Analysis of zz-www.sudokuwiki.org-0018-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=18
level: medium
position: .3.96..1.9..........74.8..5..4.5.68...........69.4.3..4..3.57..........4.7..94.2. initial
Autosolve
position: .3.96.41.94.5.......74.8..5..4.5.68........4..69.4.3..4..3.57..........4.7..94.2. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A3: 1,2 => SOL * DIS # F4: 2,7 => CTR => F4: 1,3,9 * DIS # I2: 2,8 => CTR => I2: 3,6,7 * DIS # F4: 1,2 => CTR => F4: 3,7,9 * PRF # B8: 9 => SOL * PRF # I7: 6,9 => SOL * CNT 6 HDP CHAINS / 45 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A3: 1,2 => SOL * STA A3: 1,2 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .3.96..1.9..........74.8..5..4.5.68...........69.4.3..4..3.57..........4.7..94.2. | initial |
| .3.96.41.94.5.......74.8..5..4.5.68........4..69.4.3..4..3.57..........4.7..94.2. | autosolve |
| 835967412946512873127438965714253689358679241269841357481325796592786134673194528 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) B3: 1,2 F1: 2,7 G2: 2,8 G3: 2,9 B4: 1,2 B5: 5,8 H6: 5,7 B7: 8,9 H7: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B3,B4: 1.. / B3 = 1 => 10 pairs (_) / B4 = 1 => 19 pairs (_) C7,E7: 2.. / C7 = 2 => 11 pairs (_) / E7 = 2 => 11 pairs (_) B3,B4: 2.. / B3 = 2 => 19 pairs (_) / B4 = 2 => 10 pairs (_) H8,I9: 3.. / H8 = 3 => 0 pairs (*) / I9 = 3 => 0 pairs (X) E3,H3: 3.. / E3 = 3 => 15 pairs (_) / H3 = 3 => 10 pairs (_) A4,F4: 3.. / A4 = 3 => 9 pairs (_) / F4 = 3 => 10 pairs (_) I2,I9: 3.. / I2 = 3 => 0 pairs (*) / I9 = 3 => 0 pairs (X) A1,C1: 5.. / A1 = 5 => 12 pairs (_) / C1 = 5 => 10 pairs (_) G5,H6: 5.. / G5 = 5 => 0 pairs (X) / H6 = 5 => 11 pairs (_) A6,H6: 5.. / A6 = 5 => 0 pairs (X) / H6 = 5 => 11 pairs (_) B5,B8: 5.. / B5 = 5 => 11 pairs (_) / B8 = 5 => 12 pairs (_) H6,H8: 5.. / H6 = 5 => 11 pairs (_) / H8 = 5 => 0 pairs (X) C2,A3: 6.. / C2 = 6 => 0 pairs (*) / A3 = 6 => 0 pairs (X) D5,F5: 6.. / D5 = 6 => 10 pairs (_) / F5 = 6 => 12 pairs (_) A3,H3: 6.. / A3 = 6 => 10 pairs (_) / H3 = 6 => 0 pairs (*) F5,F8: 6.. / F5 = 6 => 12 pairs (_) / F8 = 6 => 10 pairs (_) F1,I1: 7.. / F1 = 7 => 10 pairs (_) / I1 = 7 => 0 pairs (X) H2,H6: 7.. / H2 = 7 => 11 pairs (_) / H6 = 7 => 0 pairs (X) A6,D6: 8.. / A6 = 8 => 15 pairs (_) / D6 = 8 => 10 pairs (_) G3,H3: 9.. / G3 = 9 => 9 pairs (_) / H3 = 9 => 0 pairs (X) F4,F5: 9.. / F4 = 9 => 9 pairs (_) / F5 = 9 => 10 pairs (_) B7,B8: 9.. / B7 = 9 => 12 pairs (_) / B8 = 9 => 0 pairs (*) F4,I4: 9.. / F4 = 9 => 9 pairs (_) / I4 = 9 => 10 pairs (_) * DURATION: 0:00:31.256819 START: 03:44:16.312221 END: 03:44:47.569040 2017-05-01 * CP COUNT: (23) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B4,B5,B7,F1,G2,G3,H6,H7) * .3.96.41.94.5.......74.8..5..4.5.68........4..69.4.3..4..3.57..........4.7..94.2. * PAIR B3: 1,2 BLK 1 C2: 1,2,6,8 # reduction candidate for 1,2 C2: 1,2 # 19 pairs A3: 1,2,6 # reduction candidate for 1,2 A3: 1,2 => SOLVED * 835967412946512873127438965714253689358679241269841357481325796592786134673194528 A3: 6 # 10 pairs * PAIR B3: 1,2 ROW 3 E3: 1,2,3 # reduction candidate for 1,2 E3: 3 # 15 pairs E3: 1,2 # 10 pairs * PAIR F1: 2,7 BLK 2 E2: 2,7,1,3 # reduction candidate for 2,7 E2: 2,7 # 12 pairs F2: 2,7,1,3 # reduction candidate for 2,7 F2: 2,7 # 18 pairs * PAIR F1: 2,7 ROW 1 I1: 2,7,8 # reduction candidate for 2,7 I1: 8 # 18 pairs I1: 2,7 # 17 pairs * PAIR F1: 2,7 COL F F4: 2,7,1,3,9 # reduction candidate for 2,7 F4: 2,7 => CTR * .3.96.41.9415.327.627418935314.5.689...63914..6984135.4.23857.11.3..6.94.76194.23 F4: 1,3,9 # 9 pairs F5: 2,7,1,3,6,9 # reduction candidate for 2,7 F5: 2,7 # 20 pairs F6: 2,7,1 # reduction candidate for 2,7 F6: 2,7 # 12 pairs F8: 2,7,1,6 # reduction candidate for 2,7 F8: 2,7 # 16 pairs * PAIR G2: 2,8 BLK 3 I1: 2,8,7 # reduction candidate for 2,8 I1: 2,8 # 10 pairs I2: 2,8,3,6,7 # reduction candidate for 2,8 I2: 2,8 => CTR * .3.96.41.94.5.......74.89.5..4.5.68..5.....4..69.4.37.48.3.5796.9.....54.7..94.23 I2: 3,6,7 # 9 pairs * PAIR G2: 2,8 ROW 2 C2: 2,8,1,6 # reduction candidate for 2,8 C2: 1,6 # 19 pairs C2: 2,8 # 11 pairs * PAIR G3: 2,9 COL G G5: 2,9,1,5 # reduction candidate for 2,9 G5: 2,9 # 24 pairs G5: 1,5 # 11 pairs * PAIR B4: 1,2 BLK 4 A4: 1,2,3,7 # reduction candidate for 1,2 A4: 1,2 # 12 pairs A5: 1,2,3,5,7,8 # reduction candidate for 1,2 A5: 1,2 # 11 pairs C5: 1,2,3,5,8 # reduction candidate for 1,2 C5: 1,2 # 11 pairs A6: 1,2,5,7,8 # reduction candidate for 1,2 A6: 1,2 # 14 pairs * PAIR B4: 1,2 ROW 4 D4: 1,2,7 # reduction candidate for 1,2 D4: 1,2 # 12 pairs F4: 1,2,3,7,9 # reduction candidate for 1,2 F4: 1,2 => CTR * .3.96741894.5.3..66.74.89353.475.689...63914..6984135.4923857611.3276.94.76194.23 F4: 3,7,9 # 9 pairs I4: 1,2,7,9 # reduction candidate for 1,2 I4: 1,2 # 11 pairs * PAIR B5: 5,8 BLK 4 A5: 5,8,1,2,3,7 # reduction candidate for 5,8 A5: 5,8 # 13 pairs C5: 5,8,1,2,3 # reduction candidate for 5,8 C5: 5,8 # 13 pairs A6: 5,8,1,2,7 # reduction candidate for 5,8 A6: 5,8 # 10 pairs * PAIR B5: 5,8 COL B B8: 5,8,9 # reduction candidate for 5,8 B8: 9 => SOLVED * 835967412946512873127438965714253689358679241269841357481325796592786134673194528 B8: 5,8 # 12 pairs * PAIR H6: 5,7 ROW 6 A6: 5,7,1,2,8 # reduction candidate for 5,7 A6: 5,7 # 13 pairs A6: 1,2,8 # 11 pairs * PAIR B7: 8,9 BLK 7 B8: 8,9,5 # reduction candidate for 8,9 B8: 5 # 12 pairs B8: 8,9 # 11 pairs * PAIR B7: 8,9 ROW 7 I7: 8,9,1,6 # reduction candidate for 8,9 I7: 8,9 # 14 pairs I7: 1,6 # 10 pairs * PAIR H7: 6,9 BLK 9 I7: 6,9,1,8 # reduction candidate for 6,9 I7: 6,9 => SOLVED * 835967412946512873127438965714253689358679241269841357481325796592786134673194528 I7: 1,8 # 12 pairs H8: 6,9,3,5 # reduction candidate for 6,9 H8: 6,9 # 12 pairs * PAIR H7: 6,9 COL H H3: 6,9,3 # reduction candidate for 6,9 H3: 6,9 # 15 pairs H3: 3 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0018-base-pr-000.dot * REASONING * PRF # A3: 1,2 => SOL * DIS # F4: 2,7 => CTR => F4: 1,3,9 * DIS # I2: 2,8 => CTR => I2: 3,6,7 * DIS # F4: 1,2 => CTR => F4: 3,7,9 * PRF # B8: 9 => SOL * PRF # I7: 6,9 => SOL * CNT 6 HDP CHAINS / 45 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B4,B5,B7,F1,G2,G3,H6,H7) * .3.96.41.94.5.......74.8..5..4.5.68........4..69.4.3..4..3.57..........4.7..94.2. * PAIR B3: 1,2 BLK 1 C2: 1,2,6,8 # reduction candidate for 1,2 C2: 1,2 # 19 pairs A3: 1,2,6 # reduction candidate for 1,2 A3: 1,2 => SOLVED * 835967412946512873127438965714253689358679241269841357481325796592786134673194528 * DURATION: 0:00:03.377931 START: 03:45:23.098702 END: 03:45:26.476633 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0018-base-pr-001.dot * REASONING * PRF # A3: 1,2 => SOL * STA A3: 1,2 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=18
Solution
position: 835967412946512873127438965714253689358679241269841357481325796592786134673194528 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: 1,2 => UNS * PRF # A3: 1,2 => SOL * INC # A3: 6 => UNS * INC # E3: 1,2 => UNS * INC # E3: 3 => UNS * INC # E2: 2,7 => UNS * INC # F2: 2,7 => UNS * INC # I1: 2,7 => UNS * INC # I1: 8 => UNS * DIS # F4: 2,7 => CTR => F4: 1,3,9 * INC # F4: 1,3,9 => UNS * INC # F5: 2,7 => UNS * INC # F6: 2,7 => UNS * INC # F8: 2,7 => UNS * INC # I1: 2,8 => UNS * DIS # I2: 2,8 => CTR => I2: 3,6,7 * INC # I2: 3,6,7 => UNS * INC # C2: 2,8 => UNS * INC # C2: 1,6 => UNS * INC # G5: 2,9 => UNS * INC # G5: 1,5 => UNS * INC # A4: 1,2 => UNS * INC # A5: 1,2 => UNS * INC # C5: 1,2 => UNS * INC # A6: 1,2 => UNS * INC # D4: 1,2 => UNS * DIS # F4: 1,2 => CTR => F4: 3,7,9 * INC # F4: 3,7,9 => UNS * INC # I4: 1,2 => UNS * INC # A5: 5,8 => UNS * INC # C5: 5,8 => UNS * INC # A6: 5,8 => UNS * INC # B8: 5,8 => UNS * PRF # B8: 9 => SOL * INC # A6: 5,7 => UNS * INC # A6: 1,2,8 => UNS * INC # B8: 8,9 => UNS * INC # B8: 5 => UNS * INC # I7: 8,9 => UNS * INC # I7: 1,6 => UNS * PRF # I7: 6,9 => SOL * INC # I7: 1,8 => UNS * INC # H8: 6,9 => UNS * INC # H3: 6,9 => UNS * INC # H3: 3 => UNS * CNT 45 HDP CHAINS / 45 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 1,2 => UNS * PRF # A3: 1,2 => SOL * STA A3: 1,2 * CNT 2 HDP CHAINS / 2 HYP OPENED