Analysis of xx-top500-131-base.sdk
Contents
Original Sudoku
level: medium
position: 1.4...2..6..5...3...........3.....582...14................2.1...5.8.....7........ initial
Autosolve
position: 1.4.832.56.854..315.31..84..312...58285.14....67.58.1284..251.335.8.1.2471243.58. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # H1: 7,9 => SOL * PRF # H1: 7,9 => SOL * DIS # G4: 7,9 => CTR => G4: 4,6 * DIS # G5: 7,9 => CTR => G5: 3,6 * CNT 4 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # H1: 7,9 => SOL * STA H1: 7,9 * CNT 1 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.4...2..6..5...3...........3.....582...14................2.1...5.8.....7........ | initial |
| 1.4.832.56.854..315.31..84..312...58285.14....67.58.1284..251.335.8.1.2471243.58. | autosolve |
| 194683275678542931523179846931267458285314697467958312849725163356891724712436589 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) B1: 7,9 G2: 7,9 A4: 4,9 A6: 4,9 D6: 3,9 C7: 6,9 C8: 6,9 F9: 6,9 I9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,B3: 2.. / B2 = 2 => 11 pairs (_) / B3 = 2 => 10 pairs (_) F2,F3: 2.. / F2 = 2 => 10 pairs (_) / F3 = 2 => 11 pairs (_) B2,F2: 2.. / B2 = 2 => 11 pairs (_) / F2 = 2 => 10 pairs (_) B3,F3: 2.. / B3 = 2 => 10 pairs (_) / F3 = 2 => 11 pairs (_) D5,D6: 3.. / D5 = 3 => 10 pairs (_) / D6 = 3 => 9 pairs (_) G5,G6: 3.. / G5 = 3 => 9 pairs (_) / G6 = 3 => 10 pairs (_) D5,G5: 3.. / D5 = 3 => 10 pairs (_) / G5 = 3 => 9 pairs (_) D6,G6: 3.. / D6 = 3 => 9 pairs (_) / G6 = 3 => 10 pairs (_) A4,A6: 4.. / A4 = 4 => 6 pairs (_) / A6 = 4 => 13 pairs (_) G4,G6: 4.. / G4 = 4 => 13 pairs (_) / G6 = 4 => 6 pairs (_) A4,G4: 4.. / A4 = 4 => 6 pairs (_) / G4 = 4 => 13 pairs (_) A6,G6: 4.. / A6 = 4 => 13 pairs (_) / G6 = 4 => 6 pairs (_) H1,I3: 6.. / H1 = 6 => 13 pairs (_) / I3 = 6 => 0 pairs (*) C7,C8: 6.. / C7 = 6 => 11 pairs (_) / C8 = 6 => 17 pairs (_) D1,H1: 6.. / D1 = 6 => 0 pairs (*) / H1 = 6 => 0 pairs (X) F9,I9: 6.. / F9 = 6 => 14 pairs (_) / I9 = 6 => 21 pairs (_) D7,E8: 7.. / D7 = 7 => 21 pairs (_) / E8 = 7 => 15 pairs (_) H7,G8: 7.. / H7 = 7 => 15 pairs (_) / G8 = 7 => 21 pairs (_) D7,H7: 7.. / D7 = 7 => 21 pairs (_) / H7 = 7 => 15 pairs (_) E8,G8: 7.. / E8 = 7 => 15 pairs (_) / G8 = 7 => 21 pairs (_) I3,I5: 7.. / I3 = 7 => 18 pairs (_) / I5 = 7 => 11 pairs (_) A4,A6: 9.. / A4 = 9 => 13 pairs (_) / A6 = 9 => 6 pairs (_) C7,C8: 9.. / C7 = 9 => 17 pairs (_) / C8 = 9 => 11 pairs (_) F9,I9: 9.. / F9 = 9 => 21 pairs (_) / I9 = 9 => 14 pairs (_) * DURATION: 0:00:37.423016 START: 07:14:25.614384 END: 07:15:03.037400 2017-05-04 * CP COUNT: (24) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B1,C7,C8,D6,F9,G2,I9) * 1.4.832.56.854..315.31..84..312...58285.14....67.58.1284..251.335.8.1.2471243.58. * PAIR B1: 7,9 BLK 1 B2: 7,9,2 # reduction candidate for 7,9 B2: 7,9 # 10 pairs B3: 7,9,2 # reduction candidate for 7,9 B3: 7,9 # 11 pairs * PAIR B1: 7,9 ROW 1 D1: 7,9,6 # reduction candidate for 7,9 D1: 7,9 # 13 pairs H1: 7,9,6 # reduction candidate for 7,9 H1: 7,9 => SOLVED * 194683275678542931523179846931267458285314697467958312849725163356891724712436589 H1: 6 # 13 pairs * PAIR G2: 7,9 BLK 3 H1: 7,9,6 # reduction candidate for 7,9 H1: 7,9 => SOLVED * 194683275678542931523179846931267458285314697467958312849725163356891724712436589 H1: 6 # 13 pairs I3: 7,9,6 # reduction candidate for 7,9 I3: 7,9 # 13 pairs * PAIR G2: 7,9 ROW 2 B2: 7,9,2 # reduction candidate for 7,9 B2: 7,9 # 10 pairs F2: 7,9,2 # reduction candidate for 7,9 F2: 7,9 # 11 pairs * PAIR G2: 7,9 COL G G4: 7,9,4,6 # reduction candidate for 7,9 G4: 7,9 => CTR * 1.46832956.854..315.31..84.43126..58285.143..967358412846925173359871624712436589 G4: 4,6 # 10 pairs G5: 7,9,3,6 # reduction candidate for 7,9 G5: 7,9 => CTR * 1.4.832.56.854..315.31..84.9312..458285314...46795831284..251.335.8.1624712436589 G5: 3,6 # 10 pairs G8: 7,9,6 # reduction candidate for 7,9 G8: 7,9 # 16 pairs * PAIR A4: 4,9 ROW 4 G4: 4,9,6,7 # reduction candidate for 4,9 G4: 4,9 # 15 pairs G4: 6,7 # 8 pairs * PAIR A6: 4,9 ROW 6 G6: 4,9,3 # reduction candidate for 4,9 G6: 3 # 10 pairs G6: 4,9 # 9 pairs * PAIR D6: 3,9 BLK 5 D5: 3,9,6,7 # reduction candidate for 3,9 D5: 3,9 # 15 pairs D5: 6,7 # 8 pairs * PAIR D6: 3,9 ROW 6 G6: 3,9,4 # reduction candidate for 3,9 G6: 3,9 # 13 pairs G6: 4 # 6 pairs * PAIR C7: 6,9 ROW 7 D7: 6,9,7 # reduction candidate for 6,9 D7: 6,9 # 15 pairs H7: 6,9,7 # reduction candidate for 6,9 H7: 6,9 # 21 pairs * PAIR C8: 6,9 ROW 8 E8: 6,9,7 # reduction candidate for 6,9 E8: 6,9 # 21 pairs G8: 6,9,7 # reduction candidate for 6,9 G8: 6,9 # 15 pairs * PAIR F9: 6,9 BLK 8 D7: 6,9,7 # reduction candidate for 6,9 D7: 6,9 # 15 pairs E8: 6,9,7 # reduction candidate for 6,9 E8: 6,9 # 21 pairs * PAIR F9: 6,9 COL F F3: 6,9,2,7 # reduction candidate for 6,9 F3: 6,9 # 12 pairs F4: 6,9,7 # reduction candidate for 6,9 F4: 6,9 # 14 pairs * PAIR I9: 6,9 BLK 9 H7: 6,9,7 # reduction candidate for 6,9 H7: 6,9 # 21 pairs G8: 6,9,7 # reduction candidate for 6,9 G8: 6,9 # 15 pairs * PAIR I9: 6,9 COL I I3: 6,9,7 # reduction candidate for 6,9 I3: 6,9 # 11 pairs I5: 6,9,7 # reduction candidate for 6,9 I5: 6,9 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-131-base-pr-000.dot * REASONING * PRF # H1: 7,9 => SOL * PRF # H1: 7,9 => SOL * DIS # G4: 7,9 => CTR => G4: 4,6 * DIS # G5: 7,9 => CTR => G5: 3,6 * CNT 4 HDP CHAINS / 35 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B1,C7,C8,D6,F9,G2,I9) * 1.4.832.56.854..315.31..84..312...58285.14....67.58.1284..251.335.8.1.2471243.58. * PAIR B1: 7,9 BLK 1 B2: 7,9,2 # reduction candidate for 7,9 B2: 7,9 # 10 pairs B3: 7,9,2 # reduction candidate for 7,9 B3: 7,9 # 11 pairs * PAIR B1: 7,9 ROW 1 D1: 7,9,6 # reduction candidate for 7,9 D1: 7,9 # 13 pairs H1: 7,9,6 # reduction candidate for 7,9 H1: 7,9 => SOLVED * 194683275678542931523179846931267458285314697467958312849725163356891724712436589 * DURATION: 0:00:04.356644 START: 07:15:33.594500 END: 07:15:37.951144 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-131-base-pr-001.dot * REASONING * PRF # H1: 7,9 => SOL * STA H1: 7,9 * CNT 1 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 131 solution: 194683275678542931523179846931267458285314697467958312849725163356891724712436589 info: 1811 FNBWXY S8.f 26041 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 194683275678542931523179846931267458285314697467958312849725163356891724712436589 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 # B2: 7,9 => UNS * INC # B3: 7,9 => UNS * INC # D1: 7,9 => UNS * PRF # H1: 7,9 => SOL * INC # H1: 6 => UNS * PRF # H1: 7,9 => SOL * INC # H1: 6 => UNS * INC # I3: 7,9 => UNS * INC # B2: 7,9 => UNS * INC # F2: 7,9 => UNS * DIS # G4: 7,9 => CTR => G4: 4,6 * INC # G4: 4,6 => UNS * DIS # G5: 7,9 => CTR => G5: 3,6 * INC # G5: 3,6 => UNS * INC # G8: 7,9 => UNS * INC # G4: 4,9 => UNS * INC # G4: 6,7 => UNS * INC # G6: 4,9 => UNS * INC # G6: 3 => UNS * INC # D5: 3,9 => UNS * INC # D5: 6,7 => UNS * INC # G6: 3,9 => UNS * INC # G6: 4 => UNS * INC # D7: 6,9 => UNS * INC # H7: 6,9 => UNS * INC # E8: 6,9 => UNS * INC # G8: 6,9 => UNS * INC # D7: 6,9 => UNS * INC # E8: 6,9 => UNS * INC # F3: 6,9 => UNS * INC # F4: 6,9 => UNS * INC # H7: 6,9 => UNS * INC # G8: 6,9 => UNS * INC # I3: 6,9 => UNS * INC # I5: 6,9 => UNS * CNT 35 HDP CHAINS / 35 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 7,9 => UNS * INC # B3: 7,9 => UNS * INC # D1: 7,9 => UNS * PRF # H1: 7,9 => SOL * STA H1: 7,9 * CNT 4 HDP CHAINS / 4 HYP OPENED