Analysis of xx-top500-067-base.sdk
Contents
Original Sudoku
level: medium
position: 3......21.6.7........4......4.6..5......1...3.........8.1..........2.6........74. initial
Autosolve
position: 3.7.6.4212647.1....1.4.2.761426.35.77...142.3.3.27.1.4871.46..24..3276186231..74. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C3: 5,9 => SOL * DIS # E3: 5,9 => CTR => E3: 3,8 * PRF # B5: 5,9 => SOL * DIS # C6: 5,9 => CTR => C6: 6,8 * DIS # F6: 8 => CTR => F6: 5,9 * PRF # D5: 8,9 => SOL * DIS # D5: 5 => CTR => D5: 8,9 * DIS # F6: 8,9 => CTR => F6: 5 * PRF # F6: 5 => SOL * DIS # E3: 8,9 => CTR => E3: 3,5 * DIS # E9: 8,9 => CTR => E9: 5 * PRF # B5: 5,9 => SOL * PRF # C3: 5,9 => SOL * DIS # C6: 5,9 => CTR => C6: 6,8 * DIS # F9: 5,9 => CTR => F9: 8 * PRF # D1: 5,9 => SOL * PRF # G2: 3,9 => SOL * DIS # F9: 5,9 => CTR => F9: 8 * CNT 18 HDP CHAINS / 43 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C3: 5,9 => SOL * STA C3: 5,9 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 3......21.6.7........4......4.6..5......1...3.........8.1..........2.6........74. | initial |
| 3.7.6.4212647.1....1.4.2.761426.35.77...142.3.3.27.1.4871.46..24..3276186231..74. | autosolve |
| 387569421264781935519432876142693587756814293938275164871946352495327618623158749 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) A3: 5,9 H2: 3,5 I2: 5,9 A6: 5,9 E4: 8,9 H4: 8,9 B8: 5,9 C8: 5,9 D7: 5,9 G7: 3,9 H7: 3,5 I9: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,E3: 3.. / E2 = 3 => 0 pairs (X) / E3 = 3 => 16 pairs (_) G7,H7: 3.. / G7 = 3 => 16 pairs (_) / H7 = 3 => 0 pairs (X) E3,G3: 3.. / E3 = 3 => 16 pairs (_) / G3 = 3 => 0 pairs (X) H2,H7: 3.. / H2 = 3 => 16 pairs (_) / H7 = 3 => 0 pairs (X) H2,I2: 5.. / H2 = 5 => 0 pairs (X) / I2 = 5 => 16 pairs (_) D5,F6: 5.. / D5 = 5 => 0 pairs (X) / F6 = 5 => 0 pairs (_) B8,C8: 5.. / B8 = 5 => 16 pairs (_) / C8 = 5 => 15 pairs (_) H7,I9: 5.. / H7 = 5 => 16 pairs (_) / I9 = 5 => 0 pairs (X) D7,H7: 5.. / D7 = 5 => 0 pairs (X) / H7 = 5 => 16 pairs (_) A3,A6: 5.. / A3 = 5 => 0 pairs (*) / A6 = 5 => 0 pairs (X) E3,E9: 5.. / E3 = 5 => 0 pairs (X) / E9 = 5 => 16 pairs (_) H2,H7: 5.. / H2 = 5 => 0 pairs (X) / H7 = 5 => 16 pairs (_) I2,I9: 5.. / I2 = 5 => 16 pairs (_) / I9 = 5 => 0 pairs (X) C5,C6: 6.. / C5 = 6 => 13 pairs (_) / C6 = 6 => 19 pairs (_) H5,H6: 6.. / H5 = 6 => 19 pairs (_) / H6 = 6 => 13 pairs (_) C5,H5: 6.. / C5 = 6 => 13 pairs (_) / H5 = 6 => 19 pairs (_) C6,H6: 6.. / C6 = 6 => 19 pairs (_) / H6 = 6 => 13 pairs (_) B1,C3: 8.. / B1 = 8 => 0 pairs (*) / C3 = 8 => 0 pairs (X) G2,G3: 8.. / G2 = 8 => 14 pairs (_) / G3 = 8 => 0 pairs (*) E9,F9: 8.. / E9 = 8 => 0 pairs (X) / F9 = 8 => 17 pairs (_) E2,G2: 8.. / E2 = 8 => 0 pairs (*) / G2 = 8 => 0 pairs (X) E4,H4: 8.. / E4 = 8 => 18 pairs (_) / H4 = 8 => 18 pairs (_) B1,B5: 8.. / B1 = 8 => 0 pairs (*) / B5 = 8 => 0 pairs (X) D1,D5: 8.. / D1 = 8 => 18 pairs (_) / D5 = 8 => 0 pairs (*) B8,C8: 9.. / B8 = 9 => 15 pairs (_) / C8 = 9 => 16 pairs (_) G7,I9: 9.. / G7 = 9 => 0 pairs (X) / I9 = 9 => 16 pairs (_) E4,H4: 9.. / E4 = 9 => 18 pairs (_) / H4 = 9 => 18 pairs (_) D7,G7: 9.. / D7 = 9 => 16 pairs (_) / G7 = 9 => 0 pairs (X) A3,A6: 9.. / A3 = 9 => 0 pairs (X) / A6 = 9 => 0 pairs (_) I2,I9: 9.. / I2 = 9 => 0 pairs (X) / I9 = 9 => 16 pairs (_) * DURATION: 0:01:15.544092 START: 04:56:47.455392 END: 04:58:02.999484 2017-05-04 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A6,B8,C8,D7,E4,G7,H2,H4,H7,I2,I9) * 3.7.6.4212647.1....1.4.2.761426.35.77...142.3.3.27.1.4871.46..24..3276186231..74. * PAIR A3: 5,9 BLK 1 B1: 5,9,8 # reduction candidate for 5,9 B1: 5,9 # 18 pairs C3: 5,9,8 # reduction candidate for 5,9 C3: 5,9 => SOLVED * 387569421264781935519432876142693587756814293938275164871946352495327618623158749 C3: 8 # 18 pairs * PAIR A3: 5,9 ROW 3 E3: 5,9,3,8 # reduction candidate for 5,9 E3: 5,9 => CTR * 3.786.421264731859.184523761426.35.778591426393.27.1.48715469324..3276186231..745 E3: 3,8 # 16 pairs * PAIR A6: 5,9 BLK 4 B5: 5,9,8 # reduction candidate for 5,9 B5: 5,9 => SOLVED * 387569421264781935519432876142693587756814293938275164871946352495327618623158749 B5: 8 # 18 pairs C5: 5,9,6,8 # reduction candidate for 5,9 C5: 5,9 # 19 pairs C6: 5,9,6,8 # reduction candidate for 5,9 C6: 5,9 => CTR * 3.7.6.4212647.1....184.2.761426.35.7786514293.3.2781648719463524..327618623185749 C6: 6,8 # 13 pairs * PAIR A6: 5,9 ROW 6 F6: 5,9,8 # reduction candidate for 5,9 F6: 8 => CTR * 3.7.6.4212647.1....1.4.2.761426.35.77..5142.3.3.2781.48719463524..327618623185749 F6: 5,9 # 15 pairs * PAIR E4: 8,9 BLK 5 D5: 8,9,5 # reduction candidate for 8,9 D5: 8,9 => SOLVED * 387569421264781935519432876142693587756814293938275164871946352495327618623158749 D5: 5 => CTR * 3.786.421264791835.1843297614268359778951426353.27.1.48719463524..3276186231..749 F6: 8,9,5 # reduction candidate for 8,9 F6: 8,9 => CTR * 3.786.4212647.1835.184329761426.35.778.5142.39352781.48719463524..3276186231..749 F6: 5 => SOLVED * 387569421264781935519432876142693587756814293938275164871946352495327618623158749 * PAIR E4: 8,9 COL E E2: 8,9,3 # reduction candidate for 8,9 E2: 8,9 # 16 pairs E3: 8,9,3,5 # reduction candidate for 8,9 E3: 8,9 => CTR * 3.7.6.421264731859.1.4.23761426.35.77...142.3.3.27.1.48715469324..3276186231..745 E3: 3,5 # 13 pairs E9: 8,9,5 # reduction candidate for 8,9 E9: 8,9 => CTR * 3.7.6.4212647.1....1.4523761426.35.77...142.353.27.1.4871.469324.53276186231.574. E9: 5 # 16 pairs * PAIR H4: 8,9 BLK 6 H5: 8,9,6 # reduction candidate for 8,9 H5: 8,9 # 13 pairs H6: 8,9,6 # reduction candidate for 8,9 H6: 8,9 # 19 pairs * PAIR B8: 5,9 COL B B1: 5,9,8 # reduction candidate for 5,9 B1: 5,9 # 18 pairs B5: 5,9,8 # reduction candidate for 5,9 B5: 5,9 => SOLVED * 387569421264781935519432876142693587756814293938275164871946352495327618623158749 B5: 8 # 18 pairs * PAIR C8: 5,9 COL C C3: 5,9,8 # reduction candidate for 5,9 C3: 5,9 => SOLVED * 387569421264781935519432876142693587756814293938275164871946352495327618623158749 C3: 8 # 18 pairs C5: 5,9,6,8 # reduction candidate for 5,9 C5: 5,9 # 19 pairs C6: 5,9,6,8 # reduction candidate for 5,9 C6: 5,9 => CTR * 3.7.6.4212647.1....184.2.761426.35.7786514293.3.2781648719463524..327618623185749 C6: 6,8 # 13 pairs * PAIR D7: 5,9 BLK 8 E9: 5,9,8 # reduction candidate for 5,9 E9: 5,9 # 17 pairs F9: 5,9,8 # reduction candidate for 5,9 F9: 5,9 => CTR * 3.7.6.4212647.18...1845237614269358778.5142.353.2781.4871946..24..32761862318.74. F9: 8 # 17 pairs * PAIR D7: 5,9 COL D D1: 5,9,8 # reduction candidate for 5,9 D1: 5,9 => SOLVED * 387569421264781935519432876142693587756814293938275164871946352495327618623158749 D1: 8 # 18 pairs D5: 5,9,8 # reduction candidate for 5,9 D5: 5,9 # 18 pairs * PAIR G7: 3,9 COL G G2: 3,9,8 # reduction candidate for 3,9 G2: 3,9 => SOLVED * 387569421264781935519432876142693587756814293938275164871946352495327618623158749 G2: 8 # 14 pairs G3: 3,9,8 # reduction candidate for 3,9 G3: 3,9 # 14 pairs * PAIR I9: 5,9 ROW 9 E9: 5,9,8 # reduction candidate for 5,9 E9: 5,9 # 17 pairs F9: 5,9,8 # reduction candidate for 5,9 F9: 5,9 => CTR * 3.7.6.4212647.18...1845237614269358778.5142.353.2781.4871946..24..32761862318.74. F9: 8 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-067-base-pr-000.dot * REASONING * PRF # C3: 5,9 => SOL * DIS # E3: 5,9 => CTR => E3: 3,8 * PRF # B5: 5,9 => SOL * DIS # C6: 5,9 => CTR => C6: 6,8 * DIS # F6: 8 => CTR => F6: 5,9 * PRF # D5: 8,9 => SOL * DIS # D5: 5 => CTR => D5: 8,9 * DIS # F6: 8,9 => CTR => F6: 5 * PRF # F6: 5 => SOL * DIS # E3: 8,9 => CTR => E3: 3,5 * DIS # E9: 8,9 => CTR => E9: 5 * PRF # B5: 5,9 => SOL * PRF # C3: 5,9 => SOL * DIS # C6: 5,9 => CTR => C6: 6,8 * DIS # F9: 5,9 => CTR => F9: 8 * PRF # D1: 5,9 => SOL * PRF # G2: 3,9 => SOL * DIS # F9: 5,9 => CTR => F9: 8 * CNT 18 HDP CHAINS / 43 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A6,B8,C8,D7,E4,G7,H2,H4,H7,I2,I9) * 3.7.6.4212647.1....1.4.2.761426.35.77...142.3.3.27.1.4871.46..24..3276186231..74. * PAIR A3: 5,9 BLK 1 B1: 5,9,8 # reduction candidate for 5,9 B1: 5,9 # 18 pairs C3: 5,9,8 # reduction candidate for 5,9 C3: 5,9 => SOLVED * 387569421264781935519432876142693587756814293938275164871946352495327618623158749 * DURATION: 0:00:03.712569 START: 04:59:02.911588 END: 04:59:06.624157 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-067-base-pr-001.dot * REASONING * PRF # C3: 5,9 => SOL * STA C3: 5,9 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 067 solution: 387569421264781935519432876142693587756814293938275164871946352495327618623158749 info: 1444 FNBTHWX S8.f 28710 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 387569421264781935519432876142693587756814293938275164871946352495327618623158749 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 # B1: 5,9 => UNS * PRF # C3: 5,9 => SOL * INC # C3: 8 => UNS * DIS # E3: 5,9 => CTR => E3: 3,8 * INC # E3: 3,8 => UNS * PRF # B5: 5,9 => SOL * INC # B5: 8 => UNS * INC # C5: 5,9 => UNS * DIS # C6: 5,9 => CTR => C6: 6,8 * INC # C6: 6,8 => UNS * INC # F6: 5,9 => UNS * DIS # F6: 8 => CTR => F6: 5,9 * PRF # D5: 8,9 => SOL * DIS # D5: 5 => CTR => D5: 8,9 * DIS # F6: 8,9 => CTR => F6: 5 * PRF # F6: 5 => SOL * INC # E2: 8,9 => UNS * DIS # E3: 8,9 => CTR => E3: 3,5 * INC # E3: 3,5 => UNS * DIS # E9: 8,9 => CTR => E9: 5 * INC # E9: 5 => UNS * INC # H5: 8,9 => UNS * INC # H6: 8,9 => UNS * INC # B1: 5,9 => UNS * PRF # B5: 5,9 => SOL * INC # B5: 8 => UNS * PRF # C3: 5,9 => SOL * INC # C3: 8 => UNS * INC # C5: 5,9 => UNS * DIS # C6: 5,9 => CTR => C6: 6,8 * INC # C6: 6,8 => UNS * INC # E9: 5,9 => UNS * DIS # F9: 5,9 => CTR => F9: 8 * INC # F9: 8 => UNS * PRF # D1: 5,9 => SOL * INC # D1: 8 => UNS * INC # D5: 5,9 => UNS * PRF # G2: 3,9 => SOL * INC # G2: 8 => UNS * INC # G3: 3,9 => UNS * INC # E9: 5,9 => UNS * DIS # F9: 5,9 => CTR => F9: 8 * INC # F9: 8 => UNS * CNT 43 HDP CHAINS / 43 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 5,9 => UNS * PRF # C3: 5,9 => SOL * STA C3: 5,9 * CNT 2 HDP CHAINS / 2 HYP OPENED