Analysis of xx-top500-260-base.sdk
Contents
Original Sudoku
level: medium
position: ...2...193........7........6...7.3.....46.....9.....5.....857...1.9.............. initial
Autosolve
position: ...237.193......7.7........68257.3...7.46.....9....657....857...179........7..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 4,5 => CTR => B1: 6 * PRF # F5: 1,9 => SOL * DIS # F5: 3 => CTR => F5: 1,9 * DIS # F6: 1,2 => CTR => F6: 3,8 * PRF # F6: 3,8 => SOL * DIS # E9: 4 => CTR => E9: 1,2 * DIS # I9: 1,4 => CTR => I9: 2,3,5,6,8 * PRF # F5: 1,9 => SOL * DIS # F5: 3 => CTR => F5: 1,9 * DIS # B9: 4,6 => CTR => B9: 3,5 * DIS # C9: 4,6 => CTR => C9: 5,8 * DIS # H7: 4,6 => CTR => H7: 2,3,9 * DIS # I7: 4,6 => CTR => I7: 1,2,3 * DIS # C1: 4,6 => CTR => C1: 5,8 * DIS # E9: 2,4 => CTR => E9: 1 * PRF # E9: 1 => 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: 4,5 => CTR => B1: 6 * PRF B1: 6 # F5: 1,9 => SOL * STA B1: 6 + F5: 1,9 * CNT 2 HDP CHAINS / 18 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...2...193........7........6...7.3.....46.....9.....5.....857...1.9.............. | initial |
| ...237.193......7.7........68257.3...7.46.....9....657....857...179........7..... | autosolve |
| 468237519351694278729158463682571394573469182194823657946385721217946835835712946 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) C2: 1,9 C3: 1,9 E2: 5,9 E3: 5,9 G1: 4,5 A5: 1,5 C5: 3,5 A6: 1,4 C6: 3,4 F4: 1,9 E6: 1,2 H4: 4,9 I4: 1,4 G5: 1,9 H5: 2,8 I5: 2,8 C7: 4,6 E8: 2,4 G9: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,C3: 1.. / C2 = 1 => 17 pairs (_) / C3 = 1 => 17 pairs (_) A5,A6: 1.. / A5 = 1 => 0 pairs (X) / A6 = 1 => 0 pairs (_) I4,G5: 1.. / I4 = 1 => 0 pairs (X) / G5 = 1 => 0 pairs (_) F4,I4: 1.. / F4 = 1 => 0 pairs (*) / I4 = 1 => 0 pairs (X) D7,I7: 1.. / D7 = 1 => 0 pairs (X) / I7 = 1 => 0 pairs (_) E6,E9: 1.. / E6 = 1 => 0 pairs (X) / E9 = 1 => 0 pairs (_) G5,G9: 1.. / G5 = 1 => 0 pairs (*) / G9 = 1 => 0 pairs (X) B2,B3: 2.. / B2 = 2 => 20 pairs (_) / B3 = 2 => 20 pairs (_) E6,F6: 2.. / E6 = 2 => 0 pairs (*) / F6 = 2 => 0 pairs (X) H5,I5: 2.. / H5 = 2 => 17 pairs (_) / I5 = 2 => 19 pairs (_) H3,I3: 3.. / H3 = 3 => 19 pairs (_) / I3 = 3 => 19 pairs (_) C5,C6: 3.. / C5 = 3 => 0 pairs (*) / C6 = 3 => 0 pairs (X) B7,B9: 3.. / B7 = 3 => 0 pairs (X) / B9 = 3 => 24 pairs (_) C5,F5: 3.. / C5 = 3 => 0 pairs (*) / F5 = 3 => 0 pairs (X) D6,D7: 3.. / D6 = 3 => 0 pairs (X) / D7 = 3 => 0 pairs (_) F2,F3: 4.. / F2 = 4 => 20 pairs (_) / F3 = 4 => 20 pairs (_) A6,C6: 4.. / A6 = 4 => 0 pairs (X) / C6 = 4 => 0 pairs (_) H4,I4: 4.. / H4 = 4 => 0 pairs (X) / I4 = 4 => 0 pairs (_) E8,E9: 4.. / E8 = 4 => 19 pairs (_) / E9 = 4 => 0 pairs (X) E2,E3: 5.. / E2 = 5 => 17 pairs (_) / E3 = 5 => 17 pairs (_) A5,C5: 5.. / A5 = 5 => 0 pairs (*) / C5 = 5 => 0 pairs (X) B1,C1: 6.. / B1 = 6 => 20 pairs (_) / C1 = 6 => 0 pairs (X) A1,C1: 8.. / A1 = 8 => 19 pairs (_) / C1 = 8 => 23 pairs (_) D6,F6: 8.. / D6 = 8 => 0 pairs (*) / F6 = 8 => 0 pairs (X) H5,I5: 8.. / H5 = 8 => 19 pairs (_) / I5 = 8 => 17 pairs (_) C1,C9: 8.. / C1 = 8 => 23 pairs (_) / C9 = 8 => 19 pairs (_) C2,C3: 9.. / C2 = 9 => 17 pairs (_) / C3 = 9 => 17 pairs (_) E2,E3: 9.. / E2 = 9 => 17 pairs (_) / E3 = 9 => 17 pairs (_) F4,F5: 9.. / F4 = 9 => 0 pairs (X) / F5 = 9 => 0 pairs (_) H4,G5: 9.. / H4 = 9 => 0 pairs (*) / G5 = 9 => 0 pairs (X) A7,A9: 9.. / A7 = 9 => 19 pairs (_) / A9 = 9 => 0 pairs (X) C2,E2: 9.. / C2 = 9 => 17 pairs (_) / E2 = 9 => 17 pairs (_) C3,E3: 9.. / C3 = 9 => 17 pairs (_) / E3 = 9 => 17 pairs (_) F4,H4: 9.. / F4 = 9 => 0 pairs (X) / H4 = 9 => 0 pairs (_) F5,G5: 9.. / F5 = 9 => 0 pairs (*) / G5 = 9 => 0 pairs (X) A7,H7: 9.. / A7 = 9 => 19 pairs (_) / H7 = 9 => 0 pairs (X) G5,G9: 9.. / G5 = 9 => 0 pairs (X) / G9 = 9 => 0 pairs (_) * DURATION: 0:01:17.540674 START: 11:41:50.022632 END: 11:43:07.563306 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) * ...237.193......7.7........68257.3...7.46.....9....657....857...179........7..... * PAIR G1: 4,5 BLK 3 G2: 4,5,2,8 # reduction candidate for 4,5 G2: 4,5 # 22 pairs I2: 4,5,2,6,8 # reduction candidate for 4,5 I2: 4,5 # 26 pairs G3: 4,5,2,8 # reduction candidate for 4,5 G3: 4,5 # 22 pairs I3: 4,5,2,3,6,8 # reduction candidate for 4,5 I3: 4,5 # 24 pairs * PAIR G1: 4,5 ROW 1 A1: 4,5,8 # reduction candidate for 4,5 A1: 4,5 # 23 pairs B1: 4,5,6 # reduction candidate for 4,5 B1: 4,5 => CTR * 8.6237.193......7.7........68257.3...754639..493...657..43857.1.179.......87..... B1: 6 # 20 pairs C1: 4,5,6,8 # reduction candidate for 4,5 C1: 4,5 # 21 pairs * PAIR G1: 4,5 COL G G8: 4,5,2,8 # reduction candidate for 4,5 G8: 4,5 # 22 pairs G8: 2,8 # 20 pairs * PAIR F4: 1,9 BLK 5 F5: 1,9,3 # reduction candidate for 1,9 F5: 1,9 => SOLVED * 468237519351694278729158463682571394573469182194823657946385721217946835835712946 F5: 3 => CTR * ...237.193......7.7........6825793411754639..493...657....857...179........7..... * PAIR E6: 1,2 BLK 5 F6: 1,2,3,8 # reduction candidate for 1,2 F6: 1,2 => CTR * ...237.193......7.7........68257.3...7.46.....9.8..657...3857.1.179......3.7..9.. F6: 3,8 => SOLVED * 468237519351694278729158463682571394573469182194823657946385721217946835835712946 * PAIR E6: 1,2 COL E E9: 1,2,4 # reduction candidate for 1,2 E9: 4 => CTR * ...237.193......7.7........6825793411754639..493812657....857...1792.......74.... E9: 1,2 # 19 pairs * PAIR H4: 4,9 COL H H7: 4,9,2,3,6 # reduction candidate for 4,9 H7: 4,9 # 20 pairs H9: 4,9,2,3,6,8 # reduction candidate for 4,9 H9: 4,9 # 20 pairs * PAIR I4: 1,4 COL I I7: 1,4,2,3,6 # reduction candidate for 1,4 I7: 1,4 # 22 pairs I9: 1,4,2,3,5,6,8 # reduction candidate for 1,4 I9: 1,4 => CTR * ...237.193......7.7........68257.3...7.46.....9.31.657...1857...179........7..... I9: 2,3,5,6,8 # 19 pairs * PAIR G5: 1,9 ROW 5 F5: 1,9,3 # reduction candidate for 1,9 F5: 1,9 => SOLVED * 468237519351694278729158463682571394573469182194823657946385721217946835835712946 F5: 3 => CTR * ...237.193......7.7........6825793411754639..493...657....857...179........7..... * PAIR H5: 2,8 COL H H3: 2,8,3,4,6 # reduction candidate for 2,8 H3: 2,8 # 24 pairs H8: 2,8,3,4,6 # reduction candidate for 2,8 H8: 2,8 # 22 pairs H9: 2,8,3,4,6,9 # reduction candidate for 2,8 H9: 2,8 # 20 pairs * PAIR I5: 2,8 COL I I2: 2,8,4,5,6 # reduction candidate for 2,8 I2: 2,8 # 26 pairs I3: 2,8,3,4,5,6 # reduction candidate for 2,8 I3: 2,8 # 24 pairs I8: 2,8,3,4,5,6 # reduction candidate for 2,8 I8: 2,8 # 24 pairs I9: 2,8,1,3,4,5,6 # reduction candidate for 2,8 I9: 2,8 # 22 pairs * PAIR C7: 4,6 BLK 7 B7: 4,6,3 # reduction candidate for 4,6 B7: 4,6 # 24 pairs B9: 4,6,3,5 # reduction candidate for 4,6 B9: 4,6 => CTR * ...237.193......7.7........68257.3...7346.....94328657.361857...1794.......7..... B9: 3,5 # 20 pairs C9: 4,6,5,8 # reduction candidate for 4,6 C9: 4,6 => CTR * ..8237.193......7.7........68257.3...754639...93...657...3857.1.179........7..... C9: 5,8 # 20 pairs * PAIR C7: 4,6 ROW 7 H7: 4,6,2,3,9 # reduction candidate for 4,6 H7: 4,6 => CTR * ...237.193......7.7........68257.3...7.46..28.9.31.6579..1857.2.179........7..... H7: 2,3,9 # 19 pairs I7: 4,6,1,2,3 # reduction candidate for 4,6 I7: 4,6 => CTR * ...237.193......7.7........68257.3...7.46.....9.31.657...1857...179........7..... I7: 1,2,3 # 19 pairs * PAIR C7: 4,6 COL C C1: 4,6,5,8 # reduction candidate for 4,6 C1: 4,6 => CTR * 8..237.193......7.7........68257.3...754639...93...657...3857.1.179.......87..... C1: 5,8 # 21 pairs * PAIR E8: 2,4 BLK 8 E9: 2,4,1 # reduction candidate for 2,4 E9: 2,4 => CTR * ...237.193......7.7........6825793411754639..493812657....857...179........7..... E9: 1 => SOLVED * 468237519351694278729158463682571394573469182194823657946385721217946835835712946 * PAIR E8: 2,4 ROW 8 A8: 2,4,5,8 # reduction candidate for 2,4 A8: 2,4 # 22 pairs G8: 2,4,5,8 # reduction candidate for 2,4 G8: 2,4 # 24 pairs H8: 2,4,3,6,8 # reduction candidate for 2,4 H8: 2,4 # 26 pairs I8: 2,4,3,5,6,8 # reduction candidate for 2,4 I8: 2,4 # 26 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-260-base-pr-000.dot * REASONING * DIS # B1: 4,5 => CTR => B1: 6 * PRF # F5: 1,9 => SOL * DIS # F5: 3 => CTR => F5: 1,9 * DIS # F6: 1,2 => CTR => F6: 3,8 * PRF # F6: 3,8 => SOL * DIS # E9: 4 => CTR => E9: 1,2 * DIS # I9: 1,4 => CTR => I9: 2,3,5,6,8 * PRF # F5: 1,9 => SOL * DIS # F5: 3 => CTR => F5: 1,9 * DIS # B9: 4,6 => CTR => B9: 3,5 * DIS # C9: 4,6 => CTR => C9: 5,8 * DIS # H7: 4,6 => CTR => H7: 2,3,9 * DIS # I7: 4,6 => CTR => I7: 1,2,3 * DIS # C1: 4,6 => CTR => C1: 5,8 * DIS # E9: 2,4 => CTR => E9: 1 * PRF # E9: 1 => 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) * ...237.193......7.7........68257.3...7.46.....9....657....857...179........7..... * PAIR G1: 4,5 BLK 3 G2: 4,5,2,8 # reduction candidate for 4,5 G2: 4,5 # 22 pairs I2: 4,5,2,6,8 # reduction candidate for 4,5 I2: 4,5 # 26 pairs G3: 4,5,2,8 # reduction candidate for 4,5 G3: 4,5 # 22 pairs I3: 4,5,2,3,6,8 # reduction candidate for 4,5 I3: 4,5 # 24 pairs * PAIR G1: 4,5 ROW 1 A1: 4,5,8 # reduction candidate for 4,5 A1: 4,5 # 23 pairs B1: 4,5,6 # reduction candidate for 4,5 B1: 4,5 => CTR * 8.6237.193......7.7........68257.3...754639..493...657..43857.1.179.......87..... C1: 4,5,8 # reduction candidate for 4,5 C1: 4,5 # 21 pairs * PAIR G1: 4,5 COL G G8: 4,5,2,8 # reduction candidate for 4,5 G8: 4,5 # 23 pairs G8: 2,8 # 21 pairs * PAIR RESTART * PAIR G1: 4,5 BLK 3 G2: 4,5,2,8 # reduction candidate for 4,5 G2: 4,5 # 23 pairs I2: 4,5,2,6,8 # reduction candidate for 4,5 I2: 4,5 # 27 pairs G3: 4,5,2,8 # reduction candidate for 4,5 G3: 4,5 # 23 pairs I3: 4,5,2,3,6,8 # reduction candidate for 4,5 I3: 4,5 # 25 pairs * PAIR G1: 4,5 ROW 1 A1: 4,5,8 # reduction candidate for 4,5 A1: 4,5 # 23 pairs C1: 4,5,8 # reduction candidate for 4,5 C1: 4,5 # 21 pairs * PAIR G1: 4,5 COL G G8: 4,5,2,8 # reduction candidate for 4,5 G8: 4,5 # 23 pairs G8: 2,8 # 21 pairs * PAIR F4: 1,9 BLK 5 F5: 1,9,3 # reduction candidate for 1,9 F5: 1,9 => SOLVED * 468237519351694278729158463682571394573469182194823657946385721217946835835712946 * DURATION: 0:00:20.981013 START: 11:44:00.356370 END: 11:44:21.337383 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-260-base-pr-001.dot * REASONING * DIS # B1: 4,5 => CTR => B1: 6 * PRF B1: 6 # F5: 1,9 => SOL * STA B1: 6 + F5: 1,9 * CNT 2 HDP CHAINS / 18 HYP OPENED
Header Info
Top 500 Minimum 17 260 solution: 468237519351694278729158463682571394573469182194823657946385721217946835835712946 info: 2089 FNBTHWY S8.f 41036 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 468237519351694278729158463682571394573469182194823657946385721217946835835712946 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: 4,5 => UNS * INC # I2: 4,5 => UNS * INC # G3: 4,5 => UNS * INC # I3: 4,5 => UNS * INC # A1: 4,5 => UNS * DIS # B1: 4,5 => CTR => B1: 6 * INC # B1: 6 => UNS * INC # C1: 4,5 => UNS * INC # G8: 4,5 => UNS * INC # G8: 2,8 => UNS * PRF # F5: 1,9 => SOL * DIS # F5: 3 => CTR => F5: 1,9 * DIS # F6: 1,2 => CTR => F6: 3,8 * PRF # F6: 3,8 => SOL * INC # E9: 1,2 => UNS * DIS # E9: 4 => CTR => E9: 1,2 * INC # H7: 4,9 => UNS * INC # H9: 4,9 => UNS * INC # I7: 1,4 => UNS * DIS # I9: 1,4 => CTR => I9: 2,3,5,6,8 * INC # I9: 2,3,5,6,8 => UNS * PRF # F5: 1,9 => SOL * DIS # F5: 3 => CTR => F5: 1,9 * INC # H3: 2,8 => UNS * INC # H8: 2,8 => UNS * INC # H9: 2,8 => UNS * INC # I2: 2,8 => UNS * INC # I3: 2,8 => UNS * INC # I8: 2,8 => UNS * INC # I9: 2,8 => UNS * INC # B7: 4,6 => UNS * DIS # B9: 4,6 => CTR => B9: 3,5 * INC # B9: 3,5 => UNS * DIS # C9: 4,6 => CTR => C9: 5,8 * INC # C9: 5,8 => UNS * DIS # H7: 4,6 => CTR => H7: 2,3,9 * INC # H7: 2,3,9 => UNS * DIS # I7: 4,6 => CTR => I7: 1,2,3 * INC # I7: 1,2,3 => UNS * DIS # C1: 4,6 => CTR => C1: 5,8 * INC # C1: 5,8 => UNS * DIS # E9: 2,4 => CTR => E9: 1 * PRF # E9: 1 => SOL * INC # A8: 2,4 => UNS * INC # G8: 2,4 => UNS * INC # H8: 2,4 => UNS * INC # I8: 2,4 => UNS * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G2: 4,5 => UNS * INC # I2: 4,5 => UNS * INC # G3: 4,5 => UNS * INC # I3: 4,5 => UNS * INC # A1: 4,5 => UNS * DIS # B1: 4,5 => CTR => B1: 6 * INC B1: 6 # C1: 4,5 => UNS * INC B1: 6 # G8: 4,5 => UNS * INC B1: 6 # G8: 2,8 => UNS * INC B1: 6 # G2: 4,5 => UNS * INC B1: 6 # I2: 4,5 => UNS * INC B1: 6 # G3: 4,5 => UNS * INC B1: 6 # I3: 4,5 => UNS * INC B1: 6 # A1: 4,5 => UNS * INC B1: 6 # C1: 4,5 => UNS * INC B1: 6 # G8: 4,5 => UNS * INC B1: 6 # G8: 2,8 => UNS * PRF B1: 6 # F5: 1,9 => SOL * STA B1: 6 + F5: 1,9 * CNT 18 HDP CHAINS / 18 HYP OPENED