Analysis of xx-top500-207-base.sdk
Contents
Original Sudoku
level: medium
position: ....2..4.8.....1..1..9......26.5..........8...4.......9..8.1..........65...3..... initial
Autosolve
position: 69.12..488..5..19.1..98....326.58.19.19...8...48.19...9..861...481.9.365267345981 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G3: 5,7 => CTR => G3: 2,6 * PRF # F5: 3,7 => SOL * DIS # F5: 2 => CTR => F5: 3,7 * DIS # G3: 5,7 => CTR => G3: 2,6 * DIS # G6: 5,7 => CTR => G6: 2,6 * DIS # I3: 2,6 => CTR => I3: 3,7 * DIS # I6: 2,6 => CTR => I6: 3,7 * DIS # H5: 5,7 => CTR => H5: 2 * PRF # H5: 2 => SOL * DIS # G6: 5,7 => CTR => G6: 2,6 * PRF # F5: 3,7 => SOL * DIS # F5: 2 => CTR => F5: 3,7 * PRF # G7: 4,7 => SOL * DIS # G7: 2 => CTR => G7: 4,7 * PRF # D6: 2,7 => SOL * DIS # D6: 6 => CTR => D6: 2,7 * DIS # F5: 2,7 => CTR => F5: 3 * PRF # F5: 3 => SOL * DIS # G7: 2,7 => CTR => G7: 4 * PRF # G7: 4 => SOL * PRF # I7: 2,7 => SOL * DIS # I7: 4 => CTR => I7: 2,7 * DIS # H3: 2,7 => CTR => H3: 3,5 * DIS # H6: 2,7 => CTR => H6: 3,5 * CNT 24 HDP CHAINS / 37 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G3: 5,7 => CTR => G3: 2,6 * PRF G3: 2,6 # H3: 3 => SOL * STA G3: 2,6 + H3: 3 * CNT 2 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....2..4.8.....1..1..9......26.5..........8...4.......9..8.1..........65...3..... | initial |
| 69.12..488..5..19.1..98....326.58.19.19...8...48.19...9..861...481.9.365267345981 | autosolve |
| 693127548872534196154986237326458719519673824748219653935861472481792365267345981 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (23) C1: 3,5 B2: 3,7 C2: 2,4 B3: 5,7 C3: 2,4 F1: 3,7 E2: 3,7 F2: 4,6 F3: 4,6 G1: 5,7 I2: 2,6 A5: 5,7 A6: 5,7 D4: 4,7 D5: 4,6 E5: 3,7 G4: 4,7 I5: 4,6 B7: 3,5 C7: 3,5 D8: 2,7 F8: 2,7 H7: 2,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,C3: 2.. / C2 = 2 => 0 pairs (*) / C3 = 2 => 0 pairs (X) F5,D6: 2.. / F5 = 2 => 0 pairs (X) / D6 = 2 => 0 pairs (_) D8,F8: 2.. / D8 = 2 => 0 pairs (X) / F8 = 2 => 0 pairs (_) C2,I2: 2.. / C2 = 2 => 0 pairs (*) / I2 = 2 => 0 pairs (X) F5,H5: 2.. / F5 = 2 => 0 pairs (X) / H5 = 2 => 0 pairs (_) D6,D8: 2.. / D6 = 2 => 0 pairs (*) / D8 = 2 => 0 pairs (X) F5,F8: 2.. / F5 = 2 => 0 pairs (X) / F8 = 2 => 0 pairs (_) C1,B2: 3.. / C1 = 3 => 0 pairs (*) / B2 = 3 => 0 pairs (X) F1,E2: 3.. / F1 = 3 => 0 pairs (X) / E2 = 3 => 0 pairs (_) H3,I3: 3.. / H3 = 3 => 23 pairs (_) / I3 = 3 => 23 pairs (_) E5,F5: 3.. / E5 = 3 => 0 pairs (X) / F5 = 3 => 0 pairs (_) H6,I6: 3.. / H6 = 3 => 23 pairs (_) / I6 = 3 => 23 pairs (_) B7,C7: 3.. / B7 = 3 => 0 pairs (*) / C7 = 3 => 0 pairs (X) C1,F1: 3.. / C1 = 3 => 0 pairs (*) / F1 = 3 => 0 pairs (X) B2,E2: 3.. / B2 = 3 => 0 pairs (X) / E2 = 3 => 0 pairs (_) B2,B7: 3.. / B2 = 3 => 0 pairs (X) / B7 = 3 => 0 pairs (_) C1,C7: 3.. / C1 = 3 => 0 pairs (*) / C7 = 3 => 0 pairs (X) E2,E5: 3.. / E2 = 3 => 0 pairs (*) / E5 = 3 => 0 pairs (X) F1,F5: 3.. / F1 = 3 => 0 pairs (X) / F5 = 3 => 0 pairs (_) H3,H6: 3.. / H3 = 3 => 23 pairs (_) / H6 = 3 => 23 pairs (_) I3,I6: 3.. / I3 = 3 => 23 pairs (_) / I6 = 3 => 23 pairs (_) C2,C3: 4.. / C2 = 4 => 19 pairs (_) / C3 = 4 => 0 pairs (*) F2,F3: 4.. / F2 = 4 => 0 pairs (*) / F3 = 4 => 0 pairs (X) D4,D5: 4.. / D4 = 4 => 0 pairs (*) / D5 = 4 => 0 pairs (X) G4,I5: 4.. / G4 = 4 => 0 pairs (X) / I5 = 4 => 0 pairs (_) G7,I7: 4.. / G7 = 4 => 0 pairs (*) / I7 = 4 => 0 pairs (X) C2,F2: 4.. / C2 = 4 => 19 pairs (_) / F2 = 4 => 0 pairs (*) C3,F3: 4.. / C3 = 4 => 0 pairs (*) / F3 = 4 => 0 pairs (X) D4,G4: 4.. / D4 = 4 => 0 pairs (*) / G4 = 4 => 0 pairs (X) D5,I5: 4.. / D5 = 4 => 0 pairs (X) / I5 = 4 => 0 pairs (_) G4,G7: 4.. / G4 = 4 => 0 pairs (X) / G7 = 4 => 0 pairs (_) I5,I7: 4.. / I5 = 4 => 0 pairs (*) / I7 = 4 => 0 pairs (X) C1,B3: 5.. / C1 = 5 => 0 pairs (X) / B3 = 5 => 0 pairs (_) A5,A6: 5.. / A5 = 5 => 25 pairs (_) / A6 = 5 => 0 pairs (X) B7,C7: 5.. / B7 = 5 => 0 pairs (X) / C7 = 5 => 0 pairs (_) C1,G1: 5.. / C1 = 5 => 0 pairs (X) / G1 = 5 => 0 pairs (_) A5,H5: 5.. / A5 = 5 => 25 pairs (_) / H5 = 5 => 0 pairs (X) B3,B7: 5.. / B3 = 5 => 0 pairs (*) / B7 = 5 => 0 pairs (X) C1,C7: 5.. / C1 = 5 => 0 pairs (X) / C7 = 5 => 0 pairs (_) F2,F3: 6.. / F2 = 6 => 19 pairs (_) / F3 = 6 => 0 pairs (*) D5,D6: 6.. / D5 = 6 => 0 pairs (*) / D6 = 6 => 0 pairs (X) F2,I2: 6.. / F2 = 6 => 19 pairs (_) / I2 = 6 => 0 pairs (*) D5,I5: 6.. / D5 = 6 => 0 pairs (*) / I5 = 6 => 0 pairs (X) G3,G6: 6.. / G3 = 6 => 20 pairs (_) / G6 = 6 => 0 pairs (*) B2,B3: 7.. / B2 = 7 => 0 pairs (*) / B3 = 7 => 0 pairs (X) F1,E2: 7.. / F1 = 7 => 0 pairs (*) / E2 = 7 => 0 pairs (X) A5,A6: 7.. / A5 = 7 => 0 pairs (X) / A6 = 7 => 25 pairs (_) D8,F8: 7.. / D8 = 7 => 0 pairs (*) / F8 = 7 => 0 pairs (X) F1,G1: 7.. / F1 = 7 => 0 pairs (*) / G1 = 7 => 0 pairs (X) B2,E2: 7.. / B2 = 7 => 0 pairs (*) / E2 = 7 => 0 pairs (X) D4,G4: 7.. / D4 = 7 => 0 pairs (X) / G4 = 7 => 0 pairs (_) E2,E5: 7.. / E2 = 7 => 0 pairs (X) / E5 = 7 => 0 pairs (_) * DURATION: 0:01:57.683536 START: 09:52:27.259977 END: 09:54:24.943513 2017-05-04 * CP COUNT: (52) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B2,B3,B7,C1,C2,C3,C7,D4,D5,D8,E2,E5,F1,F2,F3,F8,G1,G4,H7,I2,I5) * 69.12..488..5..19.1..98....326.58.19.19...8...48.19...9..861...481.9.365267345981 * PAIR B3: 5,7 ROW 3 G3: 5,7,2,6 # reduction candidate for 5,7 G3: 5,7 => CTR * 69.12..488..5..19.1..98....326.58.19.19...8...48.196..9..861274481.9.365267345981 G3: 2,6 # 25 pairs H3: 5,7,2,3 # reduction candidate for 5,7 H3: 5,7 # 25 pairs * PAIR F1: 3,7 COL F F5: 3,7,2 # reduction candidate for 3,7 F5: 3,7 => SOLVED * 693127548872534196154986237326458719519673824748219653935861472481792365267345981 F5: 2 => CTR * 69.12374883.57.19.17.98....326758419.194328.6.48619...953861274481297365267345981 * PAIR G1: 5,7 BLK 3 G3: 5,7,2,6 # reduction candidate for 5,7 G3: 5,7 => CTR * 69.12..488..5..19.1..98....326.58.19.19...8...48.196..9..861274481.9.365267345981 G3: 2,6 # 25 pairs H3: 5,7,2,3 # reduction candidate for 5,7 H3: 5,7 # 25 pairs * PAIR G1: 5,7 COL G G6: 5,7,2,6 # reduction candidate for 5,7 G6: 5,7 => CTR * 69.1237488..5.61921.29846..326.58419.194..8.6.48619.239..861274481297365267345981 G6: 2,6 # 24 pairs * PAIR I2: 2,6 BLK 3 G3: 2,6,5,7 # reduction candidate for 2,6 G3: 2,6 # 25 pairs I3: 2,6,3,7 # reduction candidate for 2,6 I3: 2,6 => CTR * 69.12..488..5..19.1..98..3.326.58.19.19...8.4.48.196.39..861427481.9.365267345981 I3: 3,7 # 24 pairs * PAIR I2: 2,6 COL I I6: 2,6,3,7 # reduction candidate for 2,6 I6: 2,6 => CTR * 69.12..488..5..19.1..98...3326458719.196.2854548719.3.9..861427481297365267345981 I6: 3,7 # 24 pairs * PAIR A5: 5,7 ROW 5 H5: 5,7,2 # reduction candidate for 5,7 H5: 5,7 => CTR * 69.12374883.57.19.17.98....326758419.194328.6.48619...953861274481297365267345981 H5: 2 => SOLVED * 693127548872534196154986237326458719519673824748219653935861472481792365267345981 * PAIR A6: 5,7 ROW 6 G6: 5,7,2,6 # reduction candidate for 5,7 G6: 5,7 => CTR * 69.1237488..5.61921.29846..326.58419.194..8.6.48619.239..861274481297365267345981 G6: 2,6 # 24 pairs H6: 5,7,2,3 # reduction candidate for 5,7 H6: 5,7 # 26 pairs * PAIR E5: 3,7 BLK 5 F5: 3,7,2 # reduction candidate for 3,7 F5: 3,7 => SOLVED * 693127548872534196154986237326458719519673824748219653935861472481792365267345981 F5: 2 => CTR * 69.12374883.57.19.17.98....326758419.194328.6.48619...953861274481297365267345981 * PAIR G4: 4,7 COL G G7: 4,7,2 # reduction candidate for 4,7 G7: 4,7 => SOLVED * 693127548872534196154986237326458719519673824748219653935861472481792365267345981 G7: 2 => CTR * 69.12374883.576192172984653326758419.194..8.6.48619...9..861274481297365267345981 * PAIR D8: 2,7 COL D D6: 2,7,6 # reduction candidate for 2,7 D6: 2,7 => SOLVED * 693127548872534196154986237326458719519673824748219653935861472481792365267345981 D6: 6 => CTR * 69.12374883.57.19.17.98.653326758419519432876.48619...9..861...481297365267345981 * PAIR F8: 2,7 COL F F5: 2,7,3 # reduction candidate for 2,7 F5: 2,7 => CTR * 69.12374883.57.19.17.98....326758419.194328.6.48619...953861274481297365267345981 F5: 3 => SOLVED * 693127548872534196154986237326458719519673824748219653935861472481792365267345981 * PAIR H7: 2,7 BLK 9 G7: 2,7,4 # reduction candidate for 2,7 G7: 2,7 => CTR * 69.12374883.576192172984653326758419519432876.48619...9..861..4481297365267345981 G7: 4 => SOLVED * 693127548872534196154986237326458719519673824748219653935861472481792365267345981 I7: 2,7,4 # reduction candidate for 2,7 I7: 2,7 => SOLVED * 693127548872534196154986237326458719519673824748219653935861472481792365267345981 I7: 4 => CTR * 69.12374883.576192172984653326758419519432876.48619...9..861..4481297365267345981 * PAIR H7: 2,7 COL H H3: 2,7,3,5 # reduction candidate for 2,7 H3: 2,7 => CTR * 69.12374883.57.19.17.98.523326758419719432856548.19.3.9..861...481297365267345981 H3: 3,5 # 24 pairs H5: 2,7,5 # reduction candidate for 2,7 H5: 2,7 # 25 pairs H6: 2,7,3,5 # reduction candidate for 2,7 H6: 2,7 => CTR * 69.12374883.57.19.17.98.53.326758419719432856548.19..39..861...481297365267345981 H6: 3,5 # 24 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-207-base-pr-000.dot * REASONING * DIS # G3: 5,7 => CTR => G3: 2,6 * PRF # F5: 3,7 => SOL * DIS # F5: 2 => CTR => F5: 3,7 * DIS # G3: 5,7 => CTR => G3: 2,6 * DIS # G6: 5,7 => CTR => G6: 2,6 * DIS # I3: 2,6 => CTR => I3: 3,7 * DIS # I6: 2,6 => CTR => I6: 3,7 * DIS # H5: 5,7 => CTR => H5: 2 * PRF # H5: 2 => SOL * DIS # G6: 5,7 => CTR => G6: 2,6 * PRF # F5: 3,7 => SOL * DIS # F5: 2 => CTR => F5: 3,7 * PRF # G7: 4,7 => SOL * DIS # G7: 2 => CTR => G7: 4,7 * PRF # D6: 2,7 => SOL * DIS # D6: 6 => CTR => D6: 2,7 * DIS # F5: 2,7 => CTR => F5: 3 * PRF # F5: 3 => SOL * DIS # G7: 2,7 => CTR => G7: 4 * PRF # G7: 4 => SOL * PRF # I7: 2,7 => SOL * DIS # I7: 4 => CTR => I7: 2,7 * DIS # H3: 2,7 => CTR => H3: 3,5 * DIS # H6: 2,7 => CTR => H6: 3,5 * CNT 24 HDP CHAINS / 37 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B2,B3,B7,C1,C2,C3,C7,D4,D5,D8,E2,E5,F1,F2,F3,F8,G1,G4,H7,I2,I5) * 69.12..488..5..19.1..98....326.58.19.19...8...48.19...9..861...481.9.365267345981 * PAIR B3: 5,7 ROW 3 G3: 5,7,2,6 # reduction candidate for 5,7 G3: 5,7 => CTR * 69.12..488..5..19.1..98....326.58.19.19...8...48.196..9..861274481.9.365267345981 H3: 5,7,3 # reduction candidate for 5,7 H3: 5,7 # 25 pairs * RESTART * PAIR B3: 5,7 ROW 3 H3: 5,7,3 # reduction candidate for 5,7 H3: 3 => SOLVED * 693127548872534196154986237326458719519673824748219653935861472481792365267345981 * DURATION: 0:00:06.094130 START: 09:55:14.818139 END: 09:55:20.912269 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-207-base-pr-001.dot * REASONING * DIS # G3: 5,7 => CTR => G3: 2,6 * PRF G3: 2,6 # H3: 3 => SOL * STA G3: 2,6 + H3: 3 * CNT 2 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 207 solution: 693127548872534196154986237326458719519673824748219653935861472481792365267345981 info: 1910 FNBTHWY S8.f 3217 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 693127548872534196154986237326458719519673824748219653935861472481792365267345981 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:
* DIS # G3: 5,7 => CTR => G3: 2,6 * INC # G3: 2,6 => UNS * INC # H3: 5,7 => UNS * PRF # F5: 3,7 => SOL * DIS # F5: 2 => CTR => F5: 3,7 * DIS # G3: 5,7 => CTR => G3: 2,6 * INC # G3: 2,6 => UNS * INC # H3: 5,7 => UNS * DIS # G6: 5,7 => CTR => G6: 2,6 * INC # G6: 2,6 => UNS * INC # G3: 2,6 => UNS * DIS # I3: 2,6 => CTR => I3: 3,7 * INC # I3: 3,7 => UNS * DIS # I6: 2,6 => CTR => I6: 3,7 * INC # I6: 3,7 => UNS * DIS # H5: 5,7 => CTR => H5: 2 * PRF # H5: 2 => SOL * DIS # G6: 5,7 => CTR => G6: 2,6 * INC # G6: 2,6 => UNS * INC # H6: 5,7 => UNS * PRF # F5: 3,7 => SOL * DIS # F5: 2 => CTR => F5: 3,7 * PRF # G7: 4,7 => SOL * DIS # G7: 2 => CTR => G7: 4,7 * PRF # D6: 2,7 => SOL * DIS # D6: 6 => CTR => D6: 2,7 * DIS # F5: 2,7 => CTR => F5: 3 * PRF # F5: 3 => SOL * DIS # G7: 2,7 => CTR => G7: 4 * PRF # G7: 4 => SOL * PRF # I7: 2,7 => SOL * DIS # I7: 4 => CTR => I7: 2,7 * DIS # H3: 2,7 => CTR => H3: 3,5 * INC # H3: 3,5 => UNS * INC # H5: 2,7 => UNS * DIS # H6: 2,7 => CTR => H6: 3,5 * INC # H6: 3,5 => UNS * CNT 37 HDP CHAINS / 37 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # G3: 5,7 => CTR => G3: 2,6 * INC G3: 2,6 # H3: 5,7 => UNS * INC G3: 2,6 # H3: 5,7 => UNS * PRF G3: 2,6 # H3: 3 => SOL * STA G3: 2,6 + H3: 3 * CNT 4 HDP CHAINS / 4 HYP OPENED