Analysis of xx-top500-251-base.sdk
Contents
Original Sudoku
level: medium
position: 3...5............1.......4.5.....8.....7..3...8.4........23.5....4..6....1.....7. initial
Autosolve
position: 34..517....584..311.83...45537.1.8.44.17853...8.4.3157...23451..54176..3.1359847. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C1: 6,9 => SOL * DIS # C1: 2 => CTR => C1: 6,9 * DIS # B3: 2,6 => CTR => B3: 7,9 * DIS # C6: 9 => CTR => C6: 2,6 * DIS # H5: 9 => CTR => H5: 2,6 * DIS # B3: 2,6 => CTR => B3: 7,9 * DIS # C6: 6,9 => CTR => C6: 2 * PRF # C6: 2 => SOL * DIS # C6: 9 => CTR => C6: 2,6 * DIS # H5: 9 => CTR => H5: 2,6 * PRF # H5: 2,9 => SOL * DIS # H5: 6 => CTR => H5: 2,9 * PRF # C1: 6,9 => SOL * DIS # C1: 2 => CTR => C1: 6,9 * DIS # C6: 6,9 => CTR => C6: 2 * PRF # C6: 2 => SOL * PRF # G2: 2,9 => SOL * CNT 17 HDP CHAINS / 41 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C1: 6,9 => SOL * STA C1: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 3...5............1.......4.5.....8.....7..3...8.4........23.5....4..6....1.....7. | initial |
| 34..517....584..311.83...45537.1.8.44.17853...8.4.3157...23451..54176..3.1359847. | autosolve |
| 349651782625847931178329645537912864461785329982463157796234518854176293213598476 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) D1: 6,9 E3: 2,6 B5: 2,6 A6: 6,9 D4: 6,9 F4: 2,9 E6: 2,6 H4: 2,6 I5: 2,9 C7: 6,9 A9: 2,6 G8: 2,9 I9: 2,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B5,C6: 2.. / B5 = 2 => 0 pairs (X) / C6 = 2 => 0 pairs (_) F4,E6: 2.. / F4 = 2 => 0 pairs (*) / E6 = 2 => 0 pairs (X) A8,A9: 2.. / A8 = 2 => 0 pairs (X) / A9 = 2 => 13 pairs (_) F4,H4: 2.. / F4 = 2 => 0 pairs (*) / H4 = 2 => 0 pairs (X) C6,E6: 2.. / C6 = 2 => 0 pairs (*) / E6 = 2 => 0 pairs (X) A9,I9: 2.. / A9 = 2 => 13 pairs (_) / I9 = 2 => 0 pairs (X) C1,C6: 2.. / C1 = 2 => 0 pairs (X) / C6 = 2 => 0 pairs (_) E3,E6: 2.. / E3 = 2 => 0 pairs (*) / E6 = 2 => 0 pairs (X) D1,E3: 6.. / D1 = 6 => 0 pairs (*) / E3 = 6 => 0 pairs (X) G2,G3: 6.. / G2 = 6 => 15 pairs (_) / G3 = 6 => 0 pairs (*) D4,E6: 6.. / D4 = 6 => 0 pairs (X) / E6 = 6 => 0 pairs (_) H4,H5: 6.. / H4 = 6 => 0 pairs (*) / H5 = 6 => 0 pairs (X) I7,I9: 6.. / I7 = 6 => 0 pairs (X) / I9 = 6 => 13 pairs (_) C1,D1: 6.. / C1 = 6 => 0 pairs (X) / D1 = 6 => 0 pairs (_) D4,H4: 6.. / D4 = 6 => 0 pairs (X) / H4 = 6 => 0 pairs (_) B5,H5: 6.. / B5 = 6 => 0 pairs (*) / H5 = 6 => 0 pairs (X) A9,I9: 6.. / A9 = 6 => 0 pairs (X) / I9 = 6 => 13 pairs (_) D1,D4: 6.. / D1 = 6 => 0 pairs (*) / D4 = 6 => 0 pairs (X) E3,E6: 6.. / E3 = 6 => 0 pairs (X) / E6 = 6 => 0 pairs (_) F2,F3: 7.. / F2 = 7 => 17 pairs (_) / F3 = 7 => 14 pairs (_) A7,B7: 7.. / A7 = 7 => 15 pairs (_) / B7 = 7 => 15 pairs (_) B3,F3: 7.. / B3 = 7 => 17 pairs (_) / F3 = 7 => 14 pairs (_) A2,A7: 7.. / A2 = 7 => 15 pairs (_) / A7 = 7 => 15 pairs (_) H1,I1: 8.. / H1 = 8 => 13 pairs (_) / I1 = 8 => 18 pairs (_) A7,A8: 8.. / A7 = 8 => 18 pairs (_) / A8 = 8 => 13 pairs (_) I7,H8: 8.. / I7 = 8 => 13 pairs (_) / H8 = 8 => 18 pairs (_) A7,I7: 8.. / A7 = 8 => 18 pairs (_) / I7 = 8 => 13 pairs (_) A8,H8: 8.. / A8 = 8 => 13 pairs (_) / H8 = 8 => 18 pairs (_) H1,H8: 8.. / H1 = 8 => 13 pairs (_) / H8 = 8 => 18 pairs (_) I1,I7: 8.. / I1 = 8 => 18 pairs (_) / I7 = 8 => 13 pairs (_) A6,C6: 9.. / A6 = 9 => 16 pairs (_) / C6 = 9 => 0 pairs (X) D4,F4: 9.. / D4 = 9 => 0 pairs (*) / F4 = 9 => 0 pairs (X) H5,I5: 9.. / H5 = 9 => 0 pairs (X) / I5 = 9 => 18 pairs (_) D1,D4: 9.. / D1 = 9 => 0 pairs (X) / D4 = 9 => 0 pairs (_) * DURATION: 0:00:57.913145 START: 11:22:10.841598 END: 11:23:08.754743 2017-05-04 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A9,B5,C7,D1,D4,E3,E6,F4,G8,H4,I5,I9) * 34..517....584..311.83...45537.1.8.44.17853...8.4.3157...23451..54176..3.1359847. * PAIR D1: 6,9 ROW 1 C1: 6,9,2 # reduction candidate for 6,9 C1: 6,9 => SOLVED * 349651782625847931178329645537912864461785329982463157796234518854176293213598476 C1: 2 => CTR * 3426517....584..311.832..45537.1.8.44.17853...8.4.3157...23451..54176..3.1359847. * PAIR E3: 2,6 ROW 3 B3: 2,6,7,9 # reduction candidate for 2,6 B3: 2,6 => CTR * 34..517....584.6311.83.7945537.1.8.44617853..982463157...23451..541762.3213598476 B3: 7,9 # 14 pairs G3: 2,6,9 # reduction candidate for 2,6 G3: 2,6 # 16 pairs * PAIR B5: 2,6 BLK 4 C6: 2,6,9 # reduction candidate for 2,6 C6: 9 => CTR * 3426517....584..311.832..45537.1.8.44.17853...8.4.3157...23451..54176..3.1359847. C6: 2,6 # 16 pairs * PAIR B5: 2,6 ROW 5 H5: 2,6,9 # reduction candidate for 2,6 H5: 9 => CTR * 34..517....584..311.83...45537.1.864461785392982463157...23451..54176923213598476 H5: 2,6 # 18 pairs * PAIR B5: 2,6 COL B B2: 2,6,7,9 # reduction candidate for 2,6 B2: 2,6 # 16 pairs B3: 2,6,7,9 # reduction candidate for 2,6 B3: 2,6 => CTR * 34..517....584.6311.83.7945537.1.8.44617853..982463157...23451..541762.3213598476 B3: 7,9 # 14 pairs * PAIR A6: 6,9 BLK 4 C6: 6,9,2 # reduction candidate for 6,9 C6: 6,9 => CTR * 3426517....584..311.832..45537.1.8.44.17853...8.4.3157...23451..54176..3.1359847. C6: 2 => SOLVED * 349651782625847931178329645537912864461785329982463157796234518854176293213598476 * PAIR A6: 6,9 COL A A2: 6,9,7 # reduction candidate for 6,9 A2: 6,9 # 15 pairs A7: 6,9,7,8 # reduction candidate for 6,9 A7: 6,9 # 16 pairs * PAIR F4: 2,9 COL F F2: 2,9,7 # reduction candidate for 2,9 F2: 2,9 # 14 pairs F3: 2,9,7 # reduction candidate for 2,9 F3: 2,9 # 17 pairs * PAIR E6: 2,6 ROW 6 C6: 2,6,9 # reduction candidate for 2,6 C6: 9 => CTR * 3426517....584..311.832..45537.1.8.44.17853...8.4.3157...23451..54176..3.1359847. C6: 2,6 # 16 pairs * PAIR H4: 2,6 BLK 6 H5: 2,6,9 # reduction candidate for 2,6 H5: 9 => CTR * 34..517....584..311.83...45537.1.864461785392982463157...23451..54176923213598476 H5: 2,6 # 18 pairs * PAIR I5: 2,9 BLK 6 H5: 2,9,6 # reduction candidate for 2,9 H5: 2,9 => SOLVED * 349651782625847931178329645537912864461785329982463157796234518854176293213598476 H5: 6 => CTR * 34..517....584..311.83...45537619824421785369.8.423157...23451..54176..3.1359847. * PAIR I5: 2,9 COL I I1: 2,9,8 # reduction candidate for 2,9 I1: 8 # 18 pairs I1: 2,9 # 13 pairs * PAIR C7: 6,9 BLK 7 A7: 6,9,7,8 # reduction candidate for 6,9 A7: 6,9 # 16 pairs B7: 6,9,7 # reduction candidate for 6,9 B7: 6,9 # 15 pairs * PAIR C7: 6,9 ROW 7 I7: 6,9,8 # reduction candidate for 6,9 I7: 6,9 # 18 pairs I7: 8 # 13 pairs * PAIR C7: 6,9 COL C C1: 6,9,2 # reduction candidate for 6,9 C1: 6,9 => SOLVED * 349651782625847931178329645537912864461785329982463157796234518854176293213598476 C1: 2 => CTR * 3426517....584..311.832..45537.1.8.44.17853...8.4.3157...23451..54176..3.1359847. C6: 6,9,2 # reduction candidate for 6,9 C6: 6,9 => CTR * 3426517....584..311.832..45537.1.8.44.17853...8.4.3157...23451..54176..3.1359847. C6: 2 => SOLVED * 349651782625847931178329645537912864461785329982463157796234518854176293213598476 * PAIR G8: 2,9 BLK 9 H8: 2,9,8 # reduction candidate for 2,9 H8: 8 # 18 pairs H8: 2,9 # 13 pairs * PAIR G8: 2,9 ROW 8 A8: 2,9,8 # reduction candidate for 2,9 A8: 2,9 # 18 pairs A8: 8 # 13 pairs * PAIR G8: 2,9 COL G G2: 2,9,6 # reduction candidate for 2,9 G2: 2,9 => SOLVED * 349651782625847931178329645537912864461785329982463157796234518854176293213598476 G2: 6 # 15 pairs G3: 2,9,6 # reduction candidate for 2,9 G3: 2,9 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-251-base-pr-000.dot * REASONING * PRF # C1: 6,9 => SOL * DIS # C1: 2 => CTR => C1: 6,9 * DIS # B3: 2,6 => CTR => B3: 7,9 * DIS # C6: 9 => CTR => C6: 2,6 * DIS # H5: 9 => CTR => H5: 2,6 * DIS # B3: 2,6 => CTR => B3: 7,9 * DIS # C6: 6,9 => CTR => C6: 2 * PRF # C6: 2 => SOL * DIS # C6: 9 => CTR => C6: 2,6 * DIS # H5: 9 => CTR => H5: 2,6 * PRF # H5: 2,9 => SOL * DIS # H5: 6 => CTR => H5: 2,9 * PRF # C1: 6,9 => SOL * DIS # C1: 2 => CTR => C1: 6,9 * DIS # C6: 6,9 => CTR => C6: 2 * PRF # C6: 2 => SOL * PRF # G2: 2,9 => SOL * CNT 17 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A9,B5,C7,D1,D4,E3,E6,F4,G8,H4,I5,I9) * 34..517....584..311.83...45537.1.8.44.17853...8.4.3157...23451..54176..3.1359847. * PAIR D1: 6,9 ROW 1 C1: 6,9,2 # reduction candidate for 6,9 C1: 6,9 => SOLVED * 349651782625847931178329645537912864461785329982463157796234518854176293213598476 * DURATION: 0:00:02.112322 START: 11:23:49.329236 END: 11:23:51.441558 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-251-base-pr-001.dot * REASONING * PRF # C1: 6,9 => SOL * STA C1: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 251 solution: 349651782625847931178329645537912864461785329982463157796234518854176293213598476 info: 2074 FNBWX S8.f 29163 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 349651782625847931178329645537912864461785329982463157796234518854176293213598476 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 # C1: 6,9 => SOL * DIS # C1: 2 => CTR => C1: 6,9 * DIS # B3: 2,6 => CTR => B3: 7,9 * INC # B3: 7,9 => UNS * INC # G3: 2,6 => UNS * INC # C6: 2,6 => UNS * DIS # C6: 9 => CTR => C6: 2,6 * INC # H5: 2,6 => UNS * DIS # H5: 9 => CTR => H5: 2,6 * INC # B2: 2,6 => UNS * DIS # B3: 2,6 => CTR => B3: 7,9 * INC # B3: 7,9 => UNS * DIS # C6: 6,9 => CTR => C6: 2 * PRF # C6: 2 => SOL * INC # A2: 6,9 => UNS * INC # A7: 6,9 => UNS * INC # F2: 2,9 => UNS * INC # F3: 2,9 => UNS * INC # C6: 2,6 => UNS * DIS # C6: 9 => CTR => C6: 2,6 * INC # H5: 2,6 => UNS * DIS # H5: 9 => CTR => H5: 2,6 * PRF # H5: 2,9 => SOL * DIS # H5: 6 => CTR => H5: 2,9 * INC # I1: 2,9 => UNS * INC # I1: 8 => UNS * INC # A7: 6,9 => UNS * INC # B7: 6,9 => UNS * INC # I7: 6,9 => UNS * INC # I7: 8 => UNS * PRF # C1: 6,9 => SOL * DIS # C1: 2 => CTR => C1: 6,9 * DIS # C6: 6,9 => CTR => C6: 2 * PRF # C6: 2 => SOL * INC # H8: 2,9 => UNS * INC # H8: 8 => UNS * INC # A8: 2,9 => UNS * INC # A8: 8 => UNS * PRF # G2: 2,9 => SOL * INC # G2: 6 => UNS * INC # G3: 2,9 => UNS * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C1: 6,9 => SOL * STA C1: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED