Analysis of xx-top500-083-base.sdk
Contents
Original Sudoku
level: medium
position: ...2...4.8.....3...1.........2..4.......8..5..7....1.....71.6..4..5.............1 initial
Autosolve
position: .572.184.84..5731221.84.7.55821749..1...82457.74..5128.2571.6844.15.827.7.842.5.1 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 6,9 => CTR => C3: 3 * DIS # C5: 3 => CTR => C5: 6,9 * DIS # E1: 6,9 => CTR => E1: 3 * PRF # D6: 6,9 => SOL * DIS # E1: 6,9 => CTR => E1: 3 * DIS # C3: 6,9 => CTR => C3: 3 * PRF # A6: 3,9 => SOL * PRF # D5: 3,9 => SOL * DIS # B8: 3,9 => CTR => B8: 6 * PRF # D6: 6,9 => SOL * PRF # A6: 3 => SOL * DIS # E1: 6,9 => CTR => E1: 3 * DIS # B8: 3,9 => CTR => B8: 6 * PRF # A6: 3,9 => SOL * DIS # F9: 3,9 => CTR => F9: 6 * DIS # F3: 6 => CTR => F3: 3,9 * DIS # B8: 3,9 => CTR => B8: 6 * DIS # F9: 3,9 => CTR => F9: 6 * CNT 18 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 6,9 => CTR => C3: 3 * DIS C3: 3 # D5: 6,9 => CTR => D5: 3 * PRF C3: 3 + D5: 3 => SOL * STA C3: 3 + D5: 3 * CNT 3 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...2...4.8.....3...1.........2..4.......8..5..7....1.....71.6..4..5.............1 | initial |
| .572.184.84..5731221.84.7.55821749..1...82457.74..5128.2571.6844.15.827.7.842.5.1 | autosolve |
| 657231849849657312213849765582174936196382457374965128925713684461598273738426591 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) C2: 6,9 D2: 6,9 I1: 6,9 H3: 6,9 B5: 3,9 E6: 6,9 H4: 3,6 I4: 3,6 A7: 3,9 F7: 3,9 I8: 3,9 H9: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,C3: 3.. / A1 = 3 => 0 pairs (X) / C3 = 3 => 16 pairs (_) E1,F3: 3.. / E1 = 3 => 16 pairs (_) / F3 = 3 => 0 pairs (X) D5,D6: 3.. / D5 = 3 => 0 pairs (*) / D6 = 3 => 0 pairs (X) H4,I4: 3.. / H4 = 3 => 0 pairs (*) / I4 = 3 => 0 pairs (X) I8,H9: 3.. / I8 = 3 => 0 pairs (*) / H9 = 3 => 0 pairs (X) A1,E1: 3.. / A1 = 3 => 0 pairs (X) / E1 = 3 => 16 pairs (_) C3,F3: 3.. / C3 = 3 => 16 pairs (_) / F3 = 3 => 0 pairs (X) A6,D6: 3.. / A6 = 3 => 0 pairs (*) / D6 = 3 => 0 pairs (X) A7,F7: 3.. / A7 = 3 => 0 pairs (X) / F7 = 3 => 0 pairs (_) C3,C5: 3.. / C3 = 3 => 16 pairs (_) / C5 = 3 => 0 pairs (X) E1,E8: 3.. / E1 = 3 => 16 pairs (_) / E8 = 3 => 0 pairs (X) H4,H9: 3.. / H4 = 3 => 0 pairs (*) / H9 = 3 => 0 pairs (X) I4,I8: 3.. / I4 = 3 => 0 pairs (X) / I8 = 3 => 0 pairs (_) I1,H3: 6.. / I1 = 6 => 0 pairs (X) / H3 = 6 => 0 pairs (_) C5,A6: 6.. / C5 = 6 => 0 pairs (*) / A6 = 6 => 0 pairs (X) H4,I4: 6.. / H4 = 6 => 0 pairs (X) / I4 = 6 => 0 pairs (_) B8,B9: 6.. / B8 = 6 => 15 pairs (_) / B9 = 6 => 0 pairs (X) E8,F9: 6.. / E8 = 6 => 0 pairs (X) / F9 = 6 => 15 pairs (_) C2,D2: 6.. / C2 = 6 => 15 pairs (_) / D2 = 6 => 0 pairs (*) C5,D5: 6.. / C5 = 6 => 0 pairs (*) / D5 = 6 => 0 pairs (X) B8,E8: 6.. / B8 = 6 => 15 pairs (_) / E8 = 6 => 0 pairs (X) B9,F9: 6.. / B9 = 6 => 0 pairs (X) / F9 = 6 => 15 pairs (_) A1,A6: 6.. / A1 = 6 => 0 pairs (*) / A6 = 6 => 0 pairs (X) F3,F9: 6.. / F3 = 6 => 0 pairs (X) / F9 = 6 => 15 pairs (_) H3,H4: 6.. / H3 = 6 => 0 pairs (*) / H4 = 6 => 0 pairs (X) I1,I4: 6.. / I1 = 6 => 0 pairs (X) / I4 = 6 => 0 pairs (_) I1,H3: 9.. / I1 = 9 => 0 pairs (*) / H3 = 9 => 0 pairs (X) I8,H9: 9.. / I8 = 9 => 0 pairs (X) / H9 = 9 => 0 pairs (_) C2,D2: 9.. / C2 = 9 => 0 pairs (*) / D2 = 9 => 0 pairs (X) A7,F7: 9.. / A7 = 9 => 0 pairs (*) / F7 = 9 => 0 pairs (X) H3,H9: 9.. / H3 = 9 => 0 pairs (X) / H9 = 9 => 0 pairs (_) I1,I8: 9.. / I1 = 9 => 0 pairs (*) / I8 = 9 => 0 pairs (X) * DURATION: 0:00:52.002002 START: 05:37:18.618366 END: 05:38:10.620368 2017-05-04 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B5,C2,D2,E6,F7,H3,H4,H9,I1,I4,I8) * .572.184.84..5731221.84.7.55821749..1...82457.74..5128.2571.6844.15.827.7.842.5.1 * PAIR C2: 6,9 BLK 1 A1: 6,9,3 # reduction candidate for 6,9 A1: 6,9 # 16 pairs C3: 6,9,3 # reduction candidate for 6,9 C3: 6,9 => CTR * 3572.184.84..5731221.8437.55821749..1.368245767439512892571.6844.15.827.7.842.5.1 C3: 3 # 16 pairs * PAIR C2: 6,9 COL C C5: 6,9,3 # reduction candidate for 6,9 C5: 3 => CTR * 357261849846957312219843765582174936193682457674395128.2571.6844.15.827.7.842.5.1 C5: 6,9 # 16 pairs * PAIR D2: 6,9 BLK 2 E1: 6,9,3 # reduction candidate for 6,9 E1: 6,9 => CTR * 3572.184.84..5731221.8437.55821749..1.368245767439512892571.6844.15.827.7.842.5.1 E1: 3 # 16 pairs F3: 6,9,3 # reduction candidate for 6,9 F3: 6,9 # 16 pairs * PAIR D2: 6,9 COL D D5: 6,9,3 # reduction candidate for 6,9 D5: 6,9 # 14 pairs D6: 6,9,3 # reduction candidate for 6,9 D6: 6,9 => SOLVED * 657231849849657312213849765582174936196382457374965128925713684461598273738426591 D6: 3 # 14 pairs * PAIR I1: 6,9 ROW 1 A1: 6,9,3 # reduction candidate for 6,9 A1: 6,9 # 16 pairs E1: 6,9,3 # reduction candidate for 6,9 E1: 6,9 => CTR * 3572.184.84..5731221.8437.55821749..1.368245767439512892571.6844.15.827.7.842.5.1 E1: 3 # 16 pairs * PAIR H3: 6,9 ROW 3 C3: 6,9,3 # reduction candidate for 6,9 C3: 6,9 => CTR * 3572.184.84..5731221.8437.55821749..1.368245767439512892571.6844.15.827.7.842.5.1 C3: 3 # 16 pairs F3: 6,9,3 # reduction candidate for 6,9 F3: 6,9 # 16 pairs * PAIR B5: 3,9 BLK 4 C5: 3,9,6 # reduction candidate for 3,9 C5: 3,9 # 15 pairs A6: 3,9,6 # reduction candidate for 3,9 A6: 3,9 => SOLVED * 657231849849657312213849765582174936196382457374965128925713684461598273738426591 A6: 6 # 15 pairs * PAIR B5: 3,9 ROW 5 D5: 3,9,6 # reduction candidate for 3,9 D5: 3,9 => SOLVED * 657231849849657312213849765582174936196382457374965128925713684461598273738426591 D5: 6 # 15 pairs * PAIR B5: 3,9 COL B B8: 3,9,6 # reduction candidate for 3,9 B8: 3,9 => CTR * 95723184.84..573122138467955821749631...82457.74.95128.2571.684431568279768429531 B8: 6 # 15 pairs B9: 3,9,6 # reduction candidate for 3,9 B9: 3,9 # 15 pairs * PAIR E6: 6,9 BLK 5 D5: 6,9,3 # reduction candidate for 6,9 D5: 6,9 # 14 pairs D6: 6,9,3 # reduction candidate for 6,9 D6: 6,9 => SOLVED * 657231849849657312213849765582174936196382457374965128925713684461598273738426591 D6: 3 # 14 pairs * PAIR E6: 6,9 ROW 6 A6: 6,9,3 # reduction candidate for 6,9 A6: 3 => SOLVED * 657231849849657312213849765582174936196382457374965128925713684461598273738426591 A6: 6,9 # 14 pairs * PAIR E6: 6,9 COL E E1: 6,9,3 # reduction candidate for 6,9 E1: 6,9 => CTR * 3572.184.84..5731221.8437.55821749..1.368245767439512892571.6844.15.827.7.842.5.1 E1: 3 # 16 pairs E8: 6,9,3 # reduction candidate for 6,9 E8: 6,9 # 16 pairs * PAIR A7: 3,9 BLK 7 B8: 3,9,6 # reduction candidate for 3,9 B8: 3,9 => CTR * 95723184.84..573122138467955821749631...82457.74.95128.2571.684431568279768429531 B8: 6 # 15 pairs B9: 3,9,6 # reduction candidate for 3,9 B9: 3,9 # 15 pairs * PAIR A7: 3,9 COL A A1: 3,9,6 # reduction candidate for 3,9 A1: 3,9 # 15 pairs A6: 3,9,6 # reduction candidate for 3,9 A6: 3,9 => SOLVED * 657231849849657312213849765582174936196382457374965128925713684461598273738426591 A6: 6 # 15 pairs * PAIR F7: 3,9 BLK 8 E8: 3,9,6 # reduction candidate for 3,9 E8: 3,9 # 15 pairs F9: 3,9,6 # reduction candidate for 3,9 F9: 3,9 => CTR * .5723184684695731221384679558217496319..82457.74..5128.2571.6844.1568279768429531 F9: 6 # 15 pairs * PAIR F7: 3,9 COL F F3: 3,9,6 # reduction candidate for 3,9 F3: 6 => CTR * .5723184.84.9573122138467955821749631.96824576743951283257196844.15682797.842.5.1 F3: 3,9 # 15 pairs * PAIR I8: 3,9 ROW 8 B8: 3,9,6 # reduction candidate for 3,9 B8: 3,9 => CTR * 95723184.84..573122138467955821749631...82457.74.95128.2571.684431568279768429531 B8: 6 # 15 pairs E8: 3,9,6 # reduction candidate for 3,9 E8: 3,9 # 15 pairs * PAIR H9: 3,9 ROW 9 B9: 3,9,6 # reduction candidate for 3,9 B9: 3,9 # 15 pairs F9: 3,9,6 # reduction candidate for 3,9 F9: 3,9 => CTR * .5723184684695731221384679558217496319..82457.74..5128.2571.6844.1568279768429531 F9: 6 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-083-base-pr-000.dot * REASONING * DIS # C3: 6,9 => CTR => C3: 3 * DIS # C5: 3 => CTR => C5: 6,9 * DIS # E1: 6,9 => CTR => E1: 3 * PRF # D6: 6,9 => SOL * DIS # E1: 6,9 => CTR => E1: 3 * DIS # C3: 6,9 => CTR => C3: 3 * PRF # A6: 3,9 => SOL * PRF # D5: 3,9 => SOL * DIS # B8: 3,9 => CTR => B8: 6 * PRF # D6: 6,9 => SOL * PRF # A6: 3 => SOL * DIS # E1: 6,9 => CTR => E1: 3 * DIS # B8: 3,9 => CTR => B8: 6 * PRF # A6: 3,9 => SOL * DIS # F9: 3,9 => CTR => F9: 6 * DIS # F3: 6 => CTR => F3: 3,9 * DIS # B8: 3,9 => CTR => B8: 6 * DIS # F9: 3,9 => CTR => F9: 6 * CNT 18 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B5,C2,D2,E6,F7,H3,H4,H9,I1,I4,I8) * .572.184.84..5731221.84.7.55821749..1...82457.74..5128.2571.6844.15.827.7.842.5.1 * PAIR C2: 6,9 BLK 1 A1: 6,9,3 # reduction candidate for 6,9 A1: 6,9 # 16 pairs C3: 6,9,3 # reduction candidate for 6,9 C3: 6,9 => CTR * 3572.184.84..5731221.8437.55821749..1.368245767439512892571.6844.15.827.7.842.5.1 * RESTART * PAIR D2: 6,9 COL D D5: 6,9,3 # reduction candidate for 6,9 D5: 6,9 => CTR * .5723184.84..5731221384.7.55821749..13..82457.743.51283257196844.1568273768423591 D5: 3 => SOLVED * 657231849849657312213849765582174936196382457374965128925713684461598273738426591 * DURATION: 0:00:03.525360 START: 05:38:58.835083 END: 05:39:02.360443 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-083-base-pr-001.dot * REASONING * DIS # C3: 6,9 => CTR => C3: 3 * DIS C3: 3 # D5: 6,9 => CTR => D5: 3 * PRF C3: 3 + D5: 3 => SOL * STA C3: 3 + D5: 3 * CNT 3 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 083 solution: 657231849849657312213849765582174936196382457374965128925713684461598273738426591 info: 1552 FNBWXY S8.f 46913 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 657231849849657312213849765582174936196382457374965128925713684461598273738426591 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 # A1: 6,9 => UNS * DIS # C3: 6,9 => CTR => C3: 3 * INC # C3: 3 => UNS * INC # C5: 6,9 => UNS * DIS # C5: 3 => CTR => C5: 6,9 * DIS # E1: 6,9 => CTR => E1: 3 * INC # E1: 3 => UNS * INC # F3: 6,9 => UNS * INC # D5: 6,9 => UNS * PRF # D6: 6,9 => SOL * INC # D6: 3 => UNS * INC # A1: 6,9 => UNS * DIS # E1: 6,9 => CTR => E1: 3 * INC # E1: 3 => UNS * DIS # C3: 6,9 => CTR => C3: 3 * INC # C3: 3 => UNS * INC # F3: 6,9 => UNS * INC # C5: 3,9 => UNS * PRF # A6: 3,9 => SOL * INC # A6: 6 => UNS * PRF # D5: 3,9 => SOL * INC # D5: 6 => UNS * DIS # B8: 3,9 => CTR => B8: 6 * INC # B8: 6 => UNS * INC # B9: 3,9 => UNS * INC # D5: 6,9 => UNS * PRF # D6: 6,9 => SOL * INC # D6: 3 => UNS * INC # A6: 6,9 => UNS * PRF # A6: 3 => SOL * DIS # E1: 6,9 => CTR => E1: 3 * INC # E1: 3 => UNS * INC # E8: 6,9 => UNS * DIS # B8: 3,9 => CTR => B8: 6 * INC # B8: 6 => UNS * INC # B9: 3,9 => UNS * INC # A1: 3,9 => UNS * PRF # A6: 3,9 => SOL * INC # A6: 6 => UNS * INC # E8: 3,9 => UNS * DIS # F9: 3,9 => CTR => F9: 6 * INC # F9: 6 => UNS * INC # F3: 3,9 => UNS * DIS # F3: 6 => CTR => F3: 3,9 * DIS # B8: 3,9 => CTR => B8: 6 * INC # B8: 6 => UNS * INC # E8: 3,9 => UNS * INC # B9: 3,9 => UNS * DIS # F9: 3,9 => CTR => F9: 6 * INC # F9: 6 => UNS * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 6,9 => UNS * DIS # C3: 6,9 => CTR => C3: 3 * DIS C3: 3 # D5: 6,9 => CTR => D5: 3 * PRF C3: 3 + D5: 3 => SOL * STA C3: 3 + D5: 3 * CNT 4 HDP CHAINS / 3 HYP OPENED