Analysis of xx-top500-345-base.sdk
Contents
Original Sudoku
level: medium
position: 1...2..6.7.5................8.....1....5.3.....47........4..7..2.....5...6..1.... initial
Autosolve
position: 1...2..6.7.5................8.....1....5.3.....47.1......4..7..2.....5...6..1.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F3: 5,7 => CTR => F3: 4,8,9 * DIS # F9: 2,8,9 => CTR => F9: 5,7 * DIS # I3: 5,7 => CTR => I3: 2,3,4,8,9 * DIS # I4: 3,4,9 => CTR => I4: 5,7 * DIS # A4: 6,9 => CTR => A4: 3,5 * PRF # C4: 6,9 => SOL * DIS # C4: 3,7 => CTR => C4: 6,9 * DIS # C5: 6,9 => CTR => C5: 1,2,7 * DIS # A6: 6,9 => CTR => A6: 3,5 * PRF # A3: 6,9 => SOL * DIS # A3: 3,4,8 => CTR => A3: 6,9 * CNT 11 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F3: 5,7 => CTR => F3: 4,8,9 * DIS F3: 4,8,9 # F9: 2,8,9 => CTR => F9: 5,7 * DIS F3: 4,8,9 + F9: 5,7 # I3: 5,7 => CTR => I3: 2,3,4,8,9 * DIS F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 # I4: 3,4,9 => CTR => I4: 5,7 * DIS F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 + I4: 5,7 # A4: 6,9 => CTR => A4: 3,5 * PRF F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 + I4: 5,7 + A4: 3,5 # C4: 6,9 => SOL * STA F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 + I4: 5,7 + A4: 3,5 + C4: 6,9 * CNT 6 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1...2..6.7.5................8.....1....5.3.....47........4..7..2.....5...6..1.... | initial |
| 1...2..6.7.5................8.....1....5.3.....47.1......4..7..2.....5...6..1.... | autosolve |
| 198327465745698132632154978586942317971563284324781659859436721213879546467215893 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) F1: 5,7 I1: 5,7 A5: 6,9 I7: 1,6 I8: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,D3: 1.. / D2 = 1 => 5 pairs (_) / D3 = 1 => 5 pairs (_) G2,G3: 1.. / G2 = 1 => 5 pairs (_) / G3 = 1 => 5 pairs (_) B5,C5: 1.. / B5 = 1 => 0 pairs (X) / C5 = 1 => 0 pairs (_) I7,I8: 1.. / I7 = 1 => 0 pairs (*) / I8 = 1 => 0 pairs (X) D2,G2: 1.. / D2 = 1 => 5 pairs (_) / G2 = 1 => 5 pairs (_) D3,G3: 1.. / D3 = 1 => 5 pairs (_) / G3 = 1 => 5 pairs (_) D4,F4: 2.. / D4 = 2 => 5 pairs (_) / F4 = 2 => 6 pairs (_) F7,H7: 2.. / F7 = 2 => 5 pairs (_) / H7 = 2 => 5 pairs (_) C3,C5: 2.. / C3 = 2 => 0 pairs (*) / C5 = 2 => 0 pairs (X) D4,D9: 2.. / D4 = 2 => 5 pairs (_) / D9 = 2 => 6 pairs (_) B8,A9: 4.. / B8 = 4 => 0 pairs (X) / A9 = 4 => 0 pairs (_) B1,G1: 4.. / B1 = 4 => 0 pairs (X) / G1 = 4 => 6 pairs (_) B8,H8: 4.. / B8 = 4 => 0 pairs (X) / H8 = 4 => 0 pairs (_) A3,A9: 4.. / A3 = 4 => 0 pairs (X) / A9 = 4 => 0 pairs (_) F1,I1: 5.. / F1 = 5 => 0 pairs (X) / I1 = 5 => 0 pairs (_) A4,I4: 5.. / A4 = 5 => 0 pairs (*) / I4 = 5 => 0 pairs (X) A9,F9: 5.. / A9 = 5 => 0 pairs (X) / F9 = 5 => 0 pairs (_) B6,B7: 5.. / B6 = 5 => 0 pairs (X) / B7 = 5 => 0 pairs (_) E3,E7: 5.. / E3 = 5 => 0 pairs (*) / E7 = 5 => 0 pairs (X) H3,H6: 5.. / H3 = 5 => 0 pairs (X) / H6 = 5 => 0 pairs (_) A3,C3: 6.. / A3 = 6 => 0 pairs (*) / C3 = 6 => 0 pairs (X) I7,I8: 6.. / I7 = 6 => 3 pairs (_) / I8 = 6 => 0 pairs (*) F1,I1: 7.. / F1 = 7 => 0 pairs (*) / I1 = 7 => 0 pairs (X) C4,I4: 7.. / C4 = 7 => 0 pairs (X) / I4 = 7 => 0 pairs (_) C9,F9: 7.. / C9 = 7 => 0 pairs (*) / F9 = 7 => 0 pairs (X) B5,B8: 7.. / B5 = 7 => 0 pairs (*) / B8 = 7 => 0 pairs (X) E3,E8: 7.. / E3 = 7 => 0 pairs (X) / E8 = 7 => 0 pairs (_) H3,H5: 7.. / H3 = 7 => 0 pairs (*) / H5 = 7 => 0 pairs (X) E5,E6: 8.. / E5 = 8 => 6 pairs (_) / E6 = 8 => 5 pairs (_) * DURATION: 0:00:49.285408 START: 14:31:28.340028 END: 14:32:17.625436 2017-05-04 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,F1,I1,I7,I8) * 1...2..6.7.5................8.....1....5.3.....47.1......4..7..2.....5...6..1.... * PAIR F1: 5,7 BLK 2 E3: 5,7,3,4,9 # reduction candidate for 5,7 E3: 5,7 # 6 pairs F3: 5,7,4,8,9 # reduction candidate for 5,7 F3: 5,7 => CTR * 1...2..6.7.5................8.....1....5.3.....47.1......45.7..2...7.5..567.1.... F3: 4,8,9 # 6 pairs * PAIR F1: 5,7 COL F F9: 5,7,2,8,9 # reduction candidate for 5,7 F9: 2,8,9 => CTR * 1...2..6.7.5................8.....1....5.3.....47.1......4..7..2.....5..567.1.... F9: 5,7 # 7 pairs * PAIR I1: 5,7 BLK 3 H3: 5,7,2,3,4,8,9 # reduction candidate for 5,7 H3: 5,7 # 6 pairs I3: 5,7,2,3,4,8,9 # reduction candidate for 5,7 I3: 5,7 => CTR * 1...2..6.7.5...............587....1....5.3.7...47.1.5..5.4..7..27....54.46..1.... I3: 2,3,4,8,9 # 6 pairs * PAIR I1: 5,7 COL I I4: 5,7,3,4,9 # reduction candidate for 5,7 I4: 3,4,9 => CTR * 1...2..6.7.5...............587....1....5.3.....47.1....5.4..7..27....54.46..1.... I4: 5,7 # 7 pairs * PAIR A5: 6,9 BLK 4 A4: 6,9,3,5 # reduction candidate for 6,9 A4: 6,9 => CTR * 1...25.677.5.............5..87...315...5.3.7...47.1......45.7..27....54..6..1.... A4: 3,5 # 6 pairs C4: 6,9,3,7 # reduction candidate for 6,9 C4: 6,9 => SOLVED * 198327465745698132632154978586942317971563284324781659859436721213879546467215893 C4: 3,7 => CTR * 1...2..6.7.5................8.....1..1.5.3.....47.1......4..7..27....54.46..1.... C5: 6,9,1,2,7 # reduction candidate for 6,9 C5: 6,9 => CTR * 1...2..6.7.5........2.......8.....1..1.5.3....247.1....5.4..7..27....54.46..1.... C5: 1,2,7 # 5 pairs A6: 6,9,3,5 # reduction candidate for 6,9 A6: 6,9 => CTR * 1...2..6.7.5........6.......8.....1..125.3.....47.1......4..7..27....54.46..1.... A6: 3,5 # 6 pairs * PAIR A5: 6,9 ROW 5 E5: 6,9,4,8 # reduction candidate for 6,9 E5: 6,9 # 6 pairs G5: 6,9,2,4,8 # reduction candidate for 6,9 G5: 6,9 # 7 pairs * PAIR A5: 6,9 COL A A3: 6,9,3,4,8 # reduction candidate for 6,9 A3: 6,9 => SOLVED * 198327465745698132632154978586942317971563284324781659859436721213879546467215893 A3: 3,4,8 => CTR * 1...2..6.7.5........6.......8.....1..125.3.....47.1......4..7..27....54.46..1.... * INCONCLUSIVE * SAVE PR GRAPH xx-top500-345-base-pr-000.dot * REASONING * DIS # F3: 5,7 => CTR => F3: 4,8,9 * DIS # F9: 2,8,9 => CTR => F9: 5,7 * DIS # I3: 5,7 => CTR => I3: 2,3,4,8,9 * DIS # I4: 3,4,9 => CTR => I4: 5,7 * DIS # A4: 6,9 => CTR => A4: 3,5 * PRF # C4: 6,9 => SOL * DIS # C4: 3,7 => CTR => C4: 6,9 * DIS # C5: 6,9 => CTR => C5: 1,2,7 * DIS # A6: 6,9 => CTR => A6: 3,5 * PRF # A3: 6,9 => SOL * DIS # A3: 3,4,8 => CTR => A3: 6,9 * CNT 11 HDP CHAINS / 22 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,F1,I1,I7,I8) * 1...2..6.7.5................8.....1....5.3.....47.1......4..7..2.....5...6..1.... * PAIR F1: 5,7 BLK 2 E3: 5,7,3,4,9 # reduction candidate for 5,7 E3: 5,7 # 6 pairs F3: 5,7,4,8,9 # reduction candidate for 5,7 F3: 5,7 => CTR * 1...2..6.7.5................8.....1....5.3.....47.1......45.7..2...7.5..567.1.... * RESTART * PAIR F1: 5,7 COL F F9: 5,7,2,8,9 # reduction candidate for 5,7 F9: 2,8,9 => CTR * 1...2..6.7.5................8.....1....5.3.....47.1......4..7..2.....5..567.1.... * PAIR RESTART * PAIR I1: 5,7 BLK 3 H3: 5,7,2,3,4,8,9 # reduction candidate for 5,7 H3: 5,7 # 8 pairs I3: 5,7,2,3,4,8,9 # reduction candidate for 5,7 I3: 5,7 => CTR * 1...2..6.7.5...............587....1....5.3.7...47.1.5..5.4..7..27....54.46..1.... * RESTART * PAIR I1: 5,7 COL I I4: 5,7,3,4,9 # reduction candidate for 5,7 I4: 3,4,9 => CTR * 1...2..6.7.5...............587....1....5.3.....47.1....5.4..7..27....54.46..1.... * PAIR RESTART * PAIR A5: 6,9 BLK 4 A4: 6,9,3,5 # reduction candidate for 6,9 A4: 6,9 => CTR * 1...2..6.7.5................8.....15...5.3.7...47.1......4..7..27....54.46..1.... C4: 6,9,3,7 # reduction candidate for 6,9 C4: 6,9 => SOLVED * 198327465745698132632154978586942317971563284324781659859436721213879546467215893 * DURATION: 0:00:09.908188 START: 14:32:34.881706 END: 14:32:44.789894 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-345-base-pr-001.dot * REASONING * DIS # F3: 5,7 => CTR => F3: 4,8,9 * DIS F3: 4,8,9 # F9: 2,8,9 => CTR => F9: 5,7 * DIS F3: 4,8,9 + F9: 5,7 # I3: 5,7 => CTR => I3: 2,3,4,8,9 * DIS F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 # I4: 3,4,9 => CTR => I4: 5,7 * DIS F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 + I4: 5,7 # A4: 6,9 => CTR => A4: 3,5 * PRF F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 + I4: 5,7 + A4: 3,5 # C4: 6,9 => SOL * STA F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 + I4: 5,7 + A4: 3,5 + C4: 6,9 * CNT 6 HDP CHAINS / 10 HYP OPENED
Header Info
Top 500 Minimum 17 345 solution: 198327465745698132632154978586942317971563284324781659859436721213879546467215893 info: 3476 FNBHWXY S8.f 25213 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 198327465745698132632154978586942317971563284324781659859436721213879546467215893 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 # E3: 5,7 => UNS * DIS # F3: 5,7 => CTR => F3: 4,8,9 * INC # F3: 4,8,9 => UNS * INC # F9: 5,7 => UNS * DIS # F9: 2,8,9 => CTR => F9: 5,7 * INC # H3: 5,7 => UNS * DIS # I3: 5,7 => CTR => I3: 2,3,4,8,9 * INC # I3: 2,3,4,8,9 => UNS * INC # I4: 5,7 => UNS * DIS # I4: 3,4,9 => CTR => I4: 5,7 * DIS # A4: 6,9 => CTR => A4: 3,5 * INC # A4: 3,5 => UNS * PRF # C4: 6,9 => SOL * DIS # C4: 3,7 => CTR => C4: 6,9 * DIS # C5: 6,9 => CTR => C5: 1,2,7 * INC # C5: 1,2,7 => UNS * DIS # A6: 6,9 => CTR => A6: 3,5 * INC # A6: 3,5 => UNS * INC # E5: 6,9 => UNS * INC # G5: 6,9 => UNS * PRF # A3: 6,9 => SOL * DIS # A3: 3,4,8 => CTR => A3: 6,9 * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E3: 5,7 => UNS * DIS # F3: 5,7 => CTR => F3: 4,8,9 * INC F3: 4,8,9 # F9: 5,7 => UNS * DIS F3: 4,8,9 # F9: 2,8,9 => CTR => F9: 5,7 * INC F3: 4,8,9 + F9: 5,7 # H3: 5,7 => UNS * DIS F3: 4,8,9 + F9: 5,7 # I3: 5,7 => CTR => I3: 2,3,4,8,9 * INC F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 # I4: 5,7 => UNS * DIS F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 # I4: 3,4,9 => CTR => I4: 5,7 * DIS F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 + I4: 5,7 # A4: 6,9 => CTR => A4: 3,5 * PRF F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 + I4: 5,7 + A4: 3,5 # C4: 6,9 => SOL * STA F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 + I4: 5,7 + A4: 3,5 + C4: 6,9 * CNT 10 HDP CHAINS / 10 HYP OPENED