Analysis of xx-top500-356-base.sdk
Contents
Original Sudoku
level: medium
position: 8....1......4..5.....3.....1.....4.....5..2......3.....25....3..4.....7.....8...6 initial
Autosolve
position: 85..2134.2.34.85.14..3.5.281328..4.578.54.2135.4132.8..25.1.834.48.531723..284956 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 7,9 => CTR => C1: 6 * PRF # C1: 6 => SOL * PRF # D1: 7,9 => SOL * DIS # D1: 6 => CTR => D1: 7,9 * DIS # C3: 6,7 => CTR => C3: 1,9 * DIS # C3: 6,9 => CTR => C3: 1,7 * DIS # F4: 6,9 => CTR => F4: 7 * DIS # F7: 7 => CTR => F7: 6,9 * DIS # F4: 6,9 => CTR => F4: 7 * DIS # D7: 6,9 => CTR => D7: 7 * DIS # C3: 6,9 => CTR => C3: 1,7 * DIS # D7: 6,9 => CTR => D7: 7 * DIS # D1: 7 => CTR => D1: 6,9 * CNT 13 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 7,9 => CTR => C1: 6 * PRF C1: 6 => SOL * STA C1: 6 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 8....1......4..5.....3.....1.....4.....5..2......3.....25....3..4.....7.....8...6 | initial |
| 85..2134.2.34.85.14..3.5.281328..4.578.54.2135.4132.8..25.1.834.48.531723..284956 | autosolve |
| 856921347273468591491375628132897465789546213564132789625719834948653172317284956 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) I1: 7,9 H2: 6,9 G3: 6,7 C5: 6,9 B6: 6,9 F5: 6,9 H4: 6,9 G6: 6,7 I6: 7,9 A7: 6,9 A8: 6,9 B9: 1,7 C9: 1,7 D8: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B3,C3: 1.. / B3 = 1 => 17 pairs (_) / C3 = 1 => 13 pairs (_) B9,C9: 1.. / B9 = 1 => 13 pairs (_) / C9 = 1 => 17 pairs (_) B3,B9: 1.. / B3 = 1 => 17 pairs (_) / B9 = 1 => 13 pairs (_) C3,C9: 1.. / C3 = 1 => 13 pairs (_) / C9 = 1 => 17 pairs (_) H2,G3: 6.. / H2 = 6 => 0 pairs (X) / G3 = 6 => 0 pairs (_) C5,B6: 6.. / C5 = 6 => 0 pairs (X) / B6 = 6 => 0 pairs (_) H4,G6: 6.. / H4 = 6 => 0 pairs (*) / G6 = 6 => 0 pairs (X) A7,A8: 6.. / A7 = 6 => 0 pairs (*) / A8 = 6 => 0 pairs (X) C1,D1: 6.. / C1 = 6 => 0 pairs (*) / D1 = 6 => 0 pairs (X) C5,F5: 6.. / C5 = 6 => 0 pairs (X) / F5 = 6 => 0 pairs (_) B6,G6: 6.. / B6 = 6 => 0 pairs (*) / G6 = 6 => 0 pairs (X) A8,D8: 6.. / A8 = 6 => 15 pairs (_) / D8 = 6 => 0 pairs (*) G3,G6: 6.. / G3 = 6 => 0 pairs (*) / G6 = 6 => 0 pairs (X) H2,H4: 6.. / H2 = 6 => 0 pairs (X) / H4 = 6 => 0 pairs (_) I1,G3: 7.. / I1 = 7 => 0 pairs (*) / G3 = 7 => 0 pairs (X) E4,F4: 7.. / E4 = 7 => 0 pairs (X) / F4 = 7 => 17 pairs (_) G6,I6: 7.. / G6 = 7 => 0 pairs (*) / I6 = 7 => 0 pairs (X) B9,C9: 7.. / B9 = 7 => 17 pairs (_) / C9 = 7 => 13 pairs (_) D7,F7: 7.. / D7 = 7 => 17 pairs (_) / F7 = 7 => 0 pairs (X) B2,E2: 7.. / B2 = 7 => 15 pairs (_) / E2 = 7 => 20 pairs (_) D1,D7: 7.. / D1 = 7 => 0 pairs (X) / D7 = 7 => 17 pairs (_) F4,F7: 7.. / F4 = 7 => 17 pairs (_) / F7 = 7 => 0 pairs (X) G3,G6: 7.. / G3 = 7 => 0 pairs (X) / G6 = 7 => 0 pairs (_) I1,I6: 7.. / I1 = 7 => 0 pairs (*) / I6 = 7 => 0 pairs (X) I1,H2: 9.. / I1 = 9 => 0 pairs (X) / H2 = 9 => 0 pairs (_) C5,B6: 9.. / C5 = 9 => 0 pairs (*) / B6 = 9 => 0 pairs (X) H4,I6: 9.. / H4 = 9 => 0 pairs (X) / I6 = 9 => 0 pairs (_) A7,A8: 9.. / A7 = 9 => 15 pairs (_) / A8 = 9 => 0 pairs (*) C5,F5: 9.. / C5 = 9 => 0 pairs (*) / F5 = 9 => 0 pairs (X) B6,I6: 9.. / B6 = 9 => 0 pairs (X) / I6 = 9 => 0 pairs (_) A8,D8: 9.. / A8 = 9 => 0 pairs (*) / D8 = 9 => 0 pairs (X) H2,H4: 9.. / H2 = 9 => 0 pairs (*) / H4 = 9 => 0 pairs (X) I1,I6: 9.. / I1 = 9 => 0 pairs (X) / I6 = 9 => 0 pairs (_) * DURATION: 0:01:03.171936 START: 14:55:10.601952 END: 14:56:13.773888 2017-05-04 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A8,B6,B9,C5,C9,D8,F5,G3,G6,H2,H4,I1,I6) * 85..2134.2.34.85.14..3.5.281328..4.578.54.2135.4132.8..25.1.834.48.531723..284956 * PAIR I1: 7,9 ROW 1 C1: 7,9,6 # reduction candidate for 7,9 C1: 7,9 => CTR * 8576213492634.85.14..3.5.28132867495786549213594132687.257168346489531723..284956 C1: 6 => SOLVED * 856921347273468591491375628132897465789546213564132789625719834948653172317284956 D1: 7,9,6 # reduction candidate for 7,9 D1: 7,9 => SOLVED * 856921347273468591491375628132897465789546213564132789625719834948653172317284956 D1: 6 => CTR * 8576213492634.85.14..3.5.28132867495786549213594132687.257168346489531723..284956 * PAIR H2: 6,9 ROW 2 B2: 6,9,7 # reduction candidate for 6,9 B2: 6,9 # 20 pairs E2: 6,9,7 # reduction candidate for 6,9 E2: 6,9 # 15 pairs * PAIR G3: 6,7 ROW 3 B3: 6,7,1,9 # reduction candidate for 6,7 B3: 6,7 # 18 pairs C3: 6,7,1,9 # reduction candidate for 6,7 C3: 6,7 => CTR * 85..2134.2.34785.141.395.28132867495786549213594132.8..25.1.834.48.53172371284956 C3: 1,9 # 15 pairs E3: 6,7,9 # reduction candidate for 6,7 E3: 6,7 # 19 pairs * PAIR C5: 6,9 COL C C1: 6,9,7 # reduction candidate for 6,9 C1: 6,9 # 16 pairs C3: 6,9,1,7 # reduction candidate for 6,9 C3: 6,9 => CTR * 8576213492.347856141639572813286749578954.2135.4132.8..25.1.834.48.53172371284956 C3: 1,7 # 16 pairs * PAIR B6: 6,9 COL B B2: 6,9,7 # reduction candidate for 6,9 B2: 6,9 # 20 pairs B3: 6,9,1,7 # reduction candidate for 6,9 B3: 6,9 # 15 pairs * PAIR F5: 6,9 BLK 5 E4: 6,9,7 # reduction candidate for 6,9 E4: 6,9 # 17 pairs F4: 6,9,7 # reduction candidate for 6,9 F4: 6,9 => CTR * 85.7213492734985614..36572813287649578654.2135.4132.8..25.17834.48.531723..284956 F4: 7 # 17 pairs * PAIR F5: 6,9 COL F F7: 6,9,7 # reduction candidate for 6,9 F7: 7 => CTR * 85.7213492734985614..36572813287649578654.2135.4132.8..25.17834.48.531723..284956 F7: 6,9 # 17 pairs * PAIR H4: 6,9 ROW 4 E4: 6,9,7 # reduction candidate for 6,9 E4: 6,9 # 17 pairs F4: 6,9,7 # reduction candidate for 6,9 F4: 6,9 => CTR * 85.7213492734985614..36572813287649578654.2135.4132.8..25.17834.48.531723..284956 F4: 7 # 17 pairs * PAIR A7: 6,9 ROW 7 D7: 6,9,7 # reduction candidate for 6,9 D7: 6,9 => CTR * 85.7213492734985614..36572813287649578654.2135.4132.8..25.1.834.48.531723..284956 D7: 7 # 17 pairs F7: 6,9,7 # reduction candidate for 6,9 F7: 6,9 # 17 pairs * PAIR B9: 1,7 COL B B3: 1,7,6,9 # reduction candidate for 1,7 B3: 1,7 # 20 pairs B3: 6,9 # 15 pairs * PAIR C9: 1,7 COL C C3: 1,7,6,9 # reduction candidate for 1,7 C3: 6,9 => CTR * 8576213492.347856141639572813286749578954.2135.4132.8..25.1.834.48.53172371284956 C3: 1,7 # 16 pairs * PAIR D8: 6,9 BLK 8 D7: 6,9,7 # reduction candidate for 6,9 D7: 6,9 => CTR * 85.7213492734985614..36572813287649578654.2135.4132.8..25.1.834.48.531723..284956 D7: 7 # 17 pairs F7: 6,9,7 # reduction candidate for 6,9 F7: 6,9 # 17 pairs * PAIR D8: 6,9 COL D D1: 6,9,7 # reduction candidate for 6,9 D1: 7 => CTR * 8567213492734.85.14..3.5.281328..4.578.54.2135.4132.8..25.1.834.48.531723..284956 D1: 6,9 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-356-base-pr-000.dot * REASONING * DIS # C1: 7,9 => CTR => C1: 6 * PRF # C1: 6 => SOL * PRF # D1: 7,9 => SOL * DIS # D1: 6 => CTR => D1: 7,9 * DIS # C3: 6,7 => CTR => C3: 1,9 * DIS # C3: 6,9 => CTR => C3: 1,7 * DIS # F4: 6,9 => CTR => F4: 7 * DIS # F7: 7 => CTR => F7: 6,9 * DIS # F4: 6,9 => CTR => F4: 7 * DIS # D7: 6,9 => CTR => D7: 7 * DIS # C3: 6,9 => CTR => C3: 1,7 * DIS # D7: 6,9 => CTR => D7: 7 * DIS # D1: 7 => CTR => D1: 6,9 * CNT 13 HDP CHAINS / 35 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A8,B6,B9,C5,C9,D8,F5,G3,G6,H2,H4,I1,I6) * 85..2134.2.34.85.14..3.5.281328..4.578.54.2135.4132.8..25.1.834.48.531723..284956 * PAIR I1: 7,9 ROW 1 C1: 7,9,6 # reduction candidate for 7,9 C1: 7,9 => CTR * 8576213492634.85.14..3.5.28132867495786549213594132687.257168346489531723..284956 C1: 6 => SOLVED * 856921347273468591491375628132897465789546213564132789625719834948653172317284956 * DURATION: 0:00:01.846556 START: 14:56:53.156783 END: 14:56:55.003339 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-356-base-pr-001.dot * REASONING * DIS # C1: 7,9 => CTR => C1: 6 * PRF C1: 6 => SOL * STA C1: 6 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 356 solution: 856921347273468591491375628132897465789546213564132789625719834948653172317284956 info: 4889 FNBWX S8.f 45814 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 856921347273468591491375628132897465789546213564132789625719834948653172317284956 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:
* DIS # C1: 7,9 => CTR => C1: 6 * PRF # C1: 6 => SOL * PRF # D1: 7,9 => SOL * DIS # D1: 6 => CTR => D1: 7,9 * INC # B2: 6,9 => UNS * INC # E2: 6,9 => UNS * INC # B3: 6,7 => UNS * DIS # C3: 6,7 => CTR => C3: 1,9 * INC # C3: 1,9 => UNS * INC # E3: 6,7 => UNS * INC # C1: 6,9 => UNS * DIS # C3: 6,9 => CTR => C3: 1,7 * INC # C3: 1,7 => UNS * INC # B2: 6,9 => UNS * INC # B3: 6,9 => UNS * INC # E4: 6,9 => UNS * DIS # F4: 6,9 => CTR => F4: 7 * INC # F4: 7 => UNS * INC # F7: 6,9 => UNS * DIS # F7: 7 => CTR => F7: 6,9 * INC # E4: 6,9 => UNS * DIS # F4: 6,9 => CTR => F4: 7 * INC # F4: 7 => UNS * DIS # D7: 6,9 => CTR => D7: 7 * INC # D7: 7 => UNS * INC # F7: 6,9 => UNS * INC # B3: 1,7 => UNS * INC # B3: 6,9 => UNS * INC # C3: 1,7 => UNS * DIS # C3: 6,9 => CTR => C3: 1,7 * DIS # D7: 6,9 => CTR => D7: 7 * INC # D7: 7 => UNS * INC # F7: 6,9 => UNS * INC # D1: 6,9 => UNS * DIS # D1: 7 => CTR => D1: 6,9 * CNT 35 HDP CHAINS / 35 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C1: 7,9 => CTR => C1: 6 * PRF C1: 6 => SOL * STA C1: 6 * CNT 2 HDP CHAINS / 1 HYP OPENED