Analysis of xx-top500-248-base.sdk
Contents
Original Sudoku
level: medium
position: 7...1.....9.....8..........6.....1.2.4.8.9......3.....1.2...6..5......9....4..... initial
Autosolve
position: 723.184.94962...81815.9432.689.4.132341829...2573619481.298.6.45641.289.9.84.621. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # H5: 5,6 => SOL * DIS # H5: 7 => CTR => H5: 5,6 * DIS # F2: 5,7 => CTR => F2: 3 * PRF # I5: 6,7 => SOL * DIS # I5: 5 => CTR => I5: 6,7 * DIS # F2: 5,7 => CTR => F2: 3 * DIS # H5: 5,7 => CTR => H5: 6 * PRF # H5: 6 => SOL * PRF # I5: 5,7 => SOL * DIS # I5: 6 => CTR => I5: 5,7 * DIS # F7: 3,7 => CTR => F7: 5 * PRF # F7: 5 => SOL * PRF # E9: 3,7 => SOL * DIS # E9: 5 => CTR => E9: 3,7 * DIS # I9: 3,7 => CTR => I9: 5 * PRF # I9: 5 => SOL * DIS # F7: 3,7 => CTR => F7: 5 * PRF # F7: 5 => SOL * PRF # E9: 3,7 => SOL * DIS # E9: 5 => CTR => E9: 3,7 * DIS # E2: 3,7 => CTR => E2: 5 * PRF # E2: 5 => SOL * DIS # I9: 3 => CTR => I9: 5,7 * DIS # F7: 3 => CTR => F7: 5,7 * DIS # H5: 5,7 => CTR => H5: 6 * PRF # H5: 6 => SOL * DIS # I9: 3,7 => CTR => I9: 5 * PRF # I9: 5 => SOL * CNT 28 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # H5: 5,6 => SOL * STA H5: 5,6 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 7...1.....9.....8..........6.....1.2.4.8.9......3.....1.2...6..5......9....4..... | initial |
| 723.184.94962...81815.9432.689.4.132341829...2573619481.298.6.45641.289.9.84.621. | autosolve |
| 723618459496253781815794326689547132341829567257361948132985674564172893978436215 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) D1: 5,6 D3: 6,7 H1: 5,6 G2: 5,7 I3: 6,7 D4: 5,7 F4: 5,7 G5: 5,7 B7: 3,7 B9: 3,7 E8: 3,7 H7: 5,7 I8: 3,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,F2: 3.. / E2 = 3 => 0 pairs (X) / F2 = 3 => 15 pairs (_) B7,B9: 3.. / B7 = 3 => 15 pairs (_) / B9 = 3 => 0 pairs (X) I8,I9: 3.. / I8 = 3 => 15 pairs (_) / I9 = 3 => 0 pairs (X) B7,F7: 3.. / B7 = 3 => 15 pairs (_) / F7 = 3 => 0 pairs (X) E8,I8: 3.. / E8 = 3 => 0 pairs (X) / I8 = 3 => 15 pairs (_) F2,F7: 3.. / F2 = 3 => 15 pairs (_) / F7 = 3 => 0 pairs (X) H1,G2: 5.. / H1 = 5 => 0 pairs (*) / G2 = 5 => 0 pairs (X) D4,F4: 5.. / D4 = 5 => 0 pairs (*) / F4 = 5 => 0 pairs (X) F7,E9: 5.. / F7 = 5 => 0 pairs (*) / E9 = 5 => 0 pairs (X) H7,I9: 5.. / H7 = 5 => 0 pairs (X) / I9 = 5 => 0 pairs (_) D1,H1: 5.. / D1 = 5 => 0 pairs (X) / H1 = 5 => 0 pairs (_) F7,H7: 5.. / F7 = 5 => 0 pairs (*) / H7 = 5 => 0 pairs (X) E9,I9: 5.. / E9 = 5 => 0 pairs (X) / I9 = 5 => 0 pairs (_) D1,D4: 5.. / D1 = 5 => 0 pairs (X) / D4 = 5 => 0 pairs (_) E2,E9: 5.. / E2 = 5 => 0 pairs (*) / E9 = 5 => 0 pairs (X) G2,G5: 5.. / G2 = 5 => 0 pairs (X) / G5 = 5 => 0 pairs (_) I5,I9: 5.. / I5 = 5 => 0 pairs (X) / I9 = 5 => 0 pairs (_) D1,D3: 6.. / D1 = 6 => 0 pairs (*) / D3 = 6 => 0 pairs (X) H1,I3: 6.. / H1 = 6 => 0 pairs (X) / I3 = 6 => 0 pairs (_) H5,I5: 6.. / H5 = 6 => 0 pairs (*) / I5 = 6 => 0 pairs (X) D1,H1: 6.. / D1 = 6 => 0 pairs (*) / H1 = 6 => 0 pairs (X) D3,I3: 6.. / D3 = 6 => 0 pairs (X) / I3 = 6 => 0 pairs (_) H1,H5: 6.. / H1 = 6 => 0 pairs (X) / H5 = 6 => 0 pairs (_) I3,I5: 6.. / I3 = 6 => 0 pairs (*) / I5 = 6 => 0 pairs (X) G2,I3: 7.. / G2 = 7 => 0 pairs (*) / I3 = 7 => 0 pairs (X) D4,F4: 7.. / D4 = 7 => 0 pairs (X) / F4 = 7 => 0 pairs (_) B7,B9: 7.. / B7 = 7 => 0 pairs (X) / B9 = 7 => 15 pairs (_) D3,I3: 7.. / D3 = 7 => 0 pairs (*) / I3 = 7 => 0 pairs (X) E8,I8: 7.. / E8 = 7 => 15 pairs (_) / I8 = 7 => 0 pairs (X) D3,D4: 7.. / D3 = 7 => 0 pairs (*) / D4 = 7 => 0 pairs (X) G2,G5: 7.. / G2 = 7 => 0 pairs (*) / G5 = 7 => 0 pairs (X) H5,H7: 7.. / H5 = 7 => 0 pairs (X) / H7 = 7 => 0 pairs (_) * DURATION: 0:00:53.728771 START: 11:15:56.780368 END: 11:16:50.509139 2017-05-04 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,B9,D1,D3,D4,E8,F4,G2,G5,H1,H7,I3,I8) * 723.184.94962...81815.9432.689.4.132341829...2573619481.298.6.45641.289.9.84.621. * PAIR H1: 5,6 COL H H5: 5,6,7 # reduction candidate for 5,6 H5: 5,6 => SOLVED * 723618459496253781815794326689547132341829567257361948132985674564172893978436215 H5: 7 => CTR * 723.184694962..581815694327689.4.132341829...2573619481.298.6.45641.289.9.84.621. * PAIR G2: 5,7 ROW 2 E2: 5,7,3 # reduction candidate for 5,7 E2: 5,7 # 15 pairs F2: 5,7,3 # reduction candidate for 5,7 F2: 5,7 => CTR * 723.184.949623..81815.9432.689.4.132341829...2573619481.2983654564172893938456217 F2: 3 # 15 pairs * PAIR I3: 6,7 COL I I5: 6,7,5 # reduction candidate for 6,7 I5: 6,7 => SOLVED * 723618459496253781815794326689547132341829567257361948132985674564172893978436215 I5: 5 => CTR * 723.184.94962...81815.94326689.4.132341829.652573619481.298.6.45641.289.9.84.621. * PAIR F4: 5,7 COL F F2: 5,7,3 # reduction candidate for 5,7 F2: 5,7 => CTR * 723.184.949623..81815.9432.689.4.132341829...2573619481.2983654564172893938456217 F2: 3 # 15 pairs F7: 5,7,3 # reduction candidate for 5,7 F7: 5,7 # 15 pairs * PAIR G5: 5,7 BLK 6 H5: 5,7,6 # reduction candidate for 5,7 H5: 5,7 => CTR * 723.184694962..58181569432768974513234182975.2573619481.298.6.45641.289.9.84.621. H5: 6 => SOLVED * 723618459496253781815794326689547132341829567257361948132985674564172893978436215 I5: 5,7,6 # reduction candidate for 5,7 I5: 5,7 => SOLVED * 723618459496253781815794326689547132341829567257361948132985674564172893978436215 I5: 6 => CTR * 723.1846949625..81815.9432.689.4.132341829..62573619481.298.6.45641.289.9.84.6215 * PAIR B7: 3,7 ROW 7 F7: 3,7,5 # reduction candidate for 3,7 F7: 3,7 => CTR * 7235184694962..581815694327689.4.132341829...2573619481.298.6545641.289.9.845621. F7: 5 => SOLVED * 723618459496253781815794326689547132341829567257361948132985674564172893978436215 * PAIR B9: 3,7 ROW 9 E9: 3,7,5 # reduction candidate for 3,7 E9: 3,7 => SOLVED * 723618459496253781815794326689547132341829567257361948132985674564172893978436215 E9: 5 => CTR * 723.184.94962...81815.9432.689.4.132341829..52573619481.298.6545641.289.9.845621. I9: 3,7,5 # reduction candidate for 3,7 I9: 3,7 => CTR * 723.184.94962...81815.9432.689.4.132341829..52573619481.298.6545641.289.9.845621. I9: 5 => SOLVED * 723618459496253781815794326689547132341829567257361948132985674564172893978436215 * PAIR E8: 3,7 BLK 8 F7: 3,7,5 # reduction candidate for 3,7 F7: 3,7 => CTR * 7235184694962..581815694327689.4.132341829...2573619481.298.6545641.289.9.845621. F7: 5 => SOLVED * 723618459496253781815794326689547132341829567257361948132985674564172893978436215 E9: 3,7,5 # reduction candidate for 3,7 E9: 3,7 => SOLVED * 723618459496253781815794326689547132341829567257361948132985674564172893978436215 E9: 5 => CTR * 723.184.94962...81815.9432.689.4.132341829..52573619481.298.6545641.289.9.845621. * PAIR E8: 3,7 COL E E2: 3,7,5 # reduction candidate for 3,7 E2: 3,7 => CTR * 723.184.94962...81815.9432.689.4.132341829..52573619481.298.6545641.289.9.845621. E2: 5 => SOLVED * 723618459496253781815794326689547132341829567257361948132985674564172893978436215 * PAIR H7: 5,7 BLK 9 I9: 5,7,3 # reduction candidate for 5,7 I9: 3 => CTR * 723.184.94962...81815.9432.689.4.132341829..52573619481.298.6545641.28979.8456213 I9: 5,7 # 15 pairs * PAIR H7: 5,7 ROW 7 F7: 5,7,3 # reduction candidate for 5,7 F7: 3 => CTR * 723.184.94962...81815.9432.689.4.132341829...2573619481.2983654564172893938456217 F7: 5,7 # 15 pairs * PAIR H7: 5,7 COL H H5: 5,7,6 # reduction candidate for 5,7 H5: 5,7 => CTR * 723.184694962..58181569432768974513234182975.2573619481.298.6.45641.289.9.84.621. H5: 6 => SOLVED * 723618459496253781815794326689547132341829567257361948132985674564172893978436215 * PAIR I8: 3,7 BLK 9 I9: 3,7,5 # reduction candidate for 3,7 I9: 3,7 => CTR * 723.184.94962...81815.9432.689.4.132341829..52573619481.298.6545641.289.9.845621. I9: 5 => SOLVED * 723618459496253781815794326689547132341829567257361948132985674564172893978436215 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-248-base-pr-000.dot * REASONING * PRF # H5: 5,6 => SOL * DIS # H5: 7 => CTR => H5: 5,6 * DIS # F2: 5,7 => CTR => F2: 3 * PRF # I5: 6,7 => SOL * DIS # I5: 5 => CTR => I5: 6,7 * DIS # F2: 5,7 => CTR => F2: 3 * DIS # H5: 5,7 => CTR => H5: 6 * PRF # H5: 6 => SOL * PRF # I5: 5,7 => SOL * DIS # I5: 6 => CTR => I5: 5,7 * DIS # F7: 3,7 => CTR => F7: 5 * PRF # F7: 5 => SOL * PRF # E9: 3,7 => SOL * DIS # E9: 5 => CTR => E9: 3,7 * DIS # I9: 3,7 => CTR => I9: 5 * PRF # I9: 5 => SOL * DIS # F7: 3,7 => CTR => F7: 5 * PRF # F7: 5 => SOL * PRF # E9: 3,7 => SOL * DIS # E9: 5 => CTR => E9: 3,7 * DIS # E2: 3,7 => CTR => E2: 5 * PRF # E2: 5 => SOL * DIS # I9: 3 => CTR => I9: 5,7 * DIS # F7: 3 => CTR => F7: 5,7 * DIS # H5: 5,7 => CTR => H5: 6 * PRF # H5: 6 => SOL * DIS # I9: 3,7 => CTR => I9: 5 * PRF # I9: 5 => SOL * CNT 28 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,B9,D1,D3,D4,E8,F4,G2,G5,H1,H7,I3,I8) * 723.184.94962...81815.9432.689.4.132341829...2573619481.298.6.45641.289.9.84.621. * PAIR H1: 5,6 COL H H5: 5,6,7 # reduction candidate for 5,6 H5: 5,6 => SOLVED * 723618459496253781815794326689547132341829567257361948132985674564172893978436215 * DURATION: 0:00:01.987876 START: 11:17:27.374482 END: 11:17:29.362358 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-248-base-pr-001.dot * REASONING * PRF # H5: 5,6 => SOL * STA H5: 5,6 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 248 solution: 723618459496253781815794326689547132341829567257361948132985674564172893978436215 info: 2072 FNBWXY S8.f 36589 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 723618459496253781815794326689547132341829567257361948132985674564172893978436215 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:
* PRF # H5: 5,6 => SOL * DIS # H5: 7 => CTR => H5: 5,6 * INC # E2: 5,7 => UNS * DIS # F2: 5,7 => CTR => F2: 3 * INC # F2: 3 => UNS * PRF # I5: 6,7 => SOL * DIS # I5: 5 => CTR => I5: 6,7 * DIS # F2: 5,7 => CTR => F2: 3 * INC # F2: 3 => UNS * INC # F7: 5,7 => UNS * DIS # H5: 5,7 => CTR => H5: 6 * PRF # H5: 6 => SOL * PRF # I5: 5,7 => SOL * DIS # I5: 6 => CTR => I5: 5,7 * DIS # F7: 3,7 => CTR => F7: 5 * PRF # F7: 5 => SOL * PRF # E9: 3,7 => SOL * DIS # E9: 5 => CTR => E9: 3,7 * DIS # I9: 3,7 => CTR => I9: 5 * PRF # I9: 5 => SOL * DIS # F7: 3,7 => CTR => F7: 5 * PRF # F7: 5 => SOL * PRF # E9: 3,7 => SOL * DIS # E9: 5 => CTR => E9: 3,7 * DIS # E2: 3,7 => CTR => E2: 5 * PRF # E2: 5 => SOL * INC # I9: 5,7 => UNS * DIS # I9: 3 => CTR => I9: 5,7 * INC # F7: 5,7 => UNS * DIS # F7: 3 => CTR => F7: 5,7 * DIS # H5: 5,7 => CTR => H5: 6 * PRF # H5: 6 => SOL * DIS # I9: 3,7 => CTR => I9: 5 * PRF # I9: 5 => SOL * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # H5: 5,6 => SOL * STA H5: 5,6 * CNT 1 HDP CHAINS / 1 HYP OPENED