 9.. / A1 = 9 => 0 pairs (X) / A4 = 9 => 0 pairs (_) B4,B9: 9.. / B4 = 9 => 0 pairs (X) / B9 = 9 => 0 pairs (_) C3,C7: 9.. / C3 = 9 => 0 pairs (*) / C7 = 9 => 0 pairs (X) E2,E5: 9.. / E2 = 9 => 0 pairs (X) / E5 = 9 => 0 pairs (_) F1,F5: 9.. / F1 = 9 => 0 pairs (*) / F5 = 9 => 0 pairs (X) G6,G7: 9.. / G6 = 9 => 0 pairs (X) / G7 = 9 => 0 pairs (_) I2,I6: 9.. / I2 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) * DURATION: 0:01:28.584465 START: 08:15:08.144562 END: 08:16:36.729027 2017-05-04 * CP COUNT: (45) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B4,B8,B9,C3,C7,E2,E5,F1,F5,G6,G7,H3,H9,I2,I8) * .7348.2652546.378.86.5724.3..23456787862..534435768...34.826.576.895734.5.71348.6 * PAIR I2: 1,9 COL I I6: 1,9,2 # reduction candidate for 1,9 I6: 1,9 => CTR * .7348.2652546.37898695724139123456787862..534435768.2.34.826.576.8957342527134896 I6: 2 => SOLVED * 173489265254613789869572413912345678786291534435768192341826957628957341597134826 * PAIR H3: 1,9 COL H H6: 1,9,2 # reduction candidate for 1,9 H6: 1,9 => SOLVED * 173489265254613789869572413912345678786291534435768192341826957628957341597134826 H6: 2 => CTR * .7348.2652546.378.86.572413..23456787862..534435768.2.3418269576.895734.5.71348.6 * PAIR G6: 1,9 BLK 6 H6: 1,9,2 # reduction candidate for 1,9 H6: 1,9 => SOLVED * 173489265254613789869572413912345678786291534435768192341826957628957341597134826 H6: 2 => CTR * .7348.2652546.378.86.572413..23456787862..534435768.2.3418269576.895734.5.71348.6 I6: 1,9,2 # reduction candidate for 1,9 I6: 1,9 => CTR * .7348.2652546.37898695724139123456787862..534435768.2.34.826.576.8957342527134896 I6: 2 => SOLVED * 173489265254613789869572413912345678786291534435768192341826957628957341597134826 * PAIR I8: 1,2 COL I I6: 1,2,9 # reduction candidate for 1,2 I6: 1,2 => SOLVED * 173489265254613789869572413912345678786291534435768192341826957628957341597134826 I6: 9 => CTR * .7348.2652546.378.86.5724.3..23456787862..534435768.2934.8269576.895734.5.71348.6 * PAIR H9: 2,9 COL H H6: 2,9,1 # reduction candidate for 2,9 H6: 2,9 => SOLVED * 173489265254613789869572413912345678786291534435768192341826957628957341597134826 H6: 1 => CTR * .7348.2652546.378.86.5724.3..23456787862..534435768.1234.8261576.895734.5.71348.6 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-161-base-pr-000.dot * REASONING * DIS # I6: 1,9 => CTR => I6: 2 * PRF # I6: 2 => SOL * PRF # H6: 1,9 => SOL * DIS # H6: 2 => CTR => H6: 1,9 * PRF # H6: 1,9 => SOL * DIS # H6: 2 => CTR => H6: 1,9 * DIS # I6: 1,9 => CTR => I6: 2 * PRF # I6: 2 => SOL * PRF # I6: 1,2 => SOL * DIS # I6: 9 => CTR => I6: 1,2 * PRF # H6: 2,9 => SOL * DIS # H6: 1 => CTR => H6: 2,9 * CNT 12 HDP CHAINS / 12 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B4,B8,B9,C3,C7,E2,E5,F1,F5,G6,G7,H3,H9,I2,I8) * .7348.2652546.378.86.5724.3..23456787862..534435768...34.826.576.895734.5.71348.6 * PAIR I2: 1,9 COL I I6: 1,9,2 # reduction candidate for 1,9 I6: 1,9 => CTR * .7348.2652546.37898695724139123456787862..534435768.2.34.826.576.8957342527134896 I6: 2 => SOLVED * 173489265254613789869572413912345678786291534435768192341826957628957341597134826 * DURATION: 0:00:03.406077 START: 08:16:53.996517 END: 08:16:57.402594 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-161-base-pr-001.dot * REASONING * DIS # I6: 1,9 => CTR => I6: 2 * PRF I6: 2 => SOL * STA I6: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 161 solution: 173489265254613789869572413912345678786291534435768192341826957628957341597134826 info: 1819 FNBTWX S8.f 46441 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 173489265254613789869572413912345678786291534435768192341826957628957341597134826 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 # I6: 1,9 => CTR => I6: 2 * PRF # I6: 2 => SOL * PRF # H6: 1,9 => SOL * DIS # H6: 2 => CTR => H6: 1,9 * PRF # H6: 1,9 => SOL * DIS # H6: 2 => CTR => H6: 1,9 * DIS # I6: 1,9 => CTR => I6: 2 * PRF # I6: 2 => SOL * PRF # I6: 1,2 => SOL * DIS # I6: 9 => CTR => I6: 1,2 * PRF # H6: 2,9 => SOL * DIS # H6: 1 => CTR => H6: 2,9 * CNT 12 HDP CHAINS / 12 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # I6: 1,9 => CTR => I6: 2 * PRF I6: 2 => SOL * STA I6: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED