Analysis of xx-top500-262-base.sdk
Contents
Original Sudoku
level: medium
position: 63.7........9..2........1..3....5.8..4..2........1....5.2...4.....4...3.......... initial
Autosolve
position: 631782.4..549.12..2..5.41..32.645.8114..2..5...5.1..24582173496.1.4...324.32...1. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 9 => CTR => C3: 7,8 * DIS # A6: 9 => CTR => A6: 7,8 * PRF # C3: 8 => SOL * PRF # B6: 7,9 => SOL * PRF # B6: 7,9 => SOL * PRF # C8: 7,9 => SOL * PRF # B6: 7,9 => SOL * PRF # C8: 7,9 => SOL * PRF # A6: 8 => SOL * PRF # G9: 5,7 => SOL * CNT 10 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 9 => CTR => C3: 7,8 * PRF C3: 7,8 # A6: 7,8 => SOL * STA C3: 7,8 + A6: 7,8 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 63.7........9..2........1..3....5.8..4..2........1....5.2...4.....4...3.......... | initial |
| 631782.4..549.12..2..5.41..32.645.8114..2..5...5.1..24582173496.1.4...324.32...1. | autosolve |
| 631782945754931268298564173329645781146827359875319624582173496917456832463298517 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (26) A2: 7,8 B3: 7,9 E2: 3,6 E3: 3,6 G1: 5,9 I1: 5,9 H2: 6,7 I2: 3,8 H3: 6,7 I3: 3,8 C4: 7,9 C5: 6,8 D5: 3,8 F5: 7,9 D6: 3,8 F6: 7,9 G4: 7,9 G5: 3,6 I5: 7,9 G6: 3,6 A8: 7,9 E8: 5,9 F8: 6,8 E9: 5,9 F9: 6,8 I9: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,E3: 3.. / E2 = 3 => 0 pairs (*) / E3 = 3 => 0 pairs (X) I2,I3: 3.. / I2 = 3 => 16 pairs (_) / I3 = 3 => 0 pairs (*) D5,D6: 3.. / D5 = 3 => 16 pairs (_) / D6 = 3 => 0 pairs (*) G5,G6: 3.. / G5 = 3 => 0 pairs (*) / G6 = 3 => 0 pairs (X) E2,I2: 3.. / E2 = 3 => 0 pairs (*) / I2 = 3 => 0 pairs (X) E3,I3: 3.. / E3 = 3 => 16 pairs (_) / I3 = 3 => 0 pairs (*) D5,G5: 3.. / D5 = 3 => 16 pairs (_) / G5 = 3 => 0 pairs (*) D6,G6: 3.. / D6 = 3 => 0 pairs (*) / G6 = 3 => 0 pairs (X) G1,I1: 5.. / G1 = 5 => 23 pairs (_) / I1 = 5 => 0 pairs (*) E8,E9: 5.. / E8 = 5 => 26 pairs (_) / E9 = 5 => 0 pairs (X) E8,G8: 5.. / E8 = 5 => 26 pairs (_) / G8 = 5 => 0 pairs (X) I1,I9: 5.. / I1 = 5 => 0 pairs (*) / I9 = 5 => 0 pairs (X) E2,E3: 6.. / E2 = 6 => 16 pairs (_) / E3 = 6 => 0 pairs (*) H2,H3: 6.. / H2 = 6 => 0 pairs (*) / H3 = 6 => 0 pairs (X) C5,B6: 6.. / C5 = 6 => 0 pairs (*) / B6 = 6 => 0 pairs (X) G5,G6: 6.. / G5 = 6 => 16 pairs (_) / G6 = 6 => 0 pairs (*) C8,B9: 6.. / C8 = 6 => 16 pairs (_) / B9 = 6 => 0 pairs (*) F8,F9: 6.. / F8 = 6 => 0 pairs (*) / F9 = 6 => 0 pairs (X) E2,H2: 6.. / E2 = 6 => 16 pairs (_) / H2 = 6 => 0 pairs (*) E3,H3: 6.. / E3 = 6 => 0 pairs (*) / H3 = 6 => 0 pairs (X) C5,G5: 6.. / C5 = 6 => 0 pairs (*) / G5 = 6 => 0 pairs (X) B6,G6: 6.. / B6 = 6 => 16 pairs (_) / G6 = 6 => 0 pairs (*) C8,F8: 6.. / C8 = 6 => 16 pairs (_) / F8 = 6 => 0 pairs (*) B9,F9: 6.. / B9 = 6 => 0 pairs (*) / F9 = 6 => 0 pairs (X) B6,B9: 6.. / B6 = 6 => 16 pairs (_) / B9 = 6 => 0 pairs (*) C5,C8: 6.. / C5 = 6 => 0 pairs (*) / C8 = 6 => 0 pairs (X) H2,H3: 7.. / H2 = 7 => 16 pairs (_) / H3 = 7 => 0 pairs (*) F5,F6: 7.. / F5 = 7 => 0 pairs (*) / F6 = 7 => 0 pairs (X) G4,I5: 7.. / G4 = 7 => 0 pairs (*) / I5 = 7 => 0 pairs (X) A2,H2: 7.. / A2 = 7 => 0 pairs (*) / H2 = 7 => 0 pairs (X) C4,G4: 7.. / C4 = 7 => 23 pairs (_) / G4 = 7 => 0 pairs (*) F5,I5: 7.. / F5 = 7 => 0 pairs (*) / I5 = 7 => 0 pairs (X) I5,I9: 7.. / I5 = 7 => 23 pairs (_) / I9 = 7 => 0 pairs (*) A2,C3: 8.. / A2 = 8 => 16 pairs (_) / C3 = 8 => 0 pairs (*) I2,I3: 8.. / I2 = 8 => 0 pairs (*) / I3 = 8 => 0 pairs (X) C5,A6: 8.. / C5 = 8 => 16 pairs (_) / A6 = 8 => 0 pairs (*) D5,D6: 8.. / D5 = 8 => 0 pairs (*) / D6 = 8 => 0 pairs (X) F8,F9: 8.. / F8 = 8 => 16 pairs (_) / F9 = 8 => 0 pairs (*) G8,G9: 8.. / G8 = 8 => 0 pairs (*) / G9 = 8 => 0 pairs (X) A2,I2: 8.. / A2 = 8 => 16 pairs (_) / I2 = 8 => 0 pairs (*) C3,I3: 8.. / C3 = 8 => 0 pairs (*) / I3 = 8 => 0 pairs (X) C5,D5: 8.. / C5 = 8 => 16 pairs (_) / D5 = 8 => 0 pairs (*) A6,D6: 8.. / A6 = 8 => 0 pairs (*) / D6 = 8 => 0 pairs (X) F8,G8: 8.. / F8 = 8 => 16 pairs (_) / G8 = 8 => 0 pairs (*) F9,G9: 8.. / F9 = 8 => 0 pairs (*) / G9 = 8 => 0 pairs (X) A2,A6: 8.. / A2 = 8 => 16 pairs (_) / A6 = 8 => 0 pairs (*) C3,C5: 8.. / C3 = 8 => 0 pairs (*) / C5 = 8 => 0 pairs (X) B3,C3: 9.. / B3 = 9 => 27 pairs (_) / C3 = 9 => 0 pairs (X) G1,I1: 9.. / G1 = 9 => 0 pairs (*) / I1 = 9 => 0 pairs (X) F5,F6: 9.. / F5 = 9 => 23 pairs (_) / F6 = 9 => 0 pairs (*) G4,I5: 9.. / G4 = 9 => 23 pairs (_) / I5 = 9 => 0 pairs (*) E8,E9: 9.. / E8 = 9 => 0 pairs (X) / E9 = 9 => 26 pairs (_) C4,G4: 9.. / C4 = 9 => 0 pairs (*) / G4 = 9 => 0 pairs (X) F5,I5: 9.. / F5 = 9 => 23 pairs (_) / I5 = 9 => 0 pairs (*) B9,E9: 9.. / B9 = 9 => 0 pairs (X) / E9 = 9 => 26 pairs (_) A6,A8: 9.. / A6 = 9 => 0 pairs (X) / A8 = 9 => 27 pairs (_) G1,G4: 9.. / G1 = 9 => 0 pairs (*) / G4 = 9 => 0 pairs (X) I1,I5: 9.. / I1 = 9 => 23 pairs (_) / I5 = 9 => 0 pairs (*) * DURATION: 0:02:03.910817 START: 11:47:24.624162 END: 11:49:28.534979 2017-05-04 * CP COUNT: (58) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B3,C4,C5,D5,D6,E2,E3,E8,E9,F5,F6,F8,F9,G1,G4,G5,G6,H2,H3,I1,I2,I3,I5,I9) * 631782.4..549.12..2..5.41..32.645.8114..2..5...5.1..24582173496.1.4...324.32...1. * PAIR A2: 7,8 BLK 1 C3: 7,8,9 # reduction candidate for 7,8 C3: 9 => CTR * 631782.4.8549.12732795341683276459811483296579658173245821734967164985324.32...1. C3: 7,8 # 27 pairs * PAIR A2: 7,8 COL A A6: 7,8,9 # reduction candidate for 7,8 A6: 9 => CTR * 631782.4.8549.12732..53416832.645.8114832.65.965817324582173496716498532493256817 A6: 7,8 # 27 pairs * PAIR B3: 7,9 BLK 1 C3: 7,9,8 # reduction candidate for 7,9 C3: 8 => SOLVED * 631782945754931268298564173329645781146827359875319624582173496917456832463298517 C3: 7,9 # 16 pairs * PAIR B3: 7,9 COL B B6: 7,9,6 # reduction candidate for 7,9 B6: 7,9 => SOLVED * 631782945754931268298564173329645781146827359875319624582173496917456832463298517 B6: 6 # 16 pairs B9: 7,9,6 # reduction candidate for 7,9 B9: 7,9 # 16 pairs * PAIR C4: 7,9 BLK 4 A6: 7,9,8 # reduction candidate for 7,9 A6: 7,9 # 16 pairs B6: 7,9,6 # reduction candidate for 7,9 B6: 7,9 => SOLVED * 631782945754931268298564173329645781146827359875319624582173496917456832463298517 B6: 6 # 16 pairs * PAIR C4: 7,9 COL C C3: 7,9,8 # reduction candidate for 7,9 C3: 7,9 # 16 pairs C8: 7,9,6 # reduction candidate for 7,9 C8: 7,9 => SOLVED * 631782945754931268298564173329645781146827359875319624582173496917456832463298517 C8: 6 # 16 pairs * PAIR F6: 7,9 ROW 6 A6: 7,9,8 # reduction candidate for 7,9 A6: 7,9 # 16 pairs B6: 7,9,6 # reduction candidate for 7,9 B6: 7,9 => SOLVED * 631782945754931268298564173329645781146827359875319624582173496917456832463298517 B6: 6 # 16 pairs * PAIR A8: 7,9 BLK 7 C8: 7,9,6 # reduction candidate for 7,9 C8: 7,9 => SOLVED * 631782945754931268298564173329645781146827359875319624582173496917456832463298517 C8: 6 # 16 pairs B9: 7,9,6 # reduction candidate for 7,9 B9: 7,9 # 16 pairs * PAIR A8: 7,9 COL A A6: 7,9,8 # reduction candidate for 7,9 A6: 8 => SOLVED * 631782945754931268298564173329645781146827359875319624582173496917456832463298517 A6: 7,9 # 16 pairs * PAIR I9: 5,7 BLK 9 G8: 5,7,8 # reduction candidate for 5,7 G8: 5,7 # 16 pairs G9: 5,7,8 # reduction candidate for 5,7 G9: 5,7 => SOLVED * 631782945754931268298564173329645781146827359875319624582173496917456832463298517 G9: 8 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-262-base-pr-000.dot * REASONING * DIS # C3: 9 => CTR => C3: 7,8 * DIS # A6: 9 => CTR => A6: 7,8 * PRF # C3: 8 => SOL * PRF # B6: 7,9 => SOL * PRF # B6: 7,9 => SOL * PRF # C8: 7,9 => SOL * PRF # B6: 7,9 => SOL * PRF # C8: 7,9 => SOL * PRF # A6: 8 => SOL * PRF # G9: 5,7 => SOL * CNT 10 HDP CHAINS / 26 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B3,C4,C5,D5,D6,E2,E3,E8,E9,F5,F6,F8,F9,G1,G4,G5,G6,H2,H3,I1,I2,I3,I5,I9) * 631782.4..549.12..2..5.41..32.645.8114..2..5...5.1..24582173496.1.4...324.32...1. * PAIR A2: 7,8 BLK 1 C3: 7,8,9 # reduction candidate for 7,8 C3: 9 => CTR * 631782.4.8549.12732795341683276459811483296579658173245821734967164985324.32...1. * PAIR A2: 7,8 COL A A6: 7,8,9 # reduction candidate for 7,8 A6: 7,8 => SOLVED * 631782945754931268298564173329645781146827359875319624582173496917456832463298517 * DURATION: 0:00:04.874744 START: 11:50:06.076040 END: 11:50:10.950784 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-262-base-pr-001.dot * REASONING * DIS # C3: 9 => CTR => C3: 7,8 * PRF C3: 7,8 # A6: 7,8 => SOL * STA C3: 7,8 + A6: 7,8 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 262 solution: 631782945754931268298564173329645781146827359875319624582173496917456832463298517 info: 2092 FNBTWY S8.f 35866 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 631782945754931268298564173329645781146827359875319624582173496917456832463298517 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 # C3: 7,8 => UNS * DIS # C3: 9 => CTR => C3: 7,8 * INC # A6: 7,8 => UNS * DIS # A6: 9 => CTR => A6: 7,8 * INC # C3: 7,9 => UNS * PRF # C3: 8 => SOL * PRF # B6: 7,9 => SOL * INC # B6: 6 => UNS * INC # B9: 7,9 => UNS * INC # A6: 7,9 => UNS * PRF # B6: 7,9 => SOL * INC # B6: 6 => UNS * INC # C3: 7,9 => UNS * PRF # C8: 7,9 => SOL * INC # C8: 6 => UNS * INC # A6: 7,9 => UNS * PRF # B6: 7,9 => SOL * INC # B6: 6 => UNS * PRF # C8: 7,9 => SOL * INC # C8: 6 => UNS * INC # B9: 7,9 => UNS * INC # A6: 7,9 => UNS * PRF # A6: 8 => SOL * INC # G8: 5,7 => UNS * PRF # G9: 5,7 => SOL * INC # G9: 8 => UNS * CNT 26 HDP CHAINS / 26 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C3: 7,8 => UNS * DIS # C3: 9 => CTR => C3: 7,8 * PRF C3: 7,8 # A6: 7,8 => SOL * STA C3: 7,8 + A6: 7,8 * CNT 3 HDP CHAINS / 3 HYP OPENED