Analysis of xx-top500-410-base.sdk
Contents
Original Sudoku
level: medium
position: 5...2.8...6...1............3.......62...8.......5...4..416......7....9........2.. initial
Autosolve
position: 51.4268..76...142.42....6..3942175862563841..187569342.416.27...721..9...35..82.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # E3: 3,5 => SOL * DIS # I3: 3,5 => CTR => I3: 1,9 * PRF # H1: 3 => SOL * DIS # E8: 3,5 => CTR => E8: 4 * DIS # H8: 3,5 => CTR => H8: 6 * DIS # E9: 4 => CTR => E9: 7,9 * DIS # I7: 3,5 => CTR => I7: 8 * DIS # H8: 3,5 => CTR => H8: 6 * DIS # E7: 9 => CTR => E7: 3,5 * CNT 9 HDP CHAINS / 37 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # E3: 3,5 => SOL * STA E3: 3,5 * CNT 1 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 5...2.8...6...1............3.......62...8.......5...4..416......7....9........2.. | initial |
| 51.4268..76...142.42....6..3942175862563841..187569342.416.27...721..9...35..82.. | autosolve |
| 519426837763891425428753691394217586256384179187569342941632758872145963635978214 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) C1: 3,9 D2: 8,9 F3: 3,5 H5: 7,9 I5: 7,9 A7: 8,9 A8: 6,8 A9: 6,9 F8: 3,5 D9: 7,9 H7: 3,5 H9: 1,6 I9: 1,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H3,I3: 1.. / H3 = 1 => 0 pairs (X) / I3 = 1 => 11 pairs (_) H9,I9: 1.. / H9 = 1 => 11 pairs (_) / I9 = 1 => 0 pairs (X) H3,H9: 1.. / H3 = 1 => 0 pairs (X) / H9 = 1 => 11 pairs (_) I3,I9: 1.. / I3 = 1 => 11 pairs (_) / I9 = 1 => 0 pairs (X) F3,F8: 3.. / F3 = 3 => 16 pairs (_) / F8 = 3 => 17 pairs (_) E8,E9: 4.. / E8 = 4 => 11 pairs (_) / E9 = 4 => 0 pairs (X) I8,I9: 4.. / I8 = 4 => 0 pairs (X) / I9 = 4 => 11 pairs (_) E8,I8: 4.. / E8 = 4 => 11 pairs (_) / I8 = 4 => 0 pairs (X) E9,I9: 4.. / E9 = 4 => 0 pairs (X) / I9 = 4 => 11 pairs (_) E2,I2: 5.. / E2 = 5 => 22 pairs (_) / I2 = 5 => 15 pairs (_) F3,F8: 5.. / F3 = 5 => 17 pairs (_) / F8 = 5 => 16 pairs (_) A8,A9: 6.. / A8 = 6 => 0 pairs (X) / A9 = 6 => 11 pairs (_) H8,H9: 6.. / H8 = 6 => 11 pairs (_) / H9 = 6 => 0 pairs (X) A8,H8: 6.. / A8 = 6 => 0 pairs (X) / H8 = 6 => 11 pairs (_) A9,H9: 6.. / A9 = 6 => 11 pairs (_) / H9 = 6 => 0 pairs (X) D3,E3: 7.. / D3 = 7 => 9 pairs (_) / E3 = 7 => 15 pairs (_) H1,I1: 7.. / H1 = 7 => 12 pairs (_) / I1 = 7 => 13 pairs (_) H5,I5: 7.. / H5 = 7 => 13 pairs (_) / I5 = 7 => 12 pairs (_) D9,E9: 7.. / D9 = 7 => 15 pairs (_) / E9 = 7 => 9 pairs (_) D3,D9: 7.. / D3 = 7 => 9 pairs (_) / D9 = 7 => 15 pairs (_) E3,E9: 7.. / E3 = 7 => 15 pairs (_) / E9 = 7 => 9 pairs (_) H1,H5: 7.. / H1 = 7 => 12 pairs (_) / H5 = 7 => 13 pairs (_) I1,I5: 7.. / I1 = 7 => 13 pairs (_) / I5 = 7 => 12 pairs (_) C2,C3: 8.. / C2 = 8 => 15 pairs (_) / C3 = 8 => 14 pairs (_) D2,D3: 8.. / D2 = 8 => 14 pairs (_) / D3 = 8 => 15 pairs (_) A7,A8: 8.. / A7 = 8 => 0 pairs (X) / A8 = 8 => 11 pairs (_) I7,I8: 8.. / I7 = 8 => 11 pairs (_) / I8 = 8 => 0 pairs (X) C2,D2: 8.. / C2 = 8 => 15 pairs (_) / D2 = 8 => 14 pairs (_) C3,D3: 8.. / C3 = 8 => 14 pairs (_) / D3 = 8 => 15 pairs (_) A7,I7: 8.. / A7 = 8 => 0 pairs (X) / I7 = 8 => 11 pairs (_) A8,I8: 8.. / A8 = 8 => 11 pairs (_) / I8 = 8 => 0 pairs (X) H5,I5: 9.. / H5 = 9 => 12 pairs (_) / I5 = 9 => 13 pairs (_) A7,A9: 9.. / A7 = 9 => 11 pairs (_) / A9 = 9 => 0 pairs (X) A7,E7: 9.. / A7 = 9 => 11 pairs (_) / E7 = 9 => 0 pairs (X) * DURATION: 0:00:57.279415 START: 16:49:48.082247 END: 16:50:45.361662 2017-05-04 * CP COUNT: (34) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A8,A9,C1,D2,D9,F3,F8,H5,H7,H9,I5,I9) * 51.4268..76...142.42....6..3942175862563841..187569342.416.27...721..9...35..82.. * PAIR C1: 3,9 BLK 1 C2: 3,9,8 # reduction candidate for 3,9 C2: 3,9 # 14 pairs C3: 3,9,8 # reduction candidate for 3,9 C3: 3,9 # 15 pairs * PAIR C1: 3,9 ROW 1 H1: 3,9,7 # reduction candidate for 3,9 H1: 3,9 # 13 pairs I1: 3,9,7 # reduction candidate for 3,9 I1: 3,9 # 12 pairs * PAIR D2: 8,9 BLK 2 D3: 8,9,7 # reduction candidate for 8,9 D3: 8,9 # 15 pairs D3: 7 # 9 pairs * PAIR D2: 8,9 ROW 2 C2: 8,9,3 # reduction candidate for 8,9 C2: 8,9 # 17 pairs C2: 3 # 16 pairs * PAIR F3: 3,5 BLK 2 E2: 3,5,9 # reduction candidate for 3,5 E2: 3,5 # 15 pairs E3: 3,5,7,9 # reduction candidate for 3,5 E3: 3,5 => SOLVED * 519426837763891425428753691394217586256384179187569342941632758872145963635978214 E3: 7,9 # 15 pairs * PAIR F3: 3,5 ROW 3 H3: 3,5,1,9 # reduction candidate for 3,5 H3: 3,5 # 16 pairs I3: 3,5,1,9 # reduction candidate for 3,5 I3: 3,5 => CTR * 51.4268..76...142.42....61.3942175862563841..187569342.416.27..6721..9...35..8261 I3: 1,9 # 14 pairs * PAIR H5: 7,9 COL H H1: 7,9,3 # reduction candidate for 7,9 H1: 3 => SOLVED * 519426837763891425428753691394217586256384179187569342941632758872145963635978214 H1: 7,9 # 14 pairs * PAIR I5: 7,9 COL I I1: 7,9,3 # reduction candidate for 7,9 I1: 7,9 # 15 pairs I1: 3 # 15 pairs * PAIR F8: 3,5 BLK 8 E7: 3,5,9 # reduction candidate for 3,5 E7: 3,5 # 11 pairs E8: 3,5,4 # reduction candidate for 3,5 E8: 3,5 => CTR * 51.4268..76...142.42..7.61.3942175862563841..187569342.416.27.88721..964.35.482.1 E8: 4 # 11 pairs * PAIR F8: 3,5 ROW 8 H8: 3,5,6 # reduction candidate for 3,5 H8: 3,5 => CTR * 51.4268..76...142.42....6..3942175862563841..187569342.416.27..6721..9.8935748261 H8: 6 # 11 pairs I8: 3,5,4,8 # reduction candidate for 3,5 I8: 3,5 # 11 pairs * PAIR D9: 7,9 BLK 8 E9: 7,9,4 # reduction candidate for 7,9 E9: 4 => CTR * 51.4268..76...142.42..7.61.3942175862563841..187569342.416927...721..9.4935748261 E9: 7,9 # 11 pairs * PAIR D9: 7,9 COL D D3: 7,9,8 # reduction candidate for 7,9 D3: 8 # 15 pairs D3: 7,9 # 14 pairs * PAIR H7: 3,5 BLK 9 I7: 3,5,8 # reduction candidate for 3,5 I7: 3,5 => CTR * 51.4268..76...142.42....6..3942175862563841..1875693428416927..6721..9.8935748261 I7: 8 # 11 pairs H8: 3,5,6 # reduction candidate for 3,5 H8: 3,5 => CTR * 51.4268..76...142.42....6..3942175862563841..187569342.416.27..6721..9.8935748261 H8: 6 # 11 pairs I8: 3,5,4,8 # reduction candidate for 3,5 I8: 3,5 # 11 pairs * PAIR H7: 3,5 ROW 7 E7: 3,5,9 # reduction candidate for 3,5 E7: 9 => CTR * 51.4268..76...142.42..7.61.3942175862563841..1875693428416927..6721..9..935748261 E7: 3,5 # 11 pairs * PAIR H7: 3,5 COL H H3: 3,5,1,9 # reduction candidate for 3,5 H3: 3,5 # 16 pairs H3: 1,9 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-410-base-pr-000.dot * REASONING * PRF # E3: 3,5 => SOL * DIS # I3: 3,5 => CTR => I3: 1,9 * PRF # H1: 3 => SOL * DIS # E8: 3,5 => CTR => E8: 4 * DIS # H8: 3,5 => CTR => H8: 6 * DIS # E9: 4 => CTR => E9: 7,9 * DIS # I7: 3,5 => CTR => I7: 8 * DIS # H8: 3,5 => CTR => H8: 6 * DIS # E7: 9 => CTR => E7: 3,5 * CNT 9 HDP CHAINS / 37 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A8,A9,C1,D2,D9,F3,F8,H5,H7,H9,I5,I9) * 51.4268..76...142.42....6..3942175862563841..187569342.416.27...721..9...35..82.. * PAIR C1: 3,9 BLK 1 C2: 3,9,8 # reduction candidate for 3,9 C2: 3,9 # 14 pairs C3: 3,9,8 # reduction candidate for 3,9 C3: 3,9 # 15 pairs * PAIR C1: 3,9 ROW 1 H1: 3,9,7 # reduction candidate for 3,9 H1: 3,9 # 13 pairs I1: 3,9,7 # reduction candidate for 3,9 I1: 3,9 # 12 pairs * PAIR D2: 8,9 BLK 2 D3: 8,9,7 # reduction candidate for 8,9 D3: 8,9 # 15 pairs D3: 7 # 9 pairs * PAIR D2: 8,9 ROW 2 C2: 8,9,3 # reduction candidate for 8,9 C2: 8,9 # 17 pairs C2: 3 # 16 pairs * PAIR F3: 3,5 BLK 2 E2: 3,5,9 # reduction candidate for 3,5 E2: 3,5 # 15 pairs E3: 3,5,7,9 # reduction candidate for 3,5 E3: 3,5 => SOLVED * 519426837763891425428753691394217586256384179187569342941632758872145963635978214 * DURATION: 0:00:10.032555 START: 16:51:20.291086 END: 16:51:30.323641 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-410-base-pr-001.dot * REASONING * PRF # E3: 3,5 => SOL * STA E3: 3,5 * CNT 1 HDP CHAINS / 10 HYP OPENED
Header Info
Top 500 Minimum 17 410 solution: 519426837763891425428753691394217586256384179187569342941632758872145963635978214 info: 95021 FNBXK S8.f 44397 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 519426837763891425428753691394217586256384179187569342941632758872145963635978214 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 # C2: 3,9 => UNS * INC # C3: 3,9 => UNS * INC # H1: 3,9 => UNS * INC # I1: 3,9 => UNS * INC # D3: 8,9 => UNS * INC # D3: 7 => UNS * INC # C2: 8,9 => UNS * INC # C2: 3 => UNS * INC # E2: 3,5 => UNS * PRF # E3: 3,5 => SOL * INC # E3: 7,9 => UNS * INC # H3: 3,5 => UNS * DIS # I3: 3,5 => CTR => I3: 1,9 * INC # I3: 1,9 => UNS * INC # H1: 7,9 => UNS * PRF # H1: 3 => SOL * INC # I1: 7,9 => UNS * INC # I1: 3 => UNS * INC # E7: 3,5 => UNS * DIS # E8: 3,5 => CTR => E8: 4 * INC # E8: 4 => UNS * DIS # H8: 3,5 => CTR => H8: 6 * INC # H8: 6 => UNS * INC # I8: 3,5 => UNS * INC # E9: 7,9 => UNS * DIS # E9: 4 => CTR => E9: 7,9 * INC # D3: 7,9 => UNS * INC # D3: 8 => UNS * DIS # I7: 3,5 => CTR => I7: 8 * INC # I7: 8 => UNS * DIS # H8: 3,5 => CTR => H8: 6 * INC # H8: 6 => UNS * INC # I8: 3,5 => UNS * INC # E7: 3,5 => UNS * DIS # E7: 9 => CTR => E7: 3,5 * INC # H3: 3,5 => UNS * INC # H3: 1,9 => UNS * CNT 37 HDP CHAINS / 37 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 3,9 => UNS * INC # C3: 3,9 => UNS * INC # H1: 3,9 => UNS * INC # I1: 3,9 => UNS * INC # D3: 8,9 => UNS * INC # D3: 7 => UNS * INC # C2: 8,9 => UNS * INC # C2: 3 => UNS * INC # E2: 3,5 => UNS * PRF # E3: 3,5 => SOL * STA E3: 3,5 * CNT 10 HDP CHAINS / 10 HYP OPENED