Analysis of xx-top500-018-base.sdk
Contents
Original Sudoku
level: medium
position: 7..3...........14..............813..2...4....57........6.5....7..1..3..........2. initial
Autosolve
position: 7..31.2...3...714.1..4..73....781352213.45.7.578.3.4.136.5...17..1.73..4..71...23 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B9: 4,9 => CTR => B9: 5,8 * PRF # I5: 6,9 => SOL * DIS # D2: 6,9 => CTR => D2: 2,8 * PRF # I5: 6,9 => SOL * PRF # H1: 6,9 => SOL * DIS # B8: 8,9 => CTR => B8: 2,5 * DIS # B9: 8,9 => CTR => B9: 4,5 * DIS # D8: 8,9 => CTR => D8: 2,6 * DIS # G8: 8,9 => CTR => G8: 5,6 * DIS # F7: 2,9 => CTR => F7: 4,8 * DIS # F9: 6,9 => CTR => F9: 4,8 * DIS # G8: 8,9 => CTR => G8: 5,6 * CNT 12 HDP CHAINS / 55 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B9: 4,9 => CTR => B9: 5,8 * DIS B9: 5,8 # B1: 8 => CTR => B1: 4,9 * PRF B9: 5,8 + B1: 4,9 # I5: 6,9 => SOL * STA B9: 5,8 + B1: 4,9 + I5: 6,9 * CNT 3 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 7..3...........14..............813..2...4....57........6.5....7..1..3..........2. | initial |
| 7..31.2...3...714.1..4..73....781352213.45.7.578.3.4.136.5...17..1.73..4..71...23 | autosolve |
| 745319268632857149189462735496781352213945876578236491364528917921673584857194623 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) B4: 4,9 D5: 6,9 H6: 6,9 A8: 8,9 E7: 2,9 E9: 6,9 G7: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D6,F6: 2.. / D6 = 2 => 11 pairs (_) / F6 = 2 => 10 pairs (_) C7,B8: 2.. / C7 = 2 => 0 pairs (X) / B8 = 2 => 10 pairs (_) B8,D8: 2.. / B8 = 2 => 10 pairs (_) / D8 = 2 => 0 pairs (X) B3,B8: 2.. / B3 = 2 => 0 pairs (X) / B8 = 2 => 10 pairs (_) B1,C1: 4.. / B1 = 4 => 10 pairs (_) / C1 = 4 => 17 pairs (_) F7,F9: 4.. / F7 = 4 => 14 pairs (_) / F9 = 4 => 8 pairs (_) C7,F7: 4.. / C7 = 4 => 8 pairs (_) / F7 = 4 => 14 pairs (_) A4,A9: 4.. / A4 = 4 => 12 pairs (_) / A9 = 4 => 14 pairs (_) E2,E3: 5.. / E2 = 5 => 7 pairs (_) / E3 = 5 => 7 pairs (_) B8,B9: 5.. / B8 = 5 => 0 pairs (X) / B9 = 5 => 7 pairs (_) G8,G9: 5.. / G8 = 5 => 7 pairs (_) / G9 = 5 => 0 pairs (X) C1,I1: 5.. / C1 = 5 => 10 pairs (_) / I1 = 5 => 7 pairs (_) B8,G8: 5.. / B8 = 5 => 0 pairs (X) / G8 = 5 => 7 pairs (_) B9,G9: 5.. / B9 = 5 => 7 pairs (_) / G9 = 5 => 0 pairs (X) A4,C4: 6.. / A4 = 6 => 15 pairs (_) / C4 = 6 => 8 pairs (_) A2,A4: 6.. / A2 = 6 => 8 pairs (_) / A4 = 6 => 15 pairs (_) G5,I5: 8.. / G5 = 8 => 0 pairs (*) / I5 = 8 => 0 pairs (X) F7,G7: 8.. / F7 = 8 => 15 pairs (_) / G7 = 8 => 12 pairs (_) D2,D8: 8.. / D2 = 8 => 11 pairs (_) / D8 = 8 => 0 pairs (X) H1,H8: 8.. / H1 = 8 => 13 pairs (_) / H8 = 8 => 0 pairs (*) * DURATION: 0:00:29.321050 START: 03:11:44.234393 END: 03:12:13.555443 2017-05-04 * CP COUNT: (20) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B4,D5,E7,E9,G7,H6) * 7..31.2...3...714.1..4..73....781352213.45.7.578.3.4.136.5...17..1.73..4..71...23 * PAIR B4: 4,9 BLK 4 A4: 4,9,6 # reduction candidate for 4,9 A4: 4,9 # 8 pairs C4: 4,9,6 # reduction candidate for 4,9 C4: 4,9 # 15 pairs * PAIR B4: 4,9 COL B B1: 4,9,8 # reduction candidate for 4,9 B1: 4,9 # 10 pairs B9: 4,9,5,8 # reduction candidate for 4,9 B9: 4,9 => CTR * 7..31.2...3.8.714.12.4..738...781352213.4587.578.324.136259..17.51273..4..71..523 B9: 5,8 # 8 pairs * PAIR D5: 6,9 BLK 5 D6: 6,9,2 # reduction candidate for 6,9 D6: 6,9 # 10 pairs F6: 6,9,2 # reduction candidate for 6,9 F6: 6,9 # 11 pairs * PAIR D5: 6,9 ROW 5 G5: 6,9,8 # reduction candidate for 6,9 G5: 6,9 # 13 pairs I5: 6,9,8 # reduction candidate for 6,9 I5: 6,9 => SOLVED * 745319268632857149189462735496781352213945876578236491364528917921673584857194623 I5: 8 # 13 pairs * PAIR D5: 6,9 COL D D2: 6,9,2,8 # reduction candidate for 6,9 D2: 6,9 => CTR * 7..31.28.83...714.1..4.873.6..781352213.45.7857823.4.136.5.28179218735644.71...23 D2: 2,8 # 8 pairs D8: 6,9,2,8 # reduction candidate for 6,9 D8: 6,9 # 14 pairs * PAIR H6: 6,9 BLK 6 G5: 6,9,8 # reduction candidate for 6,9 G5: 6,9 # 13 pairs I5: 6,9,8 # reduction candidate for 6,9 I5: 6,9 => SOLVED * 745319268632857149189462735496781352213945876578236491364528917921673584857194623 I5: 8 # 13 pairs * PAIR H6: 6,9 ROW 6 D6: 6,9,2 # reduction candidate for 6,9 D6: 6,9 # 10 pairs F6: 6,9,2 # reduction candidate for 6,9 F6: 6,9 # 11 pairs * PAIR H6: 6,9 COL H H1: 6,9,8 # reduction candidate for 6,9 H1: 6,9 => SOLVED * 745319268632857149189462735496781352213945876578236491364528917921673584857194623 H1: 8 # 13 pairs H8: 6,9,8 # reduction candidate for 6,9 H8: 6,9 # 13 pairs * PAIR A8: 8,9 BLK 7 B8: 8,9,2,5 # reduction candidate for 8,9 B8: 8,9 => CTR * 7..31.28.83..2714.12.45.73.6..781352213.45678578.32491362594817981273564457168923 B8: 2,5 # 8 pairs A9: 8,9,4 # reduction candidate for 8,9 A9: 8,9 # 12 pairs B9: 8,9,4,5 # reduction candidate for 8,9 B9: 8,9 => CTR * 7..31.2...3.8.714.12.4..738...781352213.4587.578.324.136259..17.51273..4..71..523 B9: 4,5 # 8 pairs * PAIR A8: 8,9 ROW 8 D8: 8,9,2,6 # reduction candidate for 8,9 D8: 8,9 => CTR * 7..31.28..3.8.714.18.4..73....781352213945678578.3.49136.5...17.21.73564.571...23 D8: 2,6 # 13 pairs G8: 8,9,5,6 # reduction candidate for 8,9 G8: 8,9 => CTR * 7..31.28..3.8.714.1..4..73....781352213.45.7.578.3.4.136.5...17.51273.64..71..523 G8: 5,6 # 8 pairs H8: 8,9,6 # reduction candidate for 8,9 H8: 8,9 # 18 pairs * PAIR A8: 8,9 COL A A2: 8,9,6 # reduction candidate for 8,9 A2: 8,9 # 15 pairs A2: 6 # 8 pairs * PAIR E7: 2,9 BLK 8 F7: 2,9,4,8 # reduction candidate for 2,9 F7: 2,9 => CTR * 74.31.28..3...714.18.4..73.496781352213.45.78578.3.4.13645..817.21873564857164923 F7: 4,8 # 8 pairs D8: 2,9,6,8 # reduction candidate for 2,9 D8: 2,9 # 12 pairs * PAIR E7: 2,9 ROW 7 C7: 2,9,4 # reduction candidate for 2,9 C7: 2,9 # 14 pairs C7: 4 # 8 pairs * PAIR E7: 2,9 COL E E2: 2,9,5,6 # reduction candidate for 2,9 E2: 2,9 # 7 pairs E3: 2,9,5,6 # reduction candidate for 2,9 E3: 2,9 # 7 pairs * PAIR E9: 6,9 BLK 8 D8: 6,9,2,8 # reduction candidate for 6,9 D8: 6,9 # 14 pairs F9: 6,9,4,8 # reduction candidate for 6,9 F9: 6,9 => CTR * 7..31.28.83...714.1..4.873.6..781352213.45.78578.324.136.5248179.1873..4..71...23 F9: 4,8 # 8 pairs * PAIR E9: 6,9 ROW 9 G9: 6,9,5,8 # reduction candidate for 6,9 G9: 6,9 # 10 pairs G9: 5,8 # 8 pairs * PAIR E9: 6,9 COL E E2: 6,9,2,5 # reduction candidate for 6,9 E2: 6,9 # 13 pairs E3: 6,9,2,5 # reduction candidate for 6,9 E3: 6,9 # 10 pairs * PAIR G7: 8,9 BLK 9 G8: 8,9,5,6 # reduction candidate for 8,9 G8: 8,9 => CTR * 7..31.28..3.8.714.1..4..73....781352213.45.7.578.3.4.136.5...17.51273.64..71..523 G8: 5,6 # 8 pairs H8: 8,9,6 # reduction candidate for 8,9 H8: 8,9 # 18 pairs G9: 8,9,5,6 # reduction candidate for 8,9 G9: 8,9 # 16 pairs * PAIR G7: 8,9 ROW 7 F7: 8,9,2,4 # reduction candidate for 8,9 F7: 2,4 # 13 pairs F7: 8,9 # 9 pairs * PAIR G7: 8,9 COL G G5: 8,9,6 # reduction candidate for 8,9 G5: 8,9 # 18 pairs G5: 6 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-018-base-pr-000.dot * REASONING * DIS # B9: 4,9 => CTR => B9: 5,8 * PRF # I5: 6,9 => SOL * DIS # D2: 6,9 => CTR => D2: 2,8 * PRF # I5: 6,9 => SOL * PRF # H1: 6,9 => SOL * DIS # B8: 8,9 => CTR => B8: 2,5 * DIS # B9: 8,9 => CTR => B9: 4,5 * DIS # D8: 8,9 => CTR => D8: 2,6 * DIS # G8: 8,9 => CTR => G8: 5,6 * DIS # F7: 2,9 => CTR => F7: 4,8 * DIS # F9: 6,9 => CTR => F9: 4,8 * DIS # G8: 8,9 => CTR => G8: 5,6 * CNT 12 HDP CHAINS / 55 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B4,D5,E7,E9,G7,H6) * 7..31.2...3...714.1..4..73....781352213.45.7.578.3.4.136.5...17..1.73..4..71...23 * PAIR B4: 4,9 BLK 4 A4: 4,9,6 # reduction candidate for 4,9 A4: 4,9 # 8 pairs C4: 4,9,6 # reduction candidate for 4,9 C4: 4,9 # 15 pairs * PAIR B4: 4,9 COL B B1: 4,9,8 # reduction candidate for 4,9 B1: 4,9 # 10 pairs B9: 4,9,5,8 # reduction candidate for 4,9 B9: 4,9 => CTR * 7..31.2...3.8.714.12.4..738...781352213.4587.578.324.136259..17.51273..4..71..523 * RESTART * PAIR B4: 4,9 COL B B1: 4,9,8 # reduction candidate for 4,9 B1: 8 => CTR * 78431.2.5.3...714.1..4..73..4.781352213.45.7.578.3.4.136.5.4817..1.73..44571.8.23 * PAIR RESTART * PAIR B4: 4,9 BLK 4 A4: 4,9,6 # reduction candidate for 4,9 A4: 4,9 # 10 pairs C4: 4,9,6 # reduction candidate for 4,9 C4: 4,9 # 15 pairs * PAIR D5: 6,9 BLK 5 D6: 6,9,2 # reduction candidate for 6,9 D6: 6,9 # 13 pairs F6: 6,9,2 # reduction candidate for 6,9 F6: 6,9 # 11 pairs * PAIR D5: 6,9 ROW 5 G5: 6,9,8 # reduction candidate for 6,9 G5: 6,9 # 13 pairs I5: 6,9,8 # reduction candidate for 6,9 I5: 6,9 => SOLVED * 745319268632857149189462735496781352213945876578236491364528917921673584857194623 * DURATION: 0:00:10.911316 START: 03:12:57.555476 END: 03:13:08.466792 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-018-base-pr-001.dot * REASONING * DIS # B9: 4,9 => CTR => B9: 5,8 * DIS B9: 5,8 # B1: 8 => CTR => B1: 4,9 * PRF B9: 5,8 + B1: 4,9 # I5: 6,9 => SOL * STA B9: 5,8 + B1: 4,9 + I5: 6,9 * CNT 3 HDP CHAINS / 12 HYP OPENED
Header Info
Top 500 Minimum 17 018 solution: 745319268632857149189462735496781352213945876578236491364528917921673584857194623 info: 1311 FNBTXY S8.f 36910 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 745319268632857149189462735496781352213945876578236491364528917921673584857194623 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 # A4: 4,9 => UNS * INC # C4: 4,9 => UNS * INC # B1: 4,9 => UNS * DIS # B9: 4,9 => CTR => B9: 5,8 * INC # B9: 5,8 => UNS * INC # D6: 6,9 => UNS * INC # F6: 6,9 => UNS * INC # G5: 6,9 => UNS * PRF # I5: 6,9 => SOL * INC # I5: 8 => UNS * DIS # D2: 6,9 => CTR => D2: 2,8 * INC # D2: 2,8 => UNS * INC # D8: 6,9 => UNS * INC # G5: 6,9 => UNS * PRF # I5: 6,9 => SOL * INC # I5: 8 => UNS * INC # D6: 6,9 => UNS * INC # F6: 6,9 => UNS * PRF # H1: 6,9 => SOL * INC # H1: 8 => UNS * INC # H8: 6,9 => UNS * DIS # B8: 8,9 => CTR => B8: 2,5 * INC # B8: 2,5 => UNS * INC # A9: 8,9 => UNS * DIS # B9: 8,9 => CTR => B9: 4,5 * INC # B9: 4,5 => UNS * DIS # D8: 8,9 => CTR => D8: 2,6 * INC # D8: 2,6 => UNS * DIS # G8: 8,9 => CTR => G8: 5,6 * INC # G8: 5,6 => UNS * INC # H8: 8,9 => UNS * INC # A2: 8,9 => UNS * INC # A2: 6 => UNS * DIS # F7: 2,9 => CTR => F7: 4,8 * INC # F7: 4,8 => UNS * INC # D8: 2,9 => UNS * INC # C7: 2,9 => UNS * INC # C7: 4 => UNS * INC # E2: 2,9 => UNS * INC # E3: 2,9 => UNS * INC # D8: 6,9 => UNS * DIS # F9: 6,9 => CTR => F9: 4,8 * INC # F9: 4,8 => UNS * INC # G9: 6,9 => UNS * INC # G9: 5,8 => UNS * INC # E2: 6,9 => UNS * INC # E3: 6,9 => UNS * DIS # G8: 8,9 => CTR => G8: 5,6 * INC # G8: 5,6 => UNS * INC # H8: 8,9 => UNS * INC # G9: 8,9 => UNS * INC # F7: 8,9 => UNS * INC # F7: 2,4 => UNS * INC # G5: 8,9 => UNS * INC # G5: 6 => UNS * CNT 55 HDP CHAINS / 55 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A4: 4,9 => UNS * INC # C4: 4,9 => UNS * INC # B1: 4,9 => UNS * DIS # B9: 4,9 => CTR => B9: 5,8 * INC B9: 5,8 # B1: 4,9 => UNS * DIS B9: 5,8 # B1: 8 => CTR => B1: 4,9 * INC B9: 5,8 + B1: 4,9 # A4: 4,9 => UNS * INC B9: 5,8 + B1: 4,9 # C4: 4,9 => UNS * INC B9: 5,8 + B1: 4,9 # D6: 6,9 => UNS * INC B9: 5,8 + B1: 4,9 # F6: 6,9 => UNS * INC B9: 5,8 + B1: 4,9 # G5: 6,9 => UNS * PRF B9: 5,8 + B1: 4,9 # I5: 6,9 => SOL * STA B9: 5,8 + B1: 4,9 + I5: 6,9 * CNT 12 HDP CHAINS / 12 HYP OPENED