Analysis of xx-top500-224-base.sdk
Contents
Original Sudoku
level: medium
position: 2..1...........43......87...3.74............1.5...........6.35.1.8..2............ initial
Autosolve
position: 27.1.48..81..7.43..94..871..3174528..8...35.1.5281...3.2.461358148..2..7.6.987124 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C1: 5,6 => SOL * DIS # C1: 3 => CTR => C1: 5,6 * PRF # D2: 5,6 => SOL * DIS # D2: 2 => CTR => D2: 5,6 * DIS # I2: 5,6 => CTR => I2: 2,9 * PRF # C1: 3,5 => SOL * DIS # C1: 6 => CTR => C1: 3,5 * DIS # D3: 3,5 => CTR => D3: 2,6 * PRF # D3: 2,6 => SOL * DIS # E3: 3,5 => CTR => E3: 2 * PRF # E3: 2 => SOL * DIS # I2: 6,9 => CTR => I2: 2,5 * PRF # I2: 2,5 => SOL * PRF # I1: 6,9 => SOL * DIS # I2: 6,9 => CTR => I2: 2,5 * PRF # I2: 2,5 => SOL * DIS # A5: 4,7 => CTR => A5: 6,9 * DIS # A5: 7,9 => CTR => A5: 4,6 * DIS # A5: 4,7 => CTR => A5: 6,9 * DIS # D2: 2,6 => CTR => D2: 5 * PRF # D2: 5 => SOL * PRF # D3: 2,6 => SOL * DIS # D3: 3,5 => CTR => D3: 2,6 * PRF # I1: 6,9 => SOL * DIS # I2: 6,9 => CTR => I2: 2,5 * PRF # I2: 2,5 => SOL * DIS # A5: 4,7 => CTR => A5: 6,9 * DIS # A5: 7,9 => CTR => A5: 4,6 * PRF # C1: 3,5 => SOL * DIS # C1: 6 => CTR => C1: 3,5 * DIS # D3: 3,5 => CTR => D3: 2,6 * PRF # D3: 2,6 => SOL * PRF # E1: 3,5 => SOL * DIS # E1: 9 => CTR => E1: 3,5 * DIS # E3: 3,5 => CTR => E3: 2 * PRF # E3: 2 => SOL * CNT 36 HDP CHAINS / 44 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C1: 5,6 => SOL * STA C1: 5,6 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2..1...........43......87...3.74............1.5...........6.35.1.8..2............ | initial |
| 27.1.48..81..7.43..94..871..3174528..8...35.1.5281...3.2.461358148..2..7.6.987124 | autosolve |
| 275134869816579432394628715931745286687293541452816973729461358148352697563987124 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (22) C2: 5,6 A3: 3,5 F2: 6,9 H1: 6,9 A4: 6,9 C5: 7,9 A6: 4,7 D5: 2,6 E5: 2,9 F6: 6,9 I4: 6,9 H5: 4,7 G6: 6,9 H6: 4,7 A7: 7,9 C7: 7,9 A9: 3,5 C9: 3,5 D8: 3,5 E8: 3,5 G8: 6,9 H8: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I2,I3: 2.. / I2 = 2 => 0 pairs (*) / I3 = 2 => 0 pairs (X) D5,E5: 2.. / D5 = 2 => 0 pairs (*) / E5 = 2 => 0 pairs (X) D2,I2: 2.. / D2 = 2 => 0 pairs (X) / I2 = 2 => 0 pairs (_) E3,E5: 2.. / E3 = 2 => 0 pairs (*) / E5 = 2 => 0 pairs (X) C1,A3: 3.. / C1 = 3 => 0 pairs (X) / A3 = 3 => 0 pairs (_) A9,C9: 3.. / A9 = 3 => 0 pairs (X) / C9 = 3 => 0 pairs (_) D8,E8: 3.. / D8 = 3 => 22 pairs (_) / E8 = 3 => 0 pairs (X) C1,E1: 3.. / C1 = 3 => 0 pairs (X) / E1 = 3 => 0 pairs (_) A3,A9: 3.. / A3 = 3 => 0 pairs (*) / A9 = 3 => 0 pairs (X) C1,C9: 3.. / C1 = 3 => 0 pairs (X) / C9 = 3 => 0 pairs (_) D3,D8: 3.. / D3 = 3 => 0 pairs (X) / D8 = 3 => 22 pairs (_) A5,A6: 4.. / A5 = 4 => 0 pairs (X) / A6 = 4 => 19 pairs (_) H5,H6: 4.. / H5 = 4 => 19 pairs (_) / H6 = 4 => 0 pairs (X) A5,H5: 4.. / A5 = 4 => 0 pairs (X) / H5 = 4 => 19 pairs (_) A6,H6: 4.. / A6 = 4 => 19 pairs (_) / H6 = 4 => 0 pairs (X) A9,C9: 5.. / A9 = 5 => 0 pairs (*) / C9 = 5 => 0 pairs (X) D8,E8: 5.. / D8 = 5 => 0 pairs (X) / E8 = 5 => 22 pairs (_) A3,A9: 5.. / A3 = 5 => 0 pairs (X) / A9 = 5 => 0 pairs (_) C1,C2: 6.. / C1 = 6 => 0 pairs (X) / C2 = 6 => 0 pairs (_) A4,A5: 6.. / A4 = 6 => 0 pairs (X) / A5 = 6 => 0 pairs (_) D5,F6: 6.. / D5 = 6 => 0 pairs (X) / F6 = 6 => 0 pairs (_) I4,G6: 6.. / I4 = 6 => 0 pairs (*) / G6 = 6 => 0 pairs (X) G8,H8: 6.. / G8 = 6 => 0 pairs (*) / H8 = 6 => 0 pairs (X) D3,I3: 6.. / D3 = 6 => 0 pairs (*) / I3 = 6 => 0 pairs (X) A4,I4: 6.. / A4 = 6 => 0 pairs (X) / I4 = 6 => 0 pairs (_) A5,D5: 6.. / A5 = 6 => 0 pairs (*) / D5 = 6 => 0 pairs (X) F6,G6: 6.. / F6 = 6 => 0 pairs (*) / G6 = 6 => 0 pairs (X) F2,F6: 6.. / F2 = 6 => 0 pairs (X) / F6 = 6 => 0 pairs (_) G6,G8: 6.. / G6 = 6 => 0 pairs (X) / G8 = 6 => 0 pairs (_) H1,H8: 6.. / H1 = 6 => 0 pairs (*) / H8 = 6 => 0 pairs (X) H5,H6: 7.. / H5 = 7 => 0 pairs (X) / H6 = 7 => 19 pairs (_) A7,C7: 7.. / A7 = 7 => 17 pairs (_) / C7 = 7 => 0 pairs (X) A6,H6: 7.. / A6 = 7 => 0 pairs (X) / H6 = 7 => 19 pairs (_) C5,C7: 7.. / C5 = 7 => 17 pairs (_) / C7 = 7 => 0 pairs (X) E1,F2: 9.. / E1 = 9 => 0 pairs (X) / F2 = 9 => 0 pairs (_) E5,F6: 9.. / E5 = 9 => 0 pairs (*) / F6 = 9 => 0 pairs (X) I4,G6: 9.. / I4 = 9 => 0 pairs (X) / G6 = 9 => 0 pairs (_) A7,C7: 9.. / A7 = 9 => 0 pairs (X) / C7 = 9 => 17 pairs (_) G8,H8: 9.. / G8 = 9 => 0 pairs (X) / H8 = 9 => 0 pairs (_) F2,I2: 9.. / F2 = 9 => 0 pairs (*) / I2 = 9 => 0 pairs (X) A4,I4: 9.. / A4 = 9 => 0 pairs (*) / I4 = 9 => 0 pairs (X) F6,G6: 9.. / F6 = 9 => 0 pairs (X) / G6 = 9 => 0 pairs (_) C5,C7: 9.. / C5 = 9 => 0 pairs (X) / C7 = 9 => 17 pairs (_) E1,E5: 9.. / E1 = 9 => 0 pairs (X) / E5 = 9 => 0 pairs (_) F2,F6: 9.. / F2 = 9 => 0 pairs (*) / F6 = 9 => 0 pairs (X) G6,G8: 9.. / G6 = 9 => 0 pairs (*) / G8 = 9 => 0 pairs (X) H1,H8: 9.. / H1 = 9 => 0 pairs (X) / H8 = 9 => 0 pairs (_) * DURATION: 0:02:06.169345 START: 10:28:24.016261 END: 10:30:30.185606 2017-05-04 * CP COUNT: (47) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A6,A7,A9,C2,C5,C7,C9,D5,D8,E5,E8,F2,F6,G6,G8,H1,H5,H6,H8,I4) * 27.1.48..81..7.43..94..871..3174528..8...35.1.5281...3.2.461358148..2..7.6.987124 * PAIR C2: 5,6 BLK 1 C1: 5,6,3 # reduction candidate for 5,6 C1: 5,6 => SOLVED * 275134869816579432394628715931745286687293541452816973729461358148352697563987124 C1: 3 => CTR * 2731.48..816.7943.594638712.3174528.68...35.1.5281...3.2.461358148..2..7.6.987124 * PAIR C2: 5,6 ROW 2 D2: 5,6,2 # reduction candidate for 5,6 D2: 5,6 => SOLVED * 275134869816579432394628715931745286687293541452816973729461358148352697563987124 D2: 2 => CTR * 27.1.48..81.27.43..94..8712.3174528..8.6235.1.528196.3.2.461358148..2967.6.987124 I2: 5,6,2,9 # reduction candidate for 5,6 I2: 5,6 => CTR * 27.1.48..81.27943..946.871..3174528..8...35.1.5281...3.2.461358148..2..7.6.987124 I2: 2,9 # 23 pairs * PAIR A3: 3,5 BLK 1 C1: 3,5,6 # reduction candidate for 3,5 C1: 3,5 => SOLVED * 275134869816579432394628715931745286687293541452816973729461358148352697563987124 C1: 6 => CTR * 276134895815.7943.394..871..31745289.8..935.1.52816..3.2.461358148..2..7.6.987124 * PAIR A3: 3,5 ROW 3 D3: 3,5,2,6 # reduction candidate for 3,5 D3: 3,5 => CTR * 27.1.48..81..7.43..94..8716631745289.8.6235.1.52819..3.2.461358148..2..7.6.987124 D3: 2,6 => SOLVED * 275134869816579432394628715931745286687293541452816973729461358148352697563987124 E3: 3,5,2 # reduction candidate for 3,5 E3: 3,5 => CTR * 27.1948..81..7.43..94..871..3174528..8..235.1.528196.3.2.461358148..2967.6.987124 E3: 2 => SOLVED * 275134869816579432394628715931745286687293541452816973729461358148352697563987124 * PAIR F2: 6,9 ROW 2 I2: 6,9,2,5 # reduction candidate for 6,9 I2: 6,9 => CTR * 27.1.48..81.27.43..94..8712.3174528..8.6235.1.528196.3.2.461358148..2967.6.987124 I2: 2,5 => SOLVED * 275134869816579432394628715931745286687293541452816973729461358148352697563987124 * PAIR H1: 6,9 BLK 3 I1: 6,9,5 # reduction candidate for 6,9 I1: 6,9 => SOLVED * 275134869816579432394628715931745286687293541452816973729461358148352697563987124 I1: 5 # 25 pairs I2: 6,9,2,5 # reduction candidate for 6,9 I2: 6,9 => CTR * 27.1.48..81.27.43..94..8712.3174528..8.6235.1.528196.3.2.461358148..2967.6.987124 I2: 2,5 => SOLVED * 275134869816579432394628715931745286687293541452816973729461358148352697563987124 * PAIR A4: 6,9 BLK 4 A5: 6,9,4,7 # reduction candidate for 6,9 A5: 4,7 => CTR * 27.1.48..81..7.43..94..871.631745289.896235.1.52819..3.2.461358148..2..7.6.987124 A5: 6,9 # 17 pairs * PAIR C5: 7,9 BLK 4 A5: 7,9,4,6 # reduction candidate for 7,9 A5: 7,9 => CTR * 27.1.48..81..7.43..94..871.631745289.8.623541452819..3.2.461358148..2..7.6.987124 A5: 4,6 # 23 pairs * PAIR A6: 4,7 BLK 4 A5: 4,7,6,9 # reduction candidate for 4,7 A5: 4,7 => CTR * 27.1.48..81..7.43..94..871.631745289.896235.1.52819..3.2.461358148..2..7.6.987124 A5: 6,9 # 17 pairs * PAIR D5: 2,6 COL D D2: 2,6,5 # reduction candidate for 2,6 D2: 2,6 => CTR * 27.1.48..81..7.43..94..8716631745289.8.6235.1.52819..3.2.461358148..2..7.6.987124 D2: 5 => SOLVED * 275134869816579432394628715931745286687293541452816973729461358148352697563987124 D3: 2,6,3,5 # reduction candidate for 2,6 D3: 2,6 => SOLVED * 275134869816579432394628715931745286687293541452816973729461358148352697563987124 D3: 3,5 => CTR * 27.1.48..81..7.43..94..8716631745289.8.6235.1.52819..3.2.461358148..2..7.6.987124 * PAIR I4: 6,9 COL I I1: 6,9,5 # reduction candidate for 6,9 I1: 6,9 => SOLVED * 275134869816579432394628715931745286687293541452816973729461358148352697563987124 I1: 5 # 25 pairs I2: 6,9,2,5 # reduction candidate for 6,9 I2: 6,9 => CTR * 27.1.48..81.27.43..94..8712.3174528..8.6235.1.528196.3.2.461358148..2967.6.987124 I2: 2,5 => SOLVED * 275134869816579432394628715931745286687293541452816973729461358148352697563987124 * PAIR H5: 4,7 ROW 5 A5: 4,7,6,9 # reduction candidate for 4,7 A5: 4,7 => CTR * 27.1.48..81..7.43..94..871.631745289.896235.1.52819..3.2.461358148..2..7.6.987124 A5: 6,9 # 17 pairs * PAIR A7: 7,9 COL A A5: 7,9,4,6 # reduction candidate for 7,9 A5: 7,9 => CTR * 27.1.48..81..7.43..94..871.631745289.8.623541452819..3.2.461358148..2..7.6.987124 A5: 4,6 # 23 pairs * PAIR C9: 3,5 COL C C1: 3,5,6 # reduction candidate for 3,5 C1: 3,5 => SOLVED * 275134869816579432394628715931745286687293541452816973729461358148352697563987124 C1: 6 => CTR * 276134895815.7943.394..871..31745289.8..935.1.52816..3.2.461358148..2..7.6.987124 * PAIR D8: 3,5 COL D D3: 3,5,2,6 # reduction candidate for 3,5 D3: 3,5 => CTR * 27.1.48..81..7.43..94..8716631745289.8.6235.1.52819..3.2.461358148..2..7.6.987124 D3: 2,6 => SOLVED * 275134869816579432394628715931745286687293541452816973729461358148352697563987124 * PAIR E8: 3,5 COL E E1: 3,5,9 # reduction candidate for 3,5 E1: 3,5 => SOLVED * 275134869816579432394628715931745286687293541452816973729461358148352697563987124 E1: 9 => CTR * 273194865816.7.43..94..871..3174528..8...35.1.5281...3.2.461358148..2..7.6.987124 E3: 3,5,2 # reduction candidate for 3,5 E3: 3,5 => CTR * 27.1948..81..7.43..94..871..3174528..8..235.1.528196.3.2.461358148..2967.6.987124 E3: 2 => SOLVED * 275134869816579432394628715931745286687293541452816973729461358148352697563987124 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-224-base-pr-000.dot * REASONING * PRF # C1: 5,6 => SOL * DIS # C1: 3 => CTR => C1: 5,6 * PRF # D2: 5,6 => SOL * DIS # D2: 2 => CTR => D2: 5,6 * DIS # I2: 5,6 => CTR => I2: 2,9 * PRF # C1: 3,5 => SOL * DIS # C1: 6 => CTR => C1: 3,5 * DIS # D3: 3,5 => CTR => D3: 2,6 * PRF # D3: 2,6 => SOL * DIS # E3: 3,5 => CTR => E3: 2 * PRF # E3: 2 => SOL * DIS # I2: 6,9 => CTR => I2: 2,5 * PRF # I2: 2,5 => SOL * PRF # I1: 6,9 => SOL * DIS # I2: 6,9 => CTR => I2: 2,5 * PRF # I2: 2,5 => SOL * DIS # A5: 4,7 => CTR => A5: 6,9 * DIS # A5: 7,9 => CTR => A5: 4,6 * DIS # A5: 4,7 => CTR => A5: 6,9 * DIS # D2: 2,6 => CTR => D2: 5 * PRF # D2: 5 => SOL * PRF # D3: 2,6 => SOL * DIS # D3: 3,5 => CTR => D3: 2,6 * PRF # I1: 6,9 => SOL * DIS # I2: 6,9 => CTR => I2: 2,5 * PRF # I2: 2,5 => SOL * DIS # A5: 4,7 => CTR => A5: 6,9 * DIS # A5: 7,9 => CTR => A5: 4,6 * PRF # C1: 3,5 => SOL * DIS # C1: 6 => CTR => C1: 3,5 * DIS # D3: 3,5 => CTR => D3: 2,6 * PRF # D3: 2,6 => SOL * PRF # E1: 3,5 => SOL * DIS # E1: 9 => CTR => E1: 3,5 * DIS # E3: 3,5 => CTR => E3: 2 * PRF # E3: 2 => SOL * CNT 36 HDP CHAINS / 44 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A6,A7,A9,C2,C5,C7,C9,D5,D8,E5,E8,F2,F6,G6,G8,H1,H5,H6,H8,I4) * 27.1.48..81..7.43..94..871..3174528..8...35.1.5281...3.2.461358148..2..7.6.987124 * PAIR C2: 5,6 BLK 1 C1: 5,6,3 # reduction candidate for 5,6 C1: 5,6 => SOLVED * 275134869816579432394628715931745286687293541452816973729461358148352697563987124 * DURATION: 0:00:02.678759 START: 10:31:43.810867 END: 10:31:46.489626 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-224-base-pr-001.dot * REASONING * PRF # C1: 5,6 => SOL * STA C1: 5,6 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 224 solution: 275134869816579432394628715931745286687293541452816973729461358148352697563987124 info: 2007 FNBTHWX S8.f 40363 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 275134869816579432394628715931745286687293541452816973729461358148352697563987124 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 # C1: 5,6 => SOL * DIS # C1: 3 => CTR => C1: 5,6 * PRF # D2: 5,6 => SOL * DIS # D2: 2 => CTR => D2: 5,6 * DIS # I2: 5,6 => CTR => I2: 2,9 * INC # I2: 2,9 => UNS * PRF # C1: 3,5 => SOL * DIS # C1: 6 => CTR => C1: 3,5 * DIS # D3: 3,5 => CTR => D3: 2,6 * PRF # D3: 2,6 => SOL * DIS # E3: 3,5 => CTR => E3: 2 * PRF # E3: 2 => SOL * DIS # I2: 6,9 => CTR => I2: 2,5 * PRF # I2: 2,5 => SOL * PRF # I1: 6,9 => SOL * INC # I1: 5 => UNS * DIS # I2: 6,9 => CTR => I2: 2,5 * PRF # I2: 2,5 => SOL * INC # A5: 6,9 => UNS * DIS # A5: 4,7 => CTR => A5: 6,9 * DIS # A5: 7,9 => CTR => A5: 4,6 * INC # A5: 4,6 => UNS * DIS # A5: 4,7 => CTR => A5: 6,9 * INC # A5: 6,9 => UNS * DIS # D2: 2,6 => CTR => D2: 5 * PRF # D2: 5 => SOL * PRF # D3: 2,6 => SOL * DIS # D3: 3,5 => CTR => D3: 2,6 * PRF # I1: 6,9 => SOL * INC # I1: 5 => UNS * DIS # I2: 6,9 => CTR => I2: 2,5 * PRF # I2: 2,5 => SOL * DIS # A5: 4,7 => CTR => A5: 6,9 * INC # A5: 6,9 => UNS * DIS # A5: 7,9 => CTR => A5: 4,6 * INC # A5: 4,6 => UNS * PRF # C1: 3,5 => SOL * DIS # C1: 6 => CTR => C1: 3,5 * DIS # D3: 3,5 => CTR => D3: 2,6 * PRF # D3: 2,6 => SOL * PRF # E1: 3,5 => SOL * DIS # E1: 9 => CTR => E1: 3,5 * DIS # E3: 3,5 => CTR => E3: 2 * PRF # E3: 2 => SOL * CNT 44 HDP CHAINS / 44 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C1: 5,6 => SOL * STA C1: 5,6 * CNT 1 HDP CHAINS / 1 HYP OPENED