Analysis of xx-top500-170-base.sdk
Contents
Original Sudoku
level: medium
position: 3.8..45.....61..7..........5...38....7.....6...........6.2.....4.....3.....7..... initial
Autosolve
position: 3.89745.6...61.8736.738....5.6.387..173529468.8..67.3576.2.3.8.4..8.63.783.7.16.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B3: 1,2 => SOL * DIS # B3: 5 => CTR => B3: 1,2 * DIS # B2: 2,9 => CTR => B2: 4,5 * DIS # C2: 2,9 => CTR => C2: 4,5 * PRF # B2: 2,5 => SOL * DIS # C2: 2,5 => CTR => C2: 4,9 * DIS # B3: 2,5 => CTR => B3: 1 * PRF # B3: 1 => SOL * DIS # H3: 1,2 => CTR => H3: 4,9 * DIS # I3: 1,2 => CTR => I3: 4,9 * DIS # H4: 1,2 => CTR => H4: 9 * PRF # C6: 2,9 => SOL * PRF # G6: 1 => SOL * DIS # C8: 5,9 => CTR => C8: 1,2 * DIS # H8: 5,9 => CTR => H8: 1,2 * DIS # H8: 1,9 => CTR => H8: 2,5 * DIS # C7: 1,9 => CTR => C7: 5 * DIS # G3: 1,9 => CTR => G3: 2 * PRF # G3: 2 => SOL * PRF # G6: 1,9 => SOL * DIS # G6: 2 => CTR => G6: 1,9 * CNT 21 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 # B3: 1,2 => SOL * STA B3: 1,2 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 3.8..45.....61..7..........5...38....7.....6...........6.2.....4.....3.....7..... | initial |
| 3.89745.6...61.8736.738....5.6.387..173529468.8..67.3576.2.3.8.4..8.63.783.7.16.. | autosolve |
| 328974516954612873617385249546138792173529468289467135765243981491856327832791654 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) B1: 1,2 A2: 2,9 F2: 2,5 F3: 2,5 H1: 1,2 A6: 2,9 D4: 1,4 D6: 1,4 E8: 5,9 G7: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,B3: 1.. / B1 = 1 => 0 pairs (X) / B3 = 1 => 0 pairs (_) D4,D6: 1.. / D4 = 1 => 0 pairs (*) / D6 = 1 => 0 pairs (X) C7,C8: 1.. / C7 = 1 => 0 pairs (X) / C8 = 1 => 11 pairs (_) B1,H1: 1.. / B1 = 1 => 0 pairs (X) / H1 = 1 => 0 pairs (_) D6,G6: 1.. / D6 = 1 => 10 pairs (_) / G6 = 1 => 0 pairs (*) C8,H8: 1.. / C8 = 1 => 11 pairs (_) / H8 = 1 => 0 pairs (X) F2,F3: 2.. / F2 = 2 => 0 pairs (*) / F3 = 2 => 0 pairs (X) B1,H1: 2.. / B1 = 2 => 0 pairs (*) / H1 = 2 => 0 pairs (X) A2,A6: 2.. / A2 = 2 => 0 pairs (X) / A6 = 2 => 0 pairs (_) G3,G6: 2.. / G3 = 2 => 0 pairs (*) / G6 = 2 => 0 pairs (X) B2,C2: 4.. / B2 = 4 => 10 pairs (_) / C2 = 4 => 0 pairs (*) H3,I3: 4.. / H3 = 4 => 10 pairs (_) / I3 = 4 => 0 pairs (X) B4,C6: 4.. / B4 = 4 => 0 pairs (*) / C6 = 4 => 0 pairs (X) D4,D6: 4.. / D4 = 4 => 10 pairs (_) / D6 = 4 => 0 pairs (*) E7,E9: 4.. / E7 = 4 => 16 pairs (_) / E9 = 4 => 12 pairs (_) B4,D4: 4.. / B4 = 4 => 0 pairs (*) / D4 = 4 => 0 pairs (X) C6,D6: 4.. / C6 = 4 => 10 pairs (_) / D6 = 4 => 0 pairs (*) E7,I7: 4.. / E7 = 4 => 16 pairs (_) / I7 = 4 => 12 pairs (_) B2,B4: 4.. / B2 = 4 => 10 pairs (_) / B4 = 4 => 0 pairs (*) C2,C6: 4.. / C2 = 4 => 0 pairs (*) / C6 = 4 => 0 pairs (X) H3,H9: 4.. / H3 = 4 => 10 pairs (_) / H9 = 4 => 0 pairs (X) F2,F3: 5.. / F2 = 5 => 0 pairs (X) / F3 = 5 => 0 pairs (_) H8,H9: 5.. / H8 = 5 => 0 pairs (X) / H9 = 5 => 12 pairs (_) B3,F3: 5.. / B3 = 5 => 0 pairs (X) / F3 = 5 => 0 pairs (_) C7,E7: 5.. / C7 = 5 => 13 pairs (_) / E7 = 5 => 0 pairs (X) A2,A6: 9.. / A2 = 9 => 0 pairs (*) / A6 = 9 => 0 pairs (X) * DURATION: 0:00:43.961425 START: 08:33:00.548166 END: 08:33:44.509591 2017-05-04 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,B1,D4,D6,E8,F2,F3,G7,H1) * 3.89745.6...61.8736.738....5.6.387..173529468.8..67.3576.2.3.8.4..8.63.783.7.16.. * PAIR B1: 1,2 BLK 1 B3: 1,2,5 # reduction candidate for 1,2 B3: 1,2 => SOLVED * 328974516954612873617385249546138792173529468289467135765243981491856327832791654 B3: 5 => CTR * 3189745262..615873657382...5264387..17352946898416723576.2.3.8.4928563178357.16.2 * PAIR A2: 2,9 BLK 1 B2: 2,9,4,5 # reduction candidate for 2,9 B2: 2,9 => CTR * 3.89745.6..4615873657382...5461387..173529468.8.467.3576.2.3.8.4..8.63.783.7.16.. B2: 4,5 # 11 pairs C2: 2,9,4,5 # reduction candidate for 2,9 C2: 2,9 => CTR * 318974526249615873657382...5264387..17352946898416723576.2.3.8.4928563178357.16.2 C2: 4,5 # 11 pairs * PAIR F2: 2,5 ROW 2 B2: 2,5,4,9 # reduction candidate for 2,5 B2: 2,5 => SOLVED * 328974516954612873617385249546138792173529468289467135765243981491856327832791654 B2: 4,9 # 11 pairs C2: 2,5,4,9 # reduction candidate for 2,5 C2: 2,5 => CTR * 3289745169456128736173852..5964387211735294682841679357692531844518963.783.7.16.. C2: 4,9 # 12 pairs * PAIR F3: 2,5 ROW 3 B3: 2,5,1 # reduction candidate for 2,5 B3: 2,5 => CTR * 3189745262..615873657382...5264387..17352946898416723576.2.3.8.4928563178357.16.2 B3: 1 => SOLVED * 328974516954612873617385249546138792173529468289467135765243981491856327832791654 * PAIR H1: 1,2 BLK 3 G3: 1,2,9 # reduction candidate for 1,2 G3: 1,2 # 13 pairs H3: 1,2,4,9 # reduction candidate for 1,2 H3: 1,2 => CTR * 3.89745.62..6158736573829145264387911735294689841672357652431894918.635783.751642 H3: 4,9 # 11 pairs I3: 1,2,4,9 # reduction candidate for 1,2 I3: 1,2 => CTR * 3.89745.62..61587365738294152643871917352946898416723576.2.318449185632783.7.16.. I3: 4,9 # 11 pairs * PAIR H1: 1,2 COL H H4: 1,2,9 # reduction candidate for 1,2 H4: 1,2 => CTR * 318974526...61.8736.738....5.6.387..173529468.8..67.3576.2.3.8.4218.63.783.7.16.2 H4: 9 # 13 pairs H8: 1,2,5,9 # reduction candidate for 1,2 H8: 1,2 # 16 pairs * PAIR A6: 2,9 BLK 4 B4: 2,9,4 # reduction candidate for 2,9 B4: 2,9 # 10 pairs C6: 2,9,4 # reduction candidate for 2,9 C6: 2,9 => SOLVED * 328974516954612873617385249546138792173529468289467135765243981491856327832791654 C6: 4 # 10 pairs * PAIR A6: 2,9 ROW 6 G6: 2,9,1 # reduction candidate for 2,9 G6: 1 => SOLVED * 328974516954612873617385249546138792173529468289467135765243981491856327832791654 G6: 2,9 # 10 pairs * PAIR E8: 5,9 BLK 8 E7: 5,9,4 # reduction candidate for 5,9 E7: 5,9 # 12 pairs E9: 5,9,4 # reduction candidate for 5,9 E9: 5,9 # 16 pairs * PAIR E8: 5,9 ROW 8 B8: 5,9,2 # reduction candidate for 5,9 B8: 5,9 # 19 pairs C8: 5,9,1,2 # reduction candidate for 5,9 C8: 5,9 => CTR * 318974526...61.8736.738.14952643879117352946898416723576125398445.896317839741652 C8: 1,2 # 11 pairs H8: 5,9,1,2 # reduction candidate for 5,9 H8: 5,9 => CTR * 318974526...61.873657382...5.6.387.2173529468.8..67.3576.2.3.8.4218.63.783.7.16.. H8: 1,2 # 16 pairs * PAIR G7: 1,9 BLK 9 I7: 1,9,4 # reduction candidate for 1,9 I7: 1,9 # 16 pairs H8: 1,9,2,5 # reduction candidate for 1,9 H8: 1,9 => CTR * 32897451694561.8736.738..4.5.6.3872.173529468.8..67.3576.2.3.844..8.6397839741652 H8: 2,5 # 12 pairs * PAIR G7: 1,9 ROW 7 C7: 1,9,5 # reduction candidate for 1,9 C7: 1,9 => CTR * 32897451694561287361738524959643872.173529468.8..67.3576.253.844..8963.783.7416.. C7: 5 # 13 pairs * PAIR G7: 1,9 COL G G3: 1,9,2 # reduction candidate for 1,9 G3: 1,9 => CTR * 3.89745.62..615873657382...5264387..17352946898416723576.2.3.8.49.8563.783.7.1652 G3: 2 => SOLVED * 328974516954612873617385249546138792173529468289467135765243981491856327832791654 G6: 1,9,2 # reduction candidate for 1,9 G6: 1,9 => SOLVED * 328974516954612873617385249546138792173529468289467135765243981491856327832791654 G6: 2 => CTR * 3.89745.62..615873657382...5264387..17352946898416723576.2.3.8.49.8563.783.7.1652 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-170-base-pr-000.dot * REASONING * PRF # B3: 1,2 => SOL * DIS # B3: 5 => CTR => B3: 1,2 * DIS # B2: 2,9 => CTR => B2: 4,5 * DIS # C2: 2,9 => CTR => C2: 4,5 * PRF # B2: 2,5 => SOL * DIS # C2: 2,5 => CTR => C2: 4,9 * DIS # B3: 2,5 => CTR => B3: 1 * PRF # B3: 1 => SOL * DIS # H3: 1,2 => CTR => H3: 4,9 * DIS # I3: 1,2 => CTR => I3: 4,9 * DIS # H4: 1,2 => CTR => H4: 9 * PRF # C6: 2,9 => SOL * PRF # G6: 1 => SOL * DIS # C8: 5,9 => CTR => C8: 1,2 * DIS # H8: 5,9 => CTR => H8: 1,2 * DIS # H8: 1,9 => CTR => H8: 2,5 * DIS # C7: 1,9 => CTR => C7: 5 * DIS # G3: 1,9 => CTR => G3: 2 * PRF # G3: 2 => SOL * PRF # G6: 1,9 => SOL * DIS # G6: 2 => CTR => G6: 1,9 * CNT 21 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,B1,D4,D6,E8,F2,F3,G7,H1) * 3.89745.6...61.8736.738....5.6.387..173529468.8..67.3576.2.3.8.4..8.63.783.7.16.. * PAIR B1: 1,2 BLK 1 B3: 1,2,5 # reduction candidate for 1,2 B3: 1,2 => SOLVED * 328974516954612873617385249546138792173529468289467135765243981491856327832791654 * DURATION: 0:00:02.081533 START: 08:34:24.158211 END: 08:34:26.239744 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-170-base-pr-001.dot * REASONING * PRF # B3: 1,2 => SOL * STA B3: 1,2 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 170 solution: 328974516954612873617385249546138792173529468289467135765243981491856327832791654 info: 1825 FNBTWY S8.f 29857 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 328974516954612873617385249546138792173529468289467135765243981491856327832791654 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 # B3: 1,2 => SOL * DIS # B3: 5 => CTR => B3: 1,2 * DIS # B2: 2,9 => CTR => B2: 4,5 * INC # B2: 4,5 => UNS * DIS # C2: 2,9 => CTR => C2: 4,5 * INC # C2: 4,5 => UNS * PRF # B2: 2,5 => SOL * INC # B2: 4,9 => UNS * DIS # C2: 2,5 => CTR => C2: 4,9 * INC # C2: 4,9 => UNS * DIS # B3: 2,5 => CTR => B3: 1 * PRF # B3: 1 => SOL * INC # G3: 1,2 => UNS * DIS # H3: 1,2 => CTR => H3: 4,9 * INC # H3: 4,9 => UNS * DIS # I3: 1,2 => CTR => I3: 4,9 * INC # I3: 4,9 => UNS * DIS # H4: 1,2 => CTR => H4: 9 * INC # H4: 9 => UNS * INC # H8: 1,2 => UNS * INC # B4: 2,9 => UNS * PRF # C6: 2,9 => SOL * INC # C6: 4 => UNS * INC # G6: 2,9 => UNS * PRF # G6: 1 => SOL * INC # E7: 5,9 => UNS * INC # E9: 5,9 => UNS * INC # B8: 5,9 => UNS * DIS # C8: 5,9 => CTR => C8: 1,2 * INC # C8: 1,2 => UNS * DIS # H8: 5,9 => CTR => H8: 1,2 * INC # H8: 1,2 => UNS * INC # I7: 1,9 => UNS * DIS # H8: 1,9 => CTR => H8: 2,5 * INC # H8: 2,5 => UNS * DIS # C7: 1,9 => CTR => C7: 5 * INC # C7: 5 => UNS * DIS # G3: 1,9 => CTR => G3: 2 * PRF # G3: 2 => SOL * PRF # G6: 1,9 => SOL * DIS # G6: 2 => CTR => G6: 1,9 * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # B3: 1,2 => SOL * STA B3: 1,2 * CNT 1 HDP CHAINS / 1 HYP OPENED