Analysis of xx-top500-407-base.sdk
Contents
Original Sudoku
level: medium
position: .2..5.64.31...........8.......62....8......7.........1...3.7.....9...2.....1..... initial
Autosolve
position: 72895164331..76.......83......62....8..51..7....73...1...3.7.....98.52.....1.2... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C4: 4,5 => CTR => C4: 1,3,7 * DIS # C7: 4,5 => CTR => C7: 1,2,6 * DIS # C9: 4,5 => CTR => C9: 3,6,7 * DIS # B5: 4,9 => CTR => B5: 3,6 * DIS # C5: 2,6 => CTR => C5: 3,4 * DIS # A8: 4,6 => CTR => A8: 1 * PRF # A8: 1 => SOL * PRF # B8: 4,6 => SOL * DIS # I8: 4,6 => CTR => I8: 7 * PRF # I8: 7 => SOL * CNT 10 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C4: 4,5 => CTR => C4: 1,3,7 * DIS C4: 1,3,7 # C7: 4,5 => CTR => C7: 1,2,6 * DIS C4: 1,3,7 + C7: 1,2,6 # C9: 4,5 => CTR => C9: 3,6,7 * DIS C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 # B5: 4,9 => CTR => B5: 3,6 * DIS C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 + B5: 3,6 # G5: 3 => CTR => G5: 4,9 * DIS C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 + B5: 3,6 + G5: 4,9 # C5: 2,6 => CTR => C5: 3 * DIS C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 + B5: 3,6 + G5: 4,9 + C5: 3 # A8: 4,6 => CTR => A8: 1 * PRF C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 + B5: 3,6 + G5: 4,9 + C5: 3 + A8: 1 => SOL * STA C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 + B5: 3,6 + G5: 4,9 + C5: 3 + A8: 1 * CNT 8 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2..5.64.31...........8.......62....8......7.........1...3.7.....9...2.....1..... | initial |
| 72895164331..76.......83......62....8..51..7....73...1...3.7.....98.52.....1.2... | autosolve |
| 728951643315476829496283715971624358863519472254738961582347196149865237637192584 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) C2: 4,5 D2: 2,4 D3: 2,4 F5: 4,9 I5: 2,6 H6: 2,6 E8: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G3,H3: 1.. / G3 = 1 => 0 pairs (X) / H3 = 1 => 0 pairs (_) A4,C4: 1.. / A4 = 1 => 0 pairs (X) / C4 = 1 => 0 pairs (_) A8,H8: 1.. / A8 = 1 => 0 pairs (*) / H8 = 1 => 0 pairs (X) C4,C7: 1.. / C4 = 1 => 0 pairs (*) / C7 = 1 => 0 pairs (X) G3,G7: 1.. / G3 = 1 => 0 pairs (X) / G7 = 1 => 0 pairs (_) D2,D3: 2.. / D2 = 2 => 8 pairs (_) / D3 = 2 => 8 pairs (_) I5,H6: 2.. / I5 = 2 => 7 pairs (_) / H6 = 2 => 0 pairs (X) A7,C7: 2.. / A7 = 2 => 7 pairs (_) / C7 = 2 => 0 pairs (*) C5,I5: 2.. / C5 = 2 => 0 pairs (X) / I5 = 2 => 7 pairs (_) A6,A7: 2.. / A6 = 2 => 0 pairs (*) / A7 = 2 => 0 pairs (X) B8,H8: 3.. / B8 = 3 => 0 pairs (X) / H8 = 3 => 0 pairs (_) D2,D3: 4.. / D2 = 4 => 8 pairs (_) / D3 = 4 => 8 pairs (_) C2,D2: 4.. / C2 = 4 => 8 pairs (_) / D2 = 4 => 8 pairs (_) I5,H6: 6.. / I5 = 6 => 0 pairs (X) / H6 = 6 => 7 pairs (_) G3,I3: 7.. / G3 = 7 => 0 pairs (*) / I3 = 7 => 0 pairs (X) B4,C4: 7.. / B4 = 7 => 0 pairs (*) / C4 = 7 => 0 pairs (X) B8,I8: 7.. / B8 = 7 => 0 pairs (X) / I8 = 7 => 0 pairs (_) C4,C9: 7.. / C4 = 7 => 0 pairs (X) / C9 = 7 => 0 pairs (_) G3,G9: 7.. / G3 = 7 => 0 pairs (*) / G9 = 7 => 0 pairs (X) F4,F6: 8.. / F4 = 8 => 9 pairs (_) / F6 = 8 => 8 pairs (_) B7,B9: 8.. / B7 = 8 => 7 pairs (_) / B9 = 8 => 9 pairs (_) F6,G6: 8.. / F6 = 8 => 8 pairs (_) / G6 = 8 => 9 pairs (_) A3,B3: 9.. / A3 = 9 => 7 pairs (_) / B3 = 9 => 7 pairs (_) E7,E9: 9.. / E7 = 9 => 8 pairs (_) / E9 = 9 => 8 pairs (_) * DURATION: 0:00:34.788505 START: 16:44:58.738417 END: 16:45:33.526922 2017-05-04 * CP COUNT: (24) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C2,D2,D3,E8,F5,H6,I5) * 72895164331..76.......83......62....8..51..7....73...1...3.7.....98.52.....1.2... * PAIR C2: 4,5 BLK 1 A3: 4,5,6,9 # reduction candidate for 4,5 A3: 4,5 # 8 pairs B3: 4,5,6,9 # reduction candidate for 4,5 B3: 4,5 # 8 pairs C3: 4,5,6 # reduction candidate for 4,5 C3: 4,5 # 12 pairs * PAIR C2: 4,5 COL C C4: 4,5,1,3,7 # reduction candidate for 4,5 C4: 4,5 => CTR * 72895164331..76.......83...17.62....8..51..7....73...1..13.7.....98.5217..71.2... C4: 1,3,7 # 7 pairs C6: 4,5,2,6 # reduction candidate for 4,5 C6: 4,5 # 11 pairs C7: 4,5,1,2,6 # reduction candidate for 4,5 C7: 4,5 => CTR * 72895164331..76.2...6283715.7162.3..86351..72..273..6128.3.71..1498652376371.2... C7: 1,2,6 # 7 pairs C9: 4,5,3,6,7 # reduction candidate for 4,5 C9: 4,5 => CTR * 72895164331..76.....6.831.71.762....86351..72...73..61..13.7.....98.521....1.2... C9: 3,6,7 # 7 pairs * PAIR F5: 4,9 BLK 5 F4: 4,9,8 # reduction candidate for 4,9 F4: 4,9 # 8 pairs F6: 4,9,8 # reduction candidate for 4,9 F6: 4,9 # 9 pairs * PAIR F5: 4,9 ROW 5 B5: 4,9,3,6 # reduction candidate for 4,9 B5: 4,9 => CTR * 72895164331..76.......831.71.362....8..51.37....73...12.13.7.....98.521....1.2.3. B5: 3,6 # 8 pairs G5: 4,9,3 # reduction candidate for 4,9 G5: 4,9 # 9 pairs * PAIR I5: 2,6 ROW 5 C5: 2,6,3,4 # reduction candidate for 2,6 C5: 2,6 => CTR * 72895164331..76.......831.71..62....8..51..7....73...12.13.7.....98.521....1.2... C5: 3,4 # 8 pairs * PAIR H6: 2,6 ROW 6 A6: 2,6,4,5,9 # reduction candidate for 2,6 A6: 2,6 # 12 pairs C6: 2,6,4,5 # reduction candidate for 2,6 C6: 2,6 # 8 pairs * PAIR E8: 4,6 BLK 8 E7: 4,6,9 # reduction candidate for 4,6 E7: 4,6 # 8 pairs E9: 4,6,9 # reduction candidate for 4,6 E9: 4,6 # 8 pairs * PAIR E8: 4,6 ROW 8 A8: 4,6,1 # reduction candidate for 4,6 A8: 4,6 => CTR * 72895164331..76.......831.7...62....8..51..7....73...1...3.7.....98.521....1.2... A8: 1 => SOLVED * 728951643315476829496283715971624358863519472254738961582347196149865237637192584 B8: 4,6,3,7 # reduction candidate for 4,6 B8: 4,6 => SOLVED * 728951643315476829496283715971624358863519472254738961582347196149865237637192584 B8: 3,7 # 8 pairs I8: 4,6,7 # reduction candidate for 4,6 I8: 4,6 => CTR * 72895164331..76.......83.....762....8..51..7....73...1..13.7....798.523....1.2... I8: 7 => SOLVED * 728951643315476829496283715971624358863519472254738961582347196149865237637192584 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-407-base-pr-000.dot * REASONING * DIS # C4: 4,5 => CTR => C4: 1,3,7 * DIS # C7: 4,5 => CTR => C7: 1,2,6 * DIS # C9: 4,5 => CTR => C9: 3,6,7 * DIS # B5: 4,9 => CTR => B5: 3,6 * DIS # C5: 2,6 => CTR => C5: 3,4 * DIS # A8: 4,6 => CTR => A8: 1 * PRF # A8: 1 => SOL * PRF # B8: 4,6 => SOL * DIS # I8: 4,6 => CTR => I8: 7 * PRF # I8: 7 => SOL * CNT 10 HDP CHAINS / 27 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C2,D2,D3,E8,F5,H6,I5) * 72895164331..76.......83......62....8..51..7....73...1...3.7.....98.52.....1.2... * PAIR C2: 4,5 BLK 1 A3: 4,5,6,9 # reduction candidate for 4,5 A3: 4,5 # 8 pairs B3: 4,5,6,9 # reduction candidate for 4,5 B3: 4,5 # 8 pairs C3: 4,5,6 # reduction candidate for 4,5 C3: 4,5 # 12 pairs * PAIR C2: 4,5 COL C C4: 4,5,1,3,7 # reduction candidate for 4,5 C4: 4,5 => CTR * 72895164331..76.......83...17.62....8..51..7....73...1..13.7.....98.5217..71.2... C6: 4,5,2,6 # reduction candidate for 4,5 C6: 4,5 # 11 pairs C7: 4,5,1,2,6 # reduction candidate for 4,5 C7: 4,5 => CTR * 72895164331..76.2...6283715.7162.3..86351..72..273..6128.3.71..1498652376371.2... C9: 4,5,3,6,7 # reduction candidate for 4,5 C9: 4,5 => CTR * 72895164331..76.....6.831.71.762....86351..72...73..61..13.7.....98.521....1.2... * RESTART * PAIR C2: 4,5 COL C C6: 4,5,2,6 # reduction candidate for 4,5 C6: 4,5 # 11 pairs C6: 2,6 # 9 pairs * PAIR RESTART * PAIR C2: 4,5 BLK 1 A3: 4,5,6,9 # reduction candidate for 4,5 A3: 4,5 # 10 pairs B3: 4,5,6,9 # reduction candidate for 4,5 B3: 4,5 # 10 pairs C3: 4,5,6 # reduction candidate for 4,5 C3: 4,5 # 12 pairs * PAIR C2: 4,5 COL C C6: 4,5,2,6 # reduction candidate for 4,5 C6: 4,5 # 11 pairs C6: 2,6 # 9 pairs * PAIR F5: 4,9 BLK 5 F4: 4,9,8 # reduction candidate for 4,9 F4: 4,9 # 8 pairs F6: 4,9,8 # reduction candidate for 4,9 F6: 4,9 # 9 pairs * PAIR F5: 4,9 ROW 5 B5: 4,9,3,6 # reduction candidate for 4,9 B5: 4,9 => CTR * 72895164331..76.......831.71.362....8..51.37....73...12.13.7.....98.521....1.2.3. G5: 4,9,3 # reduction candidate for 4,9 G5: 4,9 # 10 pairs * RESTART * PAIR F5: 4,9 ROW 5 G5: 4,9,3 # reduction candidate for 4,9 G5: 3 => CTR * 728951643315476.2...62831571.362....864519372..273..612.13.7.....98.521....1.2.3. * PAIR RESTART * PAIR F5: 4,9 BLK 5 F4: 4,9,8 # reduction candidate for 4,9 F4: 4,9 # 11 pairs F6: 4,9,8 # reduction candidate for 4,9 F6: 4,9 # 12 pairs * PAIR I5: 2,6 ROW 5 C5: 2,6,3 # reduction candidate for 2,6 C5: 2,6 => CTR * 72895164331..76.......83.....762.3..83.51..7....73...1..13.7.....98.523...31.2... * PAIR RESTART * PAIR E8: 4,6 BLK 8 E7: 4,6,9 # reduction candidate for 4,6 E7: 4,6 # 11 pairs E9: 4,6,9 # reduction candidate for 4,6 E9: 4,6 # 11 pairs * PAIR E8: 4,6 ROW 8 A8: 4,6,1 # reduction candidate for 4,6 A8: 4,6 => CTR * 72895164331..76.......831.7...62....86351..72...73..61...3.7.....98.521....1.2... A8: 1 => SOLVED * 728951643315476829496283715971624358863519472254738961582347196149865237637192584 * DURATION: 0:00:21.310525 START: 16:45:54.180853 END: 16:46:15.491378 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-407-base-pr-001.dot * REASONING * DIS # C4: 4,5 => CTR => C4: 1,3,7 * DIS C4: 1,3,7 # C7: 4,5 => CTR => C7: 1,2,6 * DIS C4: 1,3,7 + C7: 1,2,6 # C9: 4,5 => CTR => C9: 3,6,7 * DIS C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 # B5: 4,9 => CTR => B5: 3,6 * DIS C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 + B5: 3,6 # G5: 3 => CTR => G5: 4,9 * DIS C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 + B5: 3,6 + G5: 4,9 # C5: 2,6 => CTR => C5: 3 * DIS C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 + B5: 3,6 + G5: 4,9 + C5: 3 # A8: 4,6 => CTR => A8: 1 * PRF C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 + B5: 3,6 + G5: 4,9 + C5: 3 + A8: 1 => SOL * STA C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 + B5: 3,6 + G5: 4,9 + C5: 3 + A8: 1 * CNT 8 HDP CHAINS / 26 HYP OPENED
Header Info
Top 500 Minimum 17 407 solution: 728951643315476829496283715971624358863519472254738961582347196149865237637192584 info: 94836 FNBHYK S8.f 48427 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 728951643315476829496283715971624358863519472254738961582347196149865237637192584 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 # A3: 4,5 => UNS * INC # B3: 4,5 => UNS * INC # C3: 4,5 => UNS * DIS # C4: 4,5 => CTR => C4: 1,3,7 * INC # C4: 1,3,7 => UNS * INC # C6: 4,5 => UNS * DIS # C7: 4,5 => CTR => C7: 1,2,6 * INC # C7: 1,2,6 => UNS * DIS # C9: 4,5 => CTR => C9: 3,6,7 * INC # C9: 3,6,7 => UNS * INC # F4: 4,9 => UNS * INC # F6: 4,9 => UNS * DIS # B5: 4,9 => CTR => B5: 3,6 * INC # B5: 3,6 => UNS * INC # G5: 4,9 => UNS * DIS # C5: 2,6 => CTR => C5: 3,4 * INC # C5: 3,4 => UNS * INC # A6: 2,6 => UNS * INC # C6: 2,6 => UNS * INC # E7: 4,6 => UNS * INC # E9: 4,6 => UNS * DIS # A8: 4,6 => CTR => A8: 1 * PRF # A8: 1 => SOL * PRF # B8: 4,6 => SOL * INC # B8: 3,7 => UNS * DIS # I8: 4,6 => CTR => I8: 7 * PRF # I8: 7 => SOL * CNT 27 HDP CHAINS / 27 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 4,5 => UNS * INC # B3: 4,5 => UNS * INC # C3: 4,5 => UNS * DIS # C4: 4,5 => CTR => C4: 1,3,7 * INC C4: 1,3,7 # C6: 4,5 => UNS * DIS C4: 1,3,7 # C7: 4,5 => CTR => C7: 1,2,6 * DIS C4: 1,3,7 + C7: 1,2,6 # C9: 4,5 => CTR => C9: 3,6,7 * INC C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 # C6: 4,5 => UNS * INC C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 # C6: 2,6 => UNS * INC C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 # A3: 4,5 => UNS * INC C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 # B3: 4,5 => UNS * INC C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 # C3: 4,5 => UNS * INC C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 # C6: 4,5 => UNS * INC C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 # C6: 2,6 => UNS * INC C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 # F4: 4,9 => UNS * INC C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 # F6: 4,9 => UNS * DIS C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 # B5: 4,9 => CTR => B5: 3,6 * INC C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 + B5: 3,6 # G5: 4,9 => UNS * INC C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 + B5: 3,6 # G5: 4,9 => UNS * DIS C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 + B5: 3,6 # G5: 3 => CTR => G5: 4,9 * INC C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 + B5: 3,6 + G5: 4,9 # F4: 4,9 => UNS * INC C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 + B5: 3,6 + G5: 4,9 # F6: 4,9 => UNS * DIS C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 + B5: 3,6 + G5: 4,9 # C5: 2,6 => CTR => C5: 3 * INC C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 + B5: 3,6 + G5: 4,9 + C5: 3 # E7: 4,6 => UNS * INC C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 + B5: 3,6 + G5: 4,9 + C5: 3 # E9: 4,6 => UNS * DIS C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 + B5: 3,6 + G5: 4,9 + C5: 3 # A8: 4,6 => CTR => A8: 1 * PRF C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 + B5: 3,6 + G5: 4,9 + C5: 3 + A8: 1 => SOL * STA C4: 1,3,7 + C7: 1,2,6 + C9: 3,6,7 + B5: 3,6 + G5: 4,9 + C5: 3 + A8: 1 * CNT 27 HDP CHAINS / 26 HYP OPENED