Analysis of xx-top500-245-base.sdk
Contents
Original Sudoku
level: medium
position: ....8.32.1.4..9.............3..2....7.......1.......5....1.7..9.2....7.....4..... initial
Autosolve
position: .7..813241.4239...2.3.7419.5319264..7928456318467139523.81.724942.3.871..174.2..3 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 5,6 => CTR => B3: 8 * DIS # I2: 5,8 => CTR => I2: 6,7 * DIS # B2: 6 => CTR => B2: 5,8 * DIS # H2: 7,8 => CTR => H2: 6 * PRF # H2: 6 => SOL * DIS # I2: 5,6 => CTR => I2: 7,8 * DIS # B3: 5,6 => CTR => B3: 8 * PRF # E8: 5,9 => SOL * DIS # E8: 6 => CTR => E8: 5,9 * PRF # E9: 6,9 => SOL * DIS # E9: 5 => CTR => E9: 6,9 * DIS # E8: 5,6 => CTR => E8: 9 * PRF # E8: 9 => SOL * PRF # E9: 5,6 => SOL * DIS # E9: 9 => CTR => E9: 5,6 * DIS # E8: 5,6 => CTR => E8: 9 * PRF # E8: 9 => SOL * DIS # I2: 5,6 => CTR => I2: 7,8 * DIS # H2: 7 => CTR => H2: 6,8 * CNT 19 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 5,6 => CTR => B3: 8 * DIS B3: 8 # H2: 7,8 => CTR => H2: 6 * PRF B3: 8 + H2: 6 => SOL * STA B3: 8 + H2: 6 * CNT 3 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....8.32.1.4..9.............3..2....7.......1.......5....1.7..9.2....7.....4..... | initial |
| .7..813241.4239...2.3.7419.5319264..7928456318467139523.81.724942.3.871..174.2..3 | autosolve |
| 679581324154239867283674195531926478792845631846713952368157249425398716917462583 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) A1: 6,9 C1: 5,9 D1: 5,6 D3: 5,6 G2: 5,8 H4: 7,8 I4: 7,8 B7: 5,6 C8: 5,9 A9: 6,9 E7: 5,6 I8: 5,6 G9: 5,8 H9: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,D3: 5.. / D1 = 5 => 0 pairs (*) / D3 = 5 => 0 pairs (X) B7,C8: 5.. / B7 = 5 => 0 pairs (X) / C8 = 5 => 0 pairs (_) I8,G9: 5.. / I8 = 5 => 0 pairs (X) / G9 = 5 => 0 pairs (_) C1,D1: 5.. / C1 = 5 => 0 pairs (X) / D1 = 5 => 0 pairs (_) B7,E7: 5.. / B7 = 5 => 0 pairs (X) / E7 = 5 => 0 pairs (_) E9,G9: 5.. / E9 = 5 => 0 pairs (X) / G9 = 5 => 0 pairs (_) C1,C8: 5.. / C1 = 5 => 0 pairs (X) / C8 = 5 => 0 pairs (_) G2,G9: 5.. / G2 = 5 => 0 pairs (X) / G9 = 5 => 0 pairs (_) D1,D3: 6.. / D1 = 6 => 0 pairs (X) / D3 = 6 => 0 pairs (_) B7,A9: 6.. / B7 = 6 => 0 pairs (*) / A9 = 6 => 0 pairs (X) I8,H9: 6.. / I8 = 6 => 0 pairs (*) / H9 = 6 => 0 pairs (X) A1,D1: 6.. / A1 = 6 => 0 pairs (*) / D1 = 6 => 0 pairs (X) B7,E7: 6.. / B7 = 6 => 0 pairs (*) / E7 = 6 => 0 pairs (X) E8,I8: 6.. / E8 = 6 => 0 pairs (X) / I8 = 6 => 0 pairs (_) A1,A9: 6.. / A1 = 6 => 0 pairs (*) / A9 = 6 => 0 pairs (X) H2,H9: 6.. / H2 = 6 => 0 pairs (*) / H9 = 6 => 0 pairs (X) H2,I2: 7.. / H2 = 7 => 0 pairs (X) / I2 = 7 => 15 pairs (_) H4,I4: 7.. / H4 = 7 => 15 pairs (_) / I4 = 7 => 0 pairs (X) H2,H4: 7.. / H2 = 7 => 0 pairs (X) / H4 = 7 => 15 pairs (_) I2,I4: 7.. / I2 = 7 => 15 pairs (_) / I4 = 7 => 0 pairs (X) B2,B3: 8.. / B2 = 8 => 0 pairs (X) / B3 = 8 => 17 pairs (_) H4,I4: 8.. / H4 = 8 => 0 pairs (X) / I4 = 8 => 15 pairs (_) G9,H9: 8.. / G9 = 8 => 0 pairs (X) / H9 = 8 => 0 pairs (_) B3,I3: 8.. / B3 = 8 => 17 pairs (_) / I3 = 8 => 0 pairs (X) G2,G9: 8.. / G2 = 8 => 0 pairs (*) / G9 = 8 => 0 pairs (X) A1,C1: 9.. / A1 = 9 => 0 pairs (X) / C1 = 9 => 0 pairs (_) C8,A9: 9.. / C8 = 9 => 0 pairs (X) / A9 = 9 => 0 pairs (_) E8,E9: 9.. / E8 = 9 => 0 pairs (*) / E9 = 9 => 0 pairs (X) C8,E8: 9.. / C8 = 9 => 0 pairs (X) / E8 = 9 => 0 pairs (_) A9,E9: 9.. / A9 = 9 => 0 pairs (*) / E9 = 9 => 0 pairs (X) A1,A9: 9.. / A1 = 9 => 0 pairs (X) / A9 = 9 => 0 pairs (_) C1,C8: 9.. / C1 = 9 => 0 pairs (*) / C8 = 9 => 0 pairs (X) * DURATION: 0:00:56.017730 START: 11:10:21.680671 END: 11:11:17.698401 2017-05-04 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A9,B7,C1,C8,D1,D3,E7,G2,G9,H4,H9,I4,I8) * .7..813241.4239...2.3.7419.5319264..7928456318467139523.81.724942.3.871..174.2..3 * PAIR D3: 5,6 ROW 3 B3: 5,6,8 # reduction candidate for 5,6 B3: 5,6 => CTR * .7..813241842395..2.3.741985319264877928456318467139523.81.724942.3.8715.17452863 B3: 8 # 17 pairs I3: 5,6,8 # reduction candidate for 5,6 I3: 5,6 # 17 pairs * PAIR G2: 5,8 BLK 3 I2: 5,8,6,7 # reduction candidate for 5,8 I2: 5,8 => CTR * .7..813241.4239.7.2.3.741965319264877928456318467139523.81.724942.368715.174.2..3 I2: 6,7 # 15 pairs I3: 5,8,6 # reduction candidate for 5,8 I3: 5,8 # 18 pairs * PAIR G2: 5,8 ROW 2 B2: 5,8,6 # reduction candidate for 5,8 B2: 6 => CTR * .7..81324164239...283.741965319264..79284563184671395235816724942935871..174.2..3 B2: 5,8 # 18 pairs * PAIR H4: 7,8 COL H H2: 7,8,6 # reduction candidate for 7,8 H2: 7,8 => CTR * 6795813241.4239..62.367419.5319264.779284563184671395236815724942.3.871..174.2.63 H2: 6 => SOLVED * 679581324154239867283674195531926478792845631846713952368157249425398716917462583 * PAIR I4: 7,8 COL I I2: 7,8,5,6 # reduction candidate for 7,8 I2: 5,6 => CTR * 67958132418423957625367419853192648779284563184671395236815724942.3.871..174.2863 I2: 7,8 # 17 pairs * PAIR B7: 5,6 COL B B2: 5,6,8 # reduction candidate for 5,6 B2: 5,6 # 17 pairs B3: 5,6,8 # reduction candidate for 5,6 B3: 5,6 => CTR * .7..813241842395..2.3.741985319264877928456318467139523.81.724942.3.8715.17452863 B3: 8 # 17 pairs * PAIR C8: 5,9 ROW 8 E8: 5,9,6 # reduction candidate for 5,9 E8: 5,9 => SOLVED * 679581324154239867283674195531926478792845631846713952368157249425398716917462583 E8: 6 => CTR * .7..813241.4239...2.3.7419.5319264..7928456318467139523.81.72494293687156174.2..3 * PAIR A9: 6,9 ROW 9 E9: 6,9,5 # reduction candidate for 6,9 E9: 6,9 => SOLVED * 679581324154239867283674195531926478792845631846713952368157249425398716917462583 E9: 5 => CTR * .7..813241.4239...2.3.7419.5319264..7928456318467139523.81.724942.398716.174.2..3 * PAIR E7: 5,6 BLK 8 E8: 5,6,9 # reduction candidate for 5,6 E8: 5,6 => CTR * 9756813241.423986.2.3.7419.5319264..7928456318467139523.81.72494293.871.617492583 E8: 9 => SOLVED * 679581324154239867283674195531926478792845631846713952368157249425398716917462583 E9: 5,6,9 # reduction candidate for 5,6 E9: 5,6 => SOLVED * 679581324154239867283674195531926478792845631846713952368157249425398716917462583 E9: 9 => CTR * 9756813241.423986.2.3.7419.5319264..7928456318467139523.81.724942.3.871..17492583 * PAIR I8: 5,6 ROW 8 E8: 5,6,9 # reduction candidate for 5,6 E8: 5,6 => CTR * 9756813241.423986.2.3.7419.5319264..7928456318467139523.81.72494293.871.617492583 E8: 9 => SOLVED * 679581324154239867283674195531926478792845631846713952368157249425398716917462583 * PAIR I8: 5,6 COL I I2: 5,6,7,8 # reduction candidate for 5,6 I2: 5,6 => CTR * 67958132418423957625367419853192648779284563184671395236815724942.3.871..174.2863 I2: 7,8 # 17 pairs I3: 5,6,8 # reduction candidate for 5,6 I3: 5,6 # 17 pairs * PAIR H9: 6,8 COL H H2: 6,8,7 # reduction candidate for 6,8 H2: 7 => CTR * 6795813241.423957625367419853192648779284563184671395236815724942.3.871..174.2863 H2: 6,8 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-245-base-pr-000.dot * REASONING * DIS # B3: 5,6 => CTR => B3: 8 * DIS # I2: 5,8 => CTR => I2: 6,7 * DIS # B2: 6 => CTR => B2: 5,8 * DIS # H2: 7,8 => CTR => H2: 6 * PRF # H2: 6 => SOL * DIS # I2: 5,6 => CTR => I2: 7,8 * DIS # B3: 5,6 => CTR => B3: 8 * PRF # E8: 5,9 => SOL * DIS # E8: 6 => CTR => E8: 5,9 * PRF # E9: 6,9 => SOL * DIS # E9: 5 => CTR => E9: 6,9 * DIS # E8: 5,6 => CTR => E8: 9 * PRF # E8: 9 => SOL * PRF # E9: 5,6 => SOL * DIS # E9: 9 => CTR => E9: 5,6 * DIS # E8: 5,6 => CTR => E8: 9 * PRF # E8: 9 => SOL * DIS # I2: 5,6 => CTR => I2: 7,8 * DIS # H2: 7 => CTR => H2: 6,8 * CNT 19 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A9,B7,C1,C8,D1,D3,E7,G2,G9,H4,H9,I4,I8) * .7..813241.4239...2.3.7419.5319264..7928456318467139523.81.724942.3.871..174.2..3 * PAIR D3: 5,6 ROW 3 B3: 5,6,8 # reduction candidate for 5,6 B3: 5,6 => CTR * .7..813241842395..2.3.741985319264877928456318467139523.81.724942.3.8715.17452863 * RESTART * PAIR RESTART * PAIR H4: 7,8 COL H H2: 7,8,6 # reduction candidate for 7,8 H2: 7,8 => CTR * .7..813241642395..2835741965319264..79284563184671395235816724942935871..174.2..3 H2: 6 => SOLVED * 679581324154239867283674195531926478792845631846713952368157249425398716917462583 * DURATION: 0:00:04.223617 START: 11:11:48.982572 END: 11:11:53.206189 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-245-base-pr-001.dot * REASONING * DIS # B3: 5,6 => CTR => B3: 8 * DIS B3: 8 # H2: 7,8 => CTR => H2: 6 * PRF B3: 8 + H2: 6 => SOL * STA B3: 8 + H2: 6 * CNT 3 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 245 solution: 679581324154239867283674195531926478792845631846713952368157249425398716917462583 info: 2071 FNBTWXY S8.f 6236 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 679581324154239867283674195531926478792845631846713952368157249425398716917462583 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 # B3: 5,6 => CTR => B3: 8 * INC # B3: 8 => UNS * INC # I3: 5,6 => UNS * DIS # I2: 5,8 => CTR => I2: 6,7 * INC # I2: 6,7 => UNS * INC # I3: 5,8 => UNS * INC # B2: 5,8 => UNS * DIS # B2: 6 => CTR => B2: 5,8 * DIS # H2: 7,8 => CTR => H2: 6 * PRF # H2: 6 => SOL * INC # I2: 7,8 => UNS * DIS # I2: 5,6 => CTR => I2: 7,8 * INC # B2: 5,6 => UNS * DIS # B3: 5,6 => CTR => B3: 8 * INC # B3: 8 => UNS * PRF # E8: 5,9 => SOL * DIS # E8: 6 => CTR => E8: 5,9 * PRF # E9: 6,9 => SOL * DIS # E9: 5 => CTR => E9: 6,9 * DIS # E8: 5,6 => CTR => E8: 9 * PRF # E8: 9 => SOL * PRF # E9: 5,6 => SOL * DIS # E9: 9 => CTR => E9: 5,6 * DIS # E8: 5,6 => CTR => E8: 9 * PRF # E8: 9 => SOL * DIS # I2: 5,6 => CTR => I2: 7,8 * INC # I2: 7,8 => UNS * INC # I3: 5,6 => UNS * INC # H2: 6,8 => UNS * DIS # H2: 7 => CTR => H2: 6,8 * CNT 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B3: 5,6 => CTR => B3: 8 * DIS B3: 8 # H2: 7,8 => CTR => H2: 6 * PRF B3: 8 + H2: 6 => SOL * STA B3: 8 + H2: 6 * CNT 3 HDP CHAINS / 2 HYP OPENED