Analysis of xx-top500-261-base.sdk
Contents
Original Sudoku
level: medium
position: ...1...852........7........6...7.2.....36.....8.....4.....947...5.8.............. initial
Autosolve
position: ...127.852......7.7........69147.2...7.36.....8....647....947...578........7..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 3,4 => CTR => B1: 6 * PRF # F5: 5,8 => SOL * DIS # F5: 2 => CTR => F5: 5,8 * DIS # F6: 1,5 => CTR => F6: 2,9 * PRF # F6: 2,9 => SOL * DIS # E9: 3 => CTR => E9: 1,5 * DIS # H9: 3,5 => CTR => H9: 1,2,6,9 * PRF # F5: 5,8 => SOL * DIS # F5: 2 => CTR => F5: 5,8 * DIS # B9: 3,6 => CTR => B9: 2,4 * DIS # C9: 3,6 => CTR => C9: 4,9 * DIS # H7: 3,6 => CTR => H7: 1,2,5 * DIS # I7: 3,6 => CTR => I7: 1,2,8 * DIS # C1: 3,6 => CTR => C1: 4,9 * DIS # E9: 1,3 => CTR => E9: 5 * PRF # E9: 5 => SOL * CNT 16 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 3,4 => CTR => B1: 6 * PRF B1: 6 # F5: 5,8 => SOL * STA B1: 6 + F5: 5,8 * CNT 2 HDP CHAINS / 18 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...1...852........7........6...7.2.....36.....8.....4.....947...5.8.............. | initial |
| ...127.852......7.7........69147.2...7.36.....8....647....947...578........7..... | autosolve |
| 369127485218549376745683192691475238472368519583912647836294751157836924924751863 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) C2: 5,8 C3: 5,8 E2: 4,8 E3: 4,8 G1: 3,4 A5: 4,5 C5: 2,4 A6: 3,5 C6: 2,3 F4: 5,8 E6: 1,5 H4: 3,5 I4: 3,8 G5: 5,8 H5: 1,9 I5: 1,9 C7: 3,6 E8: 1,3 G9: 5,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,B3: 1.. / B2 = 1 => 20 pairs (_) / B3 = 1 => 20 pairs (_) E6,F6: 1.. / E6 = 1 => 0 pairs (*) / F6 = 1 => 0 pairs (X) H5,I5: 1.. / H5 = 1 => 19 pairs (_) / I5 = 1 => 17 pairs (_) H3,I3: 2.. / H3 = 2 => 19 pairs (_) / I3 = 2 => 19 pairs (_) C5,C6: 2.. / C5 = 2 => 0 pairs (*) / C6 = 2 => 0 pairs (X) B7,B9: 2.. / B7 = 2 => 0 pairs (X) / B9 = 2 => 24 pairs (_) C5,F5: 2.. / C5 = 2 => 0 pairs (*) / F5 = 2 => 0 pairs (X) D6,D7: 2.. / D6 = 2 => 0 pairs (X) / D7 = 2 => 0 pairs (_) F2,F3: 3.. / F2 = 3 => 20 pairs (_) / F3 = 3 => 20 pairs (_) A6,C6: 3.. / A6 = 3 => 0 pairs (X) / C6 = 3 => 0 pairs (_) H4,I4: 3.. / H4 = 3 => 0 pairs (*) / I4 = 3 => 0 pairs (X) E8,E9: 3.. / E8 = 3 => 19 pairs (_) / E9 = 3 => 0 pairs (X) E2,E3: 4.. / E2 = 4 => 17 pairs (_) / E3 = 4 => 17 pairs (_) A5,C5: 4.. / A5 = 4 => 0 pairs (*) / C5 = 4 => 0 pairs (X) C2,C3: 5.. / C2 = 5 => 17 pairs (_) / C3 = 5 => 17 pairs (_) A5,A6: 5.. / A5 = 5 => 0 pairs (X) / A6 = 5 => 0 pairs (_) H4,G5: 5.. / H4 = 5 => 0 pairs (X) / G5 = 5 => 0 pairs (_) F4,H4: 5.. / F4 = 5 => 0 pairs (*) / H4 = 5 => 0 pairs (X) D7,H7: 5.. / D7 = 5 => 0 pairs (X) / H7 = 5 => 0 pairs (_) E6,E9: 5.. / E6 = 5 => 0 pairs (X) / E9 = 5 => 0 pairs (_) G5,G9: 5.. / G5 = 5 => 0 pairs (*) / G9 = 5 => 0 pairs (X) B1,C1: 6.. / B1 = 6 => 20 pairs (_) / C1 = 6 => 0 pairs (X) C2,C3: 8.. / C2 = 8 => 17 pairs (_) / C3 = 8 => 17 pairs (_) E2,E3: 8.. / E2 = 8 => 17 pairs (_) / E3 = 8 => 17 pairs (_) F4,F5: 8.. / F4 = 8 => 0 pairs (X) / F5 = 8 => 0 pairs (_) I4,G5: 8.. / I4 = 8 => 0 pairs (*) / G5 = 8 => 0 pairs (X) A7,A9: 8.. / A7 = 8 => 19 pairs (_) / A9 = 8 => 0 pairs (X) C2,E2: 8.. / C2 = 8 => 17 pairs (_) / E2 = 8 => 17 pairs (_) C3,E3: 8.. / C3 = 8 => 17 pairs (_) / E3 = 8 => 17 pairs (_) F4,I4: 8.. / F4 = 8 => 0 pairs (X) / I4 = 8 => 0 pairs (_) F5,G5: 8.. / F5 = 8 => 0 pairs (*) / G5 = 8 => 0 pairs (X) A7,I7: 8.. / A7 = 8 => 19 pairs (_) / I7 = 8 => 0 pairs (X) G5,G9: 8.. / G5 = 8 => 0 pairs (X) / G9 = 8 => 0 pairs (_) A1,C1: 9.. / A1 = 9 => 19 pairs (_) / C1 = 9 => 23 pairs (_) D6,F6: 9.. / D6 = 9 => 0 pairs (*) / F6 = 9 => 0 pairs (X) H5,I5: 9.. / H5 = 9 => 17 pairs (_) / I5 = 9 => 19 pairs (_) C1,C9: 9.. / C1 = 9 => 23 pairs (_) / C9 = 9 => 19 pairs (_) * DURATION: 0:01:16.792452 START: 11:44:37.544260 END: 11:45:54.336712 2017-05-04 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,C2,C3,C5,C6,C7,E2,E3,E6,E8,F4,G1,G5,G9,H4,H5,I4,I5) * ...127.852......7.7........69147.2...7.36.....8....647....947...578........7..... * PAIR G1: 3,4 BLK 3 G2: 3,4,1,9 # reduction candidate for 3,4 G2: 3,4 # 22 pairs I2: 3,4,1,6,9 # reduction candidate for 3,4 I2: 3,4 # 26 pairs G3: 3,4,1,9 # reduction candidate for 3,4 G3: 3,4 # 22 pairs I3: 3,4,1,2,6,9 # reduction candidate for 3,4 I3: 3,4 # 24 pairs * PAIR G1: 3,4 ROW 1 A1: 3,4,9 # reduction candidate for 3,4 A1: 3,4 # 23 pairs B1: 3,4,6 # reduction candidate for 3,4 B1: 3,4 => CTR * 9.6127.852......7.7........69147.2...743628..382...647..329475..578.......97..... B1: 6 # 20 pairs C1: 3,4,6,9 # reduction candidate for 3,4 C1: 3,4 # 21 pairs * PAIR G1: 3,4 COL G G8: 3,4,1,9 # reduction candidate for 3,4 G8: 3,4 # 22 pairs G8: 1,9 # 20 pairs * PAIR F4: 5,8 BLK 5 F5: 5,8,2 # reduction candidate for 5,8 F5: 5,8 => SOLVED * 369127485218549376745683192691475238472368519583912647836294751157836924924751863 F5: 2 => CTR * ...127.852......7.7........6914782535743628..382...647....947...578........7..... * PAIR E6: 1,5 BLK 5 F6: 1,5,2,9 # reduction candidate for 1,5 F6: 1,5 => CTR * ...127.852......7.7........69147.2...7.36.....8.9..647...29475..578......2.7..8.. F6: 2,9 => SOLVED * 369127485218549376745683192691475238472368519583912647836294751157836924924751863 * PAIR E6: 1,5 COL E E9: 1,5,3 # reduction candidate for 1,5 E9: 3 => CTR * ...127.852......7.7........6914782535743628..382951647....947...5781.......73.... E9: 1,5 # 19 pairs * PAIR H4: 3,5 COL H H7: 3,5,1,2,6 # reduction candidate for 3,5 H7: 3,5 # 22 pairs H9: 3,5,1,2,6,9 # reduction candidate for 3,5 H9: 3,5 => CTR * ...127.852......7.7........69147.2...7.36.....8.25.647...5947...578........7..... H9: 1,2,6,9 # 19 pairs * PAIR I4: 3,8 COL I I7: 3,8,1,2,6 # reduction candidate for 3,8 I7: 3,8 # 20 pairs I9: 3,8,1,2,4,6,9 # reduction candidate for 3,8 I9: 3,8 # 20 pairs * PAIR G5: 5,8 ROW 5 F5: 5,8,2 # reduction candidate for 5,8 F5: 5,8 => SOLVED * 369127485218549376745683192691475238472368519583912647836294751157836924924751863 F5: 2 => CTR * ...127.852......7.7........6914782535743628..382...647....947...578........7..... * PAIR H5: 1,9 COL H H3: 1,9,2,3,6 # reduction candidate for 1,9 H3: 1,9 # 26 pairs H8: 1,9,2,3,6 # reduction candidate for 1,9 H8: 1,9 # 24 pairs H9: 1,9,2,3,5,6 # reduction candidate for 1,9 H9: 1,9 # 22 pairs * PAIR I5: 1,9 COL I I2: 1,9,3,4,6 # reduction candidate for 1,9 I2: 1,9 # 24 pairs I3: 1,9,2,3,4,6 # reduction candidate for 1,9 I3: 1,9 # 22 pairs I8: 1,9,2,3,4,6 # reduction candidate for 1,9 I8: 1,9 # 22 pairs I9: 1,9,2,3,4,6,8 # reduction candidate for 1,9 I9: 1,9 # 20 pairs * PAIR C7: 3,6 BLK 7 B7: 3,6,2 # reduction candidate for 3,6 B7: 3,6 # 24 pairs B9: 3,6,2,4 # reduction candidate for 3,6 B9: 3,6 => CTR * ...127.852......7.7........69147.2...7236.....83219647.265947...5783.......7..... B9: 2,4 # 20 pairs C9: 3,6,4,9 # reduction candidate for 3,6 C9: 3,6 => CTR * ..9127.852......7.7........69147.2...743628...82...647...29475..578........7..... C9: 4,9 # 20 pairs * PAIR C7: 3,6 ROW 7 H7: 3,6,1,2,5 # reduction candidate for 3,6 H7: 3,6 => CTR * ...127.852......7.7........69147.2...7.36.....8.25.647...5947...578........7..... H7: 1,2,5 # 19 pairs I7: 3,6,1,2,8 # reduction candidate for 3,6 I7: 3,6 => CTR * ...127.852......7.7........69147.2...7.36..91.8.25.6478..59471..578........7..... I7: 1,2,8 # 19 pairs * PAIR C7: 3,6 COL C C1: 3,6,4,9 # reduction candidate for 3,6 C1: 3,6 => CTR * 9..127.852......7.7........69147.2...743628...82...647...29475..578.......97..... C1: 4,9 # 21 pairs * PAIR E8: 1,3 BLK 8 E9: 1,3,5 # reduction candidate for 1,3 E9: 1,3 => CTR * ...127.852......7.7........6914782535743628..382951647....947...578........7..... E9: 5 => SOLVED * 369127485218549376745683192691475238472368519583912647836294751157836924924751863 * PAIR E8: 1,3 ROW 8 A8: 1,3,4,9 # reduction candidate for 1,3 A8: 1,3 # 22 pairs G8: 1,3,4,9 # reduction candidate for 1,3 G8: 1,3 # 24 pairs H8: 1,3,2,6,9 # reduction candidate for 1,3 H8: 1,3 # 26 pairs I8: 1,3,2,4,6,9 # reduction candidate for 1,3 I8: 1,3 # 26 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-261-base-pr-000.dot * REASONING * DIS # B1: 3,4 => CTR => B1: 6 * PRF # F5: 5,8 => SOL * DIS # F5: 2 => CTR => F5: 5,8 * DIS # F6: 1,5 => CTR => F6: 2,9 * PRF # F6: 2,9 => SOL * DIS # E9: 3 => CTR => E9: 1,5 * DIS # H9: 3,5 => CTR => H9: 1,2,6,9 * PRF # F5: 5,8 => SOL * DIS # F5: 2 => CTR => F5: 5,8 * DIS # B9: 3,6 => CTR => B9: 2,4 * DIS # C9: 3,6 => CTR => C9: 4,9 * DIS # H7: 3,6 => CTR => H7: 1,2,5 * DIS # I7: 3,6 => CTR => I7: 1,2,8 * DIS # C1: 3,6 => CTR => C1: 4,9 * DIS # E9: 1,3 => CTR => E9: 5 * PRF # E9: 5 => SOL * CNT 16 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,C2,C3,C5,C6,C7,E2,E3,E6,E8,F4,G1,G5,G9,H4,H5,I4,I5) * ...127.852......7.7........69147.2...7.36.....8....647....947...578........7..... * PAIR G1: 3,4 BLK 3 G2: 3,4,1,9 # reduction candidate for 3,4 G2: 3,4 # 22 pairs I2: 3,4,1,6,9 # reduction candidate for 3,4 I2: 3,4 # 26 pairs G3: 3,4,1,9 # reduction candidate for 3,4 G3: 3,4 # 22 pairs I3: 3,4,1,2,6,9 # reduction candidate for 3,4 I3: 3,4 # 24 pairs * PAIR G1: 3,4 ROW 1 A1: 3,4,9 # reduction candidate for 3,4 A1: 3,4 # 23 pairs B1: 3,4,6 # reduction candidate for 3,4 B1: 3,4 => CTR * 9.6127.852......7.7........69147.2...743628..382...647..329475..578.......97..... C1: 3,4,9 # reduction candidate for 3,4 C1: 3,4 # 21 pairs * PAIR G1: 3,4 COL G G8: 3,4,1,9 # reduction candidate for 3,4 G8: 3,4 # 23 pairs G8: 1,9 # 21 pairs * PAIR RESTART * PAIR G1: 3,4 BLK 3 G2: 3,4,1,9 # reduction candidate for 3,4 G2: 3,4 # 23 pairs I2: 3,4,1,6,9 # reduction candidate for 3,4 I2: 3,4 # 27 pairs G3: 3,4,1,9 # reduction candidate for 3,4 G3: 3,4 # 23 pairs I3: 3,4,1,2,6,9 # reduction candidate for 3,4 I3: 3,4 # 25 pairs * PAIR G1: 3,4 ROW 1 A1: 3,4,9 # reduction candidate for 3,4 A1: 3,4 # 23 pairs C1: 3,4,9 # reduction candidate for 3,4 C1: 3,4 # 21 pairs * PAIR G1: 3,4 COL G G8: 3,4,1,9 # reduction candidate for 3,4 G8: 3,4 # 23 pairs G8: 1,9 # 21 pairs * PAIR F4: 5,8 BLK 5 F5: 5,8,2 # reduction candidate for 5,8 F5: 5,8 => SOLVED * 369127485218549376745683192691475238472368519583912647836294751157836924924751863 * DURATION: 0:00:21.274999 START: 11:46:47.529411 END: 11:47:08.804410 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-261-base-pr-001.dot * REASONING * DIS # B1: 3,4 => CTR => B1: 6 * PRF B1: 6 # F5: 5,8 => SOL * STA B1: 6 + F5: 5,8 * CNT 2 HDP CHAINS / 18 HYP OPENED
Header Info
Top 500 Minimum 17 261 solution: 369127485218549376745683192691475238472368519583912647836294751157836924924751863 info: 2089 FNBTHWY S8.f 41037 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 369127485218549376745683192691475238472368519583912647836294751157836924924751863 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 # G2: 3,4 => UNS * INC # I2: 3,4 => UNS * INC # G3: 3,4 => UNS * INC # I3: 3,4 => UNS * INC # A1: 3,4 => UNS * DIS # B1: 3,4 => CTR => B1: 6 * INC # B1: 6 => UNS * INC # C1: 3,4 => UNS * INC # G8: 3,4 => UNS * INC # G8: 1,9 => UNS * PRF # F5: 5,8 => SOL * DIS # F5: 2 => CTR => F5: 5,8 * DIS # F6: 1,5 => CTR => F6: 2,9 * PRF # F6: 2,9 => SOL * INC # E9: 1,5 => UNS * DIS # E9: 3 => CTR => E9: 1,5 * INC # H7: 3,5 => UNS * DIS # H9: 3,5 => CTR => H9: 1,2,6,9 * INC # H9: 1,2,6,9 => UNS * INC # I7: 3,8 => UNS * INC # I9: 3,8 => UNS * PRF # F5: 5,8 => SOL * DIS # F5: 2 => CTR => F5: 5,8 * INC # H3: 1,9 => UNS * INC # H8: 1,9 => UNS * INC # H9: 1,9 => UNS * INC # I2: 1,9 => UNS * INC # I3: 1,9 => UNS * INC # I8: 1,9 => UNS * INC # I9: 1,9 => UNS * INC # B7: 3,6 => UNS * DIS # B9: 3,6 => CTR => B9: 2,4 * INC # B9: 2,4 => UNS * DIS # C9: 3,6 => CTR => C9: 4,9 * INC # C9: 4,9 => UNS * DIS # H7: 3,6 => CTR => H7: 1,2,5 * INC # H7: 1,2,5 => UNS * DIS # I7: 3,6 => CTR => I7: 1,2,8 * INC # I7: 1,2,8 => UNS * DIS # C1: 3,6 => CTR => C1: 4,9 * INC # C1: 4,9 => UNS * DIS # E9: 1,3 => CTR => E9: 5 * PRF # E9: 5 => SOL * INC # A8: 1,3 => UNS * INC # G8: 1,3 => UNS * INC # H8: 1,3 => UNS * INC # I8: 1,3 => UNS * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G2: 3,4 => UNS * INC # I2: 3,4 => UNS * INC # G3: 3,4 => UNS * INC # I3: 3,4 => UNS * INC # A1: 3,4 => UNS * DIS # B1: 3,4 => CTR => B1: 6 * INC B1: 6 # C1: 3,4 => UNS * INC B1: 6 # G8: 3,4 => UNS * INC B1: 6 # G8: 1,9 => UNS * INC B1: 6 # G2: 3,4 => UNS * INC B1: 6 # I2: 3,4 => UNS * INC B1: 6 # G3: 3,4 => UNS * INC B1: 6 # I3: 3,4 => UNS * INC B1: 6 # A1: 3,4 => UNS * INC B1: 6 # C1: 3,4 => UNS * INC B1: 6 # G8: 3,4 => UNS * INC B1: 6 # G8: 1,9 => UNS * PRF B1: 6 # F5: 5,8 => SOL * STA B1: 6 + F5: 5,8 * CNT 18 HDP CHAINS / 18 HYP OPENED