Analysis of xx-top500-259-base.sdk
Contents
Original Sudoku
level: medium
position: .7.3.....5......1......9.5..2....7.8...61.....4.......6..7..2..1.9............... initial
Autosolve
position: 97.351...56.4..91.41..69.57321945768.9561.....46...19565479.2.11.9524.7.2.71.6549 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C2: 2,8 => SOL * DIS # C2: 3 => CTR => C2: 2,8 * DIS # C3: 2,8 => CTR => C3: 3 * PRF # C3: 3 => SOL * PRF # F2: 7,8 => SOL * DIS # F2: 2 => CTR => F2: 7,8 * DIS # E6: 7,8 => CTR => E6: 3 * PRF # E6: 3 => SOL * DIS # F2: 7 => CTR => F2: 2,8 * DIS # C3: 2,8 => CTR => C3: 3 * PRF # C3: 3 => SOL * PRF # C2: 2,3 => SOL * DIS # C2: 8 => CTR => C2: 2,3 * DIS # I5: 4 => CTR => I5: 2,3 * PRF # C3: 3,8 => SOL * DIS # C3: 2 => CTR => C3: 3,8 * DIS # G8: 6 => CTR => G8: 3,8 * DIS # E6: 7,8 => CTR => E6: 3 * PRF # E6: 3 => SOL * DIS # F6: 7,8 => CTR => F6: 2,3 * DIS # E6: 7,8 => CTR => E6: 3 * PRF # E6: 3 => SOL * DIS # F6: 7,8 => CTR => F6: 2,3 * PRF # F2: 7,8 => SOL * DIS # F2: 2 => CTR => F2: 7,8 * PRF # F6: 2,8 => SOL * DIS # F6: 3,7 => CTR => F6: 2,8 * DIS # I5: 3,4 => CTR => I5: 2 * PRF # I5: 2 => SOL * DIS # I5: 4 => CTR => I5: 2,3 * DIS # G8: 6 => CTR => G8: 3,8 * DIS # F6: 3,8 => CTR => F6: 2,7 * PRF # F6: 2,7 => SOL * DIS # E6: 7 => CTR => E6: 3,8 * DIS # G8: 6 => CTR => G8: 3,8 * PRF # G8: 3,6 => SOL * DIS # G8: 8 => CTR => G8: 3,6 * CNT 37 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C2: 2,8 => SOL * STA C2: 2,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .7.3.....5......1......9.5..2....7.8...61.....4.......6..7..2..1.9............... | initial |
| 97.351...56.4..91.41..69.57321945768.9561.....46...19565479.2.11.9524.7.2.71.6549 | autosolve |
| 978351624562478913413269857321945768895617432746832195654793281189524376237186549 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) C1: 2,8 E2: 7,8 D3: 2,8 G1: 4,6 H1: 2,8 I1: 4,6 I2: 2,3 G3: 3,8 A5: 7,8 A6: 7,8 F5: 7,8 D6: 2,8 G5: 3,4 H5: 2,3 B8: 3,8 B9: 3,8 F7: 3,8 E9: 3,8 H7: 3,8 I8: 3,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F2,D3: 2.. / F2 = 2 => 0 pairs (X) / D3 = 2 => 0 pairs (_) H1,I2: 2.. / H1 = 2 => 0 pairs (*) / I2 = 2 => 0 pairs (X) D6,F6: 2.. / D6 = 2 => 0 pairs (X) / F6 = 2 => 0 pairs (_) H5,I5: 2.. / H5 = 2 => 0 pairs (X) / I5 = 2 => 0 pairs (_) C1,H1: 2.. / C1 = 2 => 0 pairs (X) / H1 = 2 => 0 pairs (_) C3,D3: 2.. / C3 = 2 => 0 pairs (X) / D3 = 2 => 0 pairs (_) D3,D6: 2.. / D3 = 2 => 0 pairs (*) / D6 = 2 => 0 pairs (X) F2,F6: 2.. / F2 = 2 => 0 pairs (X) / F6 = 2 => 0 pairs (_) H1,H5: 2.. / H1 = 2 => 0 pairs (*) / H5 = 2 => 0 pairs (X) I2,I5: 2.. / I2 = 2 => 0 pairs (X) / I5 = 2 => 0 pairs (_) C2,C3: 3.. / C2 = 3 => 0 pairs (X) / C3 = 3 => 0 pairs (_) I2,G3: 3.. / I2 = 3 => 0 pairs (*) / G3 = 3 => 0 pairs (X) E6,F6: 3.. / E6 = 3 => 0 pairs (*) / F6 = 3 => 0 pairs (X) B8,B9: 3.. / B8 = 3 => 0 pairs (X) / B9 = 3 => 0 pairs (_) F7,E9: 3.. / F7 = 3 => 0 pairs (*) / E9 = 3 => 0 pairs (X) C2,I2: 3.. / C2 = 3 => 0 pairs (X) / I2 = 3 => 0 pairs (_) C3,G3: 3.. / C3 = 3 => 0 pairs (*) / G3 = 3 => 0 pairs (X) F7,H7: 3.. / F7 = 3 => 0 pairs (*) / H7 = 3 => 0 pairs (X) B9,E9: 3.. / B9 = 3 => 0 pairs (*) / E9 = 3 => 0 pairs (X) E6,E9: 3.. / E6 = 3 => 0 pairs (*) / E9 = 3 => 0 pairs (X) F6,F7: 3.. / F6 = 3 => 0 pairs (X) / F7 = 3 => 0 pairs (_) H5,H7: 3.. / H5 = 3 => 0 pairs (*) / H7 = 3 => 0 pairs (X) G1,I1: 4.. / G1 = 4 => 0 pairs (X) / I1 = 4 => 18 pairs (_) G5,I5: 4.. / G5 = 4 => 18 pairs (_) / I5 = 4 => 0 pairs (X) G1,G5: 4.. / G1 = 4 => 0 pairs (X) / G5 = 4 => 18 pairs (_) I1,I5: 4.. / I1 = 4 => 18 pairs (_) / I5 = 4 => 0 pairs (X) G1,I1: 6.. / G1 = 6 => 18 pairs (_) / I1 = 6 => 0 pairs (X) G8,I8: 6.. / G8 = 6 => 0 pairs (X) / I8 = 6 => 18 pairs (_) G1,G8: 6.. / G1 = 6 => 18 pairs (_) / G8 = 6 => 0 pairs (X) I1,I8: 6.. / I1 = 6 => 0 pairs (X) / I8 = 6 => 18 pairs (_) E2,F2: 7.. / E2 = 7 => 21 pairs (_) / F2 = 7 => 0 pairs (X) A5,A6: 7.. / A5 = 7 => 0 pairs (X) / A6 = 7 => 18 pairs (_) A5,F5: 7.. / A5 = 7 => 0 pairs (X) / F5 = 7 => 18 pairs (_) E2,E6: 7.. / E2 = 7 => 21 pairs (_) / E6 = 7 => 0 pairs (X) H1,G3: 8.. / H1 = 8 => 0 pairs (X) / G3 = 8 => 0 pairs (_) A5,A6: 8.. / A5 = 8 => 18 pairs (_) / A6 = 8 => 0 pairs (X) B8,B9: 8.. / B8 = 8 => 0 pairs (*) / B9 = 8 => 0 pairs (X) F7,E9: 8.. / F7 = 8 => 0 pairs (X) / E9 = 8 => 0 pairs (_) H7,G8: 8.. / H7 = 8 => 0 pairs (*) / G8 = 8 => 0 pairs (X) C1,H1: 8.. / C1 = 8 => 0 pairs (*) / H1 = 8 => 0 pairs (X) A5,F5: 8.. / A5 = 8 => 18 pairs (_) / F5 = 8 => 0 pairs (X) F7,H7: 8.. / F7 = 8 => 0 pairs (X) / H7 = 8 => 0 pairs (_) B8,G8: 8.. / B8 = 8 => 0 pairs (*) / G8 = 8 => 0 pairs (X) B9,E9: 8.. / B9 = 8 => 0 pairs (X) / E9 = 8 => 0 pairs (_) D3,D6: 8.. / D3 = 8 => 0 pairs (X) / D6 = 8 => 0 pairs (_) G3,G8: 8.. / G3 = 8 => 0 pairs (*) / G8 = 8 => 0 pairs (X) H1,H7: 8.. / H1 = 8 => 0 pairs (X) / H7 = 8 => 0 pairs (_) * DURATION: 0:01:16.876403 START: 11:39:25.478638 END: 11:40:42.355041 2017-05-04 * CP COUNT: (47) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B8,B9,C1,D3,D6,E2,E9,F5,F7,G1,G3,G5,H1,H5,H7,I1,I2,I8) * 97.351...56.4..91.41..69.57321945768.9561.....46...19565479.2.11.9524.7.2.71.6549 * PAIR C1: 2,8 BLK 1 C2: 2,8,3 # reduction candidate for 2,8 C2: 2,8 => SOLVED * 978351624562478913413269857321945768895617432746832195654793281189524376237186549 C2: 3 => CTR * 97.351...5634..91241.269357321945768.9561.423.468.21956547932811.9524.7.2.71.6549 C3: 2,8,3 # reduction candidate for 2,8 C3: 2,8 => CTR * 97.351...5634..91241.269357321945768.9561.423.468.21956547932811.9524.7.2.71.6549 C3: 3 => SOLVED * 978351624562478913413269857321945768895617432746832195654793281189524376237186549 * PAIR E2: 7,8 BLK 2 F2: 7,8,2 # reduction candidate for 7,8 F2: 7,8 => SOLVED * 978351624562478913413269857321945768895617432746832195654793281189524376237186549 F2: 2 => CTR * 97.351...56.47291341..69.57321945768.9561.....46...19565479.2.11.9524.7.2.71.6549 * PAIR E2: 7,8 COL E E6: 7,8,3 # reduction candidate for 7,8 E6: 7,8 => CTR * 97.35168456.4.291341..69.57321945768.9561.....46..3195654798231139524876287136549 E6: 3 => SOLVED * 978351624562478913413269857321945768895617432746832195654793281189524376237186549 * PAIR D3: 2,8 BLK 2 F2: 2,8,7 # reduction candidate for 2,8 F2: 7 => CTR * 97.351...56.4.791.41.269.57321945768795618....46...19565479.2.11.9524.7.2.71.6549 F2: 2,8 # 21 pairs * PAIR D3: 2,8 ROW 3 C3: 2,8,3 # reduction candidate for 2,8 C3: 2,8 => CTR * 97.351...5634..91241.269357321945768.9561.423.468.21956547932811.9524.7.2.71.6549 C3: 3 => SOLVED * 978351624562478913413269857321945768895617432746832195654793281189524376237186549 * PAIR I2: 2,3 ROW 2 C2: 2,3,8 # reduction candidate for 2,3 C2: 2,3 => SOLVED * 978351624562478913413269857321945768895617432746832195654793281189524376237186549 C2: 8 => CTR * 97.351...56847291341..69.57321945768.9561.....46...19565479.2.11.9524.7.2.71.6549 * PAIR I2: 2,3 COL I I5: 2,3,4 # reduction candidate for 2,3 I5: 4 => CTR * 97.351...56.4..91241.269357321945768.9561.4...46...19565479.2.11.9524.7.2.71.6549 I5: 2,3 # 18 pairs * PAIR G3: 3,8 ROW 3 C3: 3,8,2 # reduction candidate for 3,8 C3: 3,8 => SOLVED * 978351624562478913413269857321945768895617432746832195654793281189524376237186549 C3: 2 => CTR * 97.351...5634..912412.69.57321945768.9561.....46...19565479.2.11.9524.7.2.71.6549 * PAIR G3: 3,8 COL G G8: 3,8,6 # reduction candidate for 3,8 G8: 6 => CTR * 97.351...56.4..91.41..69857321945768.9561.32..46...19565479.2.11.9524.7.2.71.6549 G8: 3,8 # 18 pairs * PAIR A6: 7,8 ROW 6 E6: 7,8,3 # reduction candidate for 7,8 E6: 7,8 => CTR * 97.35168456.4.291341..69.57321945768.9561.....46..3195654798231139524876287136549 E6: 3 => SOLVED * 978351624562478913413269857321945768895617432746832195654793281189524376237186549 F6: 7,8,2,3 # reduction candidate for 7,8 F6: 7,8 => CTR * 97.351...56.4.291341..69.57321945768.9561.....46...19565479.2.11.9524.7.2.71.6549 F6: 2,3 # 21 pairs * PAIR F5: 7,8 BLK 5 E6: 7,8,3 # reduction candidate for 7,8 E6: 7,8 => CTR * 97.35168456.4.291341..69.57321945768.9561.....46..3195654798231139524876287136549 E6: 3 => SOLVED * 978351624562478913413269857321945768895617432746832195654793281189524376237186549 F6: 7,8,2,3 # reduction candidate for 7,8 F6: 7,8 => CTR * 97.351...56.4.291341..69.57321945768.9561.....46...19565479.2.11.9524.7.2.71.6549 F6: 2,3 # 21 pairs * PAIR F5: 7,8 COL F F2: 7,8,2 # reduction candidate for 7,8 F2: 7,8 => SOLVED * 978351624562478913413269857321945768895617432746832195654793281189524376237186549 F2: 2 => CTR * 97.351...56.47291341..69.57321945768.9561.....46...19565479.2.11.9524.7.2.71.6549 * PAIR D6: 2,8 BLK 5 F6: 2,8,3,7 # reduction candidate for 2,8 F6: 2,8 => SOLVED * 978351624562478913413269857321945768895617432746832195654793281189524376237186549 F6: 3,7 => CTR * 97.351...56.4.291341..69.57321945768.9561.....46...19565479.2.11.9524.7.2.71.6549 * PAIR G5: 3,4 BLK 6 I5: 3,4,2 # reduction candidate for 3,4 I5: 3,4 => CTR * 97.351...56.4..91241.269357321945768.9561.423.468.21956547932811.9524.7.2.71.6549 I5: 2 => SOLVED * 978351624562478913413269857321945768895617432746832195654793281189524376237186549 * PAIR H5: 2,3 BLK 6 I5: 2,3,4 # reduction candidate for 2,3 I5: 4 => CTR * 97.351...56.4..91241.269357321945768.9561.4...46...19565479.2.11.9524.7.2.71.6549 I5: 2,3 # 18 pairs * PAIR B8: 3,8 ROW 8 G8: 3,8,6 # reduction candidate for 3,8 G8: 6 => CTR * 97.351...56.4..91.41..69857321945768.9561.32..46...19565479.2.11.9524.7.2.71.6549 G8: 3,8 # 18 pairs * PAIR F7: 3,8 COL F F6: 3,8,2,7 # reduction candidate for 3,8 F6: 3,8 => CTR * 97.351...56.4.291341..69.57321945768.9561.....46...19565479.2.11.9524.7.2.71.6549 F6: 2,7 => SOLVED * 978351624562478913413269857321945768895617432746832195654793281189524376237186549 * PAIR E9: 3,8 COL E E6: 3,8,7 # reduction candidate for 3,8 E6: 7 => CTR * 97.351...56.4..91.41..69.57321945768.9561.....46.731956547982.11.9524.7.2.71.6549 E6: 3,8 # 21 pairs * PAIR H7: 3,8 BLK 9 G8: 3,8,6 # reduction candidate for 3,8 G8: 6 => CTR * 97.351...56.4..91.41..69857321945768.9561.32..46...19565479.2.11.9524.7.2.71.6549 G8: 3,8 # 18 pairs * PAIR I8: 3,6 BLK 9 G8: 3,6,8 # reduction candidate for 3,6 G8: 3,6 => SOLVED * 978351624562478913413269857321945768895617432746832195654793281189524376237186549 G8: 8 => CTR * 97.35168456.4..91241.269357321945768.9561.423.468..19565479.2.11.9524876287136549 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-259-base-pr-000.dot * REASONING * PRF # C2: 2,8 => SOL * DIS # C2: 3 => CTR => C2: 2,8 * DIS # C3: 2,8 => CTR => C3: 3 * PRF # C3: 3 => SOL * PRF # F2: 7,8 => SOL * DIS # F2: 2 => CTR => F2: 7,8 * DIS # E6: 7,8 => CTR => E6: 3 * PRF # E6: 3 => SOL * DIS # F2: 7 => CTR => F2: 2,8 * DIS # C3: 2,8 => CTR => C3: 3 * PRF # C3: 3 => SOL * PRF # C2: 2,3 => SOL * DIS # C2: 8 => CTR => C2: 2,3 * DIS # I5: 4 => CTR => I5: 2,3 * PRF # C3: 3,8 => SOL * DIS # C3: 2 => CTR => C3: 3,8 * DIS # G8: 6 => CTR => G8: 3,8 * DIS # E6: 7,8 => CTR => E6: 3 * PRF # E6: 3 => SOL * DIS # F6: 7,8 => CTR => F6: 2,3 * DIS # E6: 7,8 => CTR => E6: 3 * PRF # E6: 3 => SOL * DIS # F6: 7,8 => CTR => F6: 2,3 * PRF # F2: 7,8 => SOL * DIS # F2: 2 => CTR => F2: 7,8 * PRF # F6: 2,8 => SOL * DIS # F6: 3,7 => CTR => F6: 2,8 * DIS # I5: 3,4 => CTR => I5: 2 * PRF # I5: 2 => SOL * DIS # I5: 4 => CTR => I5: 2,3 * DIS # G8: 6 => CTR => G8: 3,8 * DIS # F6: 3,8 => CTR => F6: 2,7 * PRF # F6: 2,7 => SOL * DIS # E6: 7 => CTR => E6: 3,8 * DIS # G8: 6 => CTR => G8: 3,8 * PRF # G8: 3,6 => SOL * DIS # G8: 8 => CTR => G8: 3,6 * CNT 37 HDP CHAINS / 46 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B8,B9,C1,D3,D6,E2,E9,F5,F7,G1,G3,G5,H1,H5,H7,I1,I2,I8) * 97.351...56.4..91.41..69.57321945768.9561.....46...19565479.2.11.9524.7.2.71.6549 * PAIR C1: 2,8 BLK 1 C2: 2,8,3 # reduction candidate for 2,8 C2: 2,8 => SOLVED * 978351624562478913413269857321945768895617432746832195654793281189524376237186549 * DURATION: 0:00:01.956792 START: 11:41:28.383529 END: 11:41:30.340321 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-259-base-pr-001.dot * REASONING * PRF # C2: 2,8 => SOL * STA C2: 2,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 259 solution: 978351624562478913413269857321945768895617432746832195654793281189524376237186549 info: 2081 FNBTWXY S8.f 22615 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 978351624562478913413269857321945768895617432746832195654793281189524376237186549 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 # C2: 2,8 => SOL * DIS # C2: 3 => CTR => C2: 2,8 * DIS # C3: 2,8 => CTR => C3: 3 * PRF # C3: 3 => SOL * PRF # F2: 7,8 => SOL * DIS # F2: 2 => CTR => F2: 7,8 * DIS # E6: 7,8 => CTR => E6: 3 * PRF # E6: 3 => SOL * INC # F2: 2,8 => UNS * DIS # F2: 7 => CTR => F2: 2,8 * DIS # C3: 2,8 => CTR => C3: 3 * PRF # C3: 3 => SOL * PRF # C2: 2,3 => SOL * DIS # C2: 8 => CTR => C2: 2,3 * INC # I5: 2,3 => UNS * DIS # I5: 4 => CTR => I5: 2,3 * PRF # C3: 3,8 => SOL * DIS # C3: 2 => CTR => C3: 3,8 * INC # G8: 3,8 => UNS * DIS # G8: 6 => CTR => G8: 3,8 * DIS # E6: 7,8 => CTR => E6: 3 * PRF # E6: 3 => SOL * DIS # F6: 7,8 => CTR => F6: 2,3 * INC # F6: 2,3 => UNS * DIS # E6: 7,8 => CTR => E6: 3 * PRF # E6: 3 => SOL * DIS # F6: 7,8 => CTR => F6: 2,3 * INC # F6: 2,3 => UNS * PRF # F2: 7,8 => SOL * DIS # F2: 2 => CTR => F2: 7,8 * PRF # F6: 2,8 => SOL * DIS # F6: 3,7 => CTR => F6: 2,8 * DIS # I5: 3,4 => CTR => I5: 2 * PRF # I5: 2 => SOL * INC # I5: 2,3 => UNS * DIS # I5: 4 => CTR => I5: 2,3 * INC # G8: 3,8 => UNS * DIS # G8: 6 => CTR => G8: 3,8 * DIS # F6: 3,8 => CTR => F6: 2,7 * PRF # F6: 2,7 => SOL * INC # E6: 3,8 => UNS * DIS # E6: 7 => CTR => E6: 3,8 * INC # G8: 3,8 => UNS * DIS # G8: 6 => CTR => G8: 3,8 * PRF # G8: 3,6 => SOL * DIS # G8: 8 => CTR => G8: 3,6 * CNT 46 HDP CHAINS / 46 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C2: 2,8 => SOL * STA C2: 2,8 * CNT 1 HDP CHAINS / 1 HYP OPENED