Analysis of zz-www.sudokuwiki.org-0057-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=57
level: medium
position: .........8.13.....37..2..65..98..2...1..9..8...2..76..24..1..97.....45.6......... initial
Autosolve
position: .........8.13.....374.2..65..98..2...1..9..8..82..76.924..1..97.....45.6......... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 5,6 => CTR => A1: 9 * DIS # B1: 5,6 => CTR => B1: 2,9 * DIS # C5: 5,6 => CTR => C5: 3,7 * DIS # D1: 1,9 => CTR => D1: 4,5,6,7 * DIS # I1: 2,4 => CTR => I1: 1,3,8 * DIS # A4: 4,5 => CTR => A4: 6,7 * DIS # H4: 3,4 => CTR => H4: 1,5,7 * DIS # D9: 5,6 => CTR => D9: 2,7,9 * DIS # F9: 5,6 => CTR => F9: 2,3,8,9 * CNT 9 HDP CHAINS / 55 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 5,6 => CTR => A1: 9 * DIS A1: 9 # B1: 5,6 => CTR => B1: 2 * DIS A1: 9 + B1: 2 # C5: 5,6 => CTR => C5: 3,7 * DIS A1: 9 + B1: 2 + C5: 3,7 # D1: 5,6 => CTR => D1: 1,4,7 * DIS A1: 9 + B1: 2 + C5: 3,7 + D1: 1,4,7 # F3: 1,9 => CTR => F3: 8 * PRF A1: 9 + B1: 2 + C5: 3,7 + D1: 1,4,7 + F3: 8 # H2: 7 => SOL * STA A1: 9 + B1: 2 + C5: 3,7 + D1: 1,4,7 + F3: 8 + H2: 7 * CNT 6 HDP CHAINS / 20 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .........8.13.....37..2..65..98..2...1..9..8...2..76..24..1..97.....45.6......... | initial |
| .........8.13.....374.2..65..98..2...1..9..8..82..76.924..1..97.....45.6......... | autosolve |
| 926475138851369472374128965769841253513296784482537619245613897137984526698752341 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) C1: 5,6 D3: 1,9 I2: 2,4 A6: 4,5 I5: 3,4 B8: 3,9 D7: 5,6 G7: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F4,D6: 1.. / F4 = 1 => 18 pairs (_) / D6 = 1 => 11 pairs (_) A8,A9: 1.. / A8 = 1 => 9 pairs (_) / A9 = 1 => 11 pairs (_) D6,H6: 1.. / D6 = 1 => 11 pairs (_) / H6 = 1 => 18 pairs (_) A8,H8: 1.. / A8 = 1 => 9 pairs (_) / H8 = 1 => 11 pairs (_) B1,B2: 2.. / B1 = 2 => 8 pairs (_) / B2 = 2 => 0 pairs (X) D5,F5: 2.. / D5 = 2 => 0 pairs (*) / F5 = 2 => 0 pairs (X) D8,H8: 2.. / D8 = 2 => 9 pairs (_) / H8 = 2 => 10 pairs (_) F5,F9: 2.. / F5 = 2 => 8 pairs (_) / F9 = 2 => 0 pairs (*) B4,C5: 3.. / B4 = 3 => 11 pairs (_) / C5 = 3 => 16 pairs (_) E6,H6: 3.. / E6 = 3 => 9 pairs (_) / H6 = 3 => 24 pairs (_) H4,H6: 5.. / H4 = 5 => 11 pairs (_) / H6 = 5 => 17 pairs (_) H4,G5: 7.. / H4 = 7 => 22 pairs (_) / G5 = 7 => 10 pairs (_) A4,H4: 7.. / A4 = 7 => 10 pairs (_) / H4 = 7 => 22 pairs (_) F3,G3: 8.. / F3 = 8 => 9 pairs (_) / G3 = 8 => 15 pairs (_) C8,E8: 8.. / C8 = 8 => 9 pairs (_) / E8 = 8 => 9 pairs (_) I1,I9: 8.. / I1 = 8 => 9 pairs (_) / I9 = 8 => 11 pairs (_) * DURATION: 0:00:18.636499 START: 04:26:57.393372 END: 04:27:16.029871 2017-05-01 * CP COUNT: (16) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B8,C1,D3,D7,G7,I2,I5) * .........8.13.....374.2..65..98..2...1..9..8..82..76.924..1..97.....45.6......... * PAIR C1: 5,6 BLK 1 A1: 5,6,9 # reduction candidate for 5,6 A1: 5,6 => CTR * .2.47....8913..47237412..657.98412.3.1329678448253761924.6138971379845269.8752341 A1: 9 # 9 pairs B1: 5,6,2,9 # reduction candidate for 5,6 B1: 5,6 => CTR * 9........8213..97437492..657398..2.1.1..92783.821376.924..1389719...4536..3.89412 B1: 2,9 # 9 pairs B2: 5,6,2,9 # reduction candidate for 5,6 B2: 5,6 # 10 pairs * PAIR C1: 5,6 ROW 1 D1: 5,6,1,4,7,9 # reduction candidate for 5,6 D1: 5,6 # 21 pairs E1: 5,6,4,7,8 # reduction candidate for 5,6 E1: 5,6 # 16 pairs F1: 5,6,1,8,9 # reduction candidate for 5,6 F1: 5,6 # 11 pairs * PAIR C1: 5,6 COL C C5: 5,6,3,7 # reduction candidate for 5,6 C5: 5,6 => CTR * 92.7..3418.134.9.237412..65.398.1254.1..92783.82.3761924..1..9719.2.4536...9.3.2. C5: 3,7 # 11 pairs C7: 5,6,3,8 # reduction candidate for 5,6 C7: 5,6 # 13 pairs C9: 5,6,3,7,8 # reduction candidate for 5,6 C9: 5,6 # 14 pairs * PAIR D3: 1,9 BLK 2 D1: 1,9,4,5,6,7 # reduction candidate for 1,9 D1: 1,9 => CTR * 92.1....88.13..9.2374928165..98.125..1..9278..82.3761924..13897197284536.38759421 D1: 4,5,6,7 # 8 pairs F1: 1,9,5,6,8 # reduction candidate for 1,9 F1: 1,9 # 11 pairs F3: 1,9,8 # reduction candidate for 1,9 F3: 1,9 # 15 pairs * PAIR D3: 1,9 ROW 3 G3: 1,9,8 # reduction candidate for 1,9 G3: 8 # 15 pairs G3: 1,9 # 9 pairs * PAIR I2: 2,4 BLK 3 H1: 2,4,1,3,7 # reduction candidate for 2,4 H1: 2,4 # 13 pairs I1: 2,4,1,3,8 # reduction candidate for 2,4 I1: 2,4 => CTR * .......3.8.13.....37492..65.398..2.1.1..92.83.821376.924..1.397.93.845.6.....3..8 I1: 1,3,8 # 8 pairs H2: 2,4,7 # reduction candidate for 2,4 H2: 2,4 # 10 pairs * PAIR I2: 2,4 COL I I9: 2,4,1,3,8 # reduction candidate for 2,4 I9: 2,4 # 20 pairs I9: 1,3,8 # 9 pairs * PAIR A6: 4,5 BLK 4 A4: 4,5,6,7 # reduction candidate for 4,5 A4: 4,5 => CTR * 9..4.....8.13.59..37492..65539846271.1.592.8.482137659245613897.9...45.6.6..59... A4: 6,7 # 9 pairs A5: 4,5,6,7 # reduction candidate for 4,5 A5: 4,5 # 12 pairs * PAIR A6: 4,5 ROW 6 D6: 4,5,1 # reduction candidate for 4,5 D6: 4,5 # 18 pairs E6: 4,5,3 # reduction candidate for 4,5 E6: 4,5 # 24 pairs H6: 4,5,1,3 # reduction candidate for 4,5 H6: 4,5 # 17 pairs * PAIR I5: 3,4 BLK 6 H4: 3,4,1,5,7 # reduction candidate for 3,4 H4: 3,4 => CTR * ...4.13.88.13..9423749281657.984.231.13.9278448213765924..13897.3.2.45161..7.9423 H4: 1,5,7 # 8 pairs I4: 3,4,1 # reduction candidate for 3,4 I4: 3,4 # 16 pairs G5: 3,4,7 # reduction candidate for 3,4 G5: 3,4 # 22 pairs H6: 3,4,1,5 # reduction candidate for 3,4 H6: 3,4 # 20 pairs * PAIR I5: 3,4 COL I I1: 3,4,1,2,8 # reduction candidate for 3,4 I1: 3,4 # 24 pairs I9: 3,4,1,2,8 # reduction candidate for 3,4 I9: 3,4 # 12 pairs * PAIR B8: 3,9 BLK 7 B9: 3,9,5,6 # reduction candidate for 3,9 B9: 3,9 # 19 pairs B9: 5,6 # 9 pairs * PAIR D7: 5,6 BLK 8 F7: 5,6,3,8 # reduction candidate for 5,6 F7: 5,6 # 10 pairs D9: 5,6,2,7,9 # reduction candidate for 5,6 D9: 5,6 => CTR * ...7.....8.13.....37412..654.98.12...1.29..8..824.761924..1..971..9.4526.....2... D9: 2,7,9 # 8 pairs E9: 5,6,3,7,8 # reduction candidate for 5,6 E9: 5,6 # 14 pairs F9: 5,6,2,3,8,9 # reduction candidate for 5,6 F9: 5,6 => CTR * .2.74.1388.13..4723741289657.9861254.1..92783.82.3761924.61389713.9.4526...2..341 F9: 2,3,8,9 # 8 pairs * PAIR D7: 5,6 ROW 7 C7: 5,6,3,8 # reduction candidate for 5,6 C7: 5,6 # 13 pairs C7: 3,8 # 10 pairs * PAIR D7: 5,6 COL D D1: 5,6,1,4,7,9 # reduction candidate for 5,6 D1: 5,6 # 21 pairs D5: 5,6,2,4 # reduction candidate for 5,6 D5: 5,6 # 10 pairs * PAIR G7: 3,8 BLK 9 G9: 3,8,1,4 # reduction candidate for 3,8 G9: 3,8 # 13 pairs I9: 3,8,1,2,4 # reduction candidate for 3,8 I9: 3,8 # 12 pairs * PAIR G7: 3,8 ROW 7 C7: 3,8,5,6 # reduction candidate for 3,8 C7: 3,8 # 10 pairs F7: 3,8,5,6 # reduction candidate for 3,8 F7: 3,8 # 13 pairs * PAIR G7: 3,8 COL G G1: 3,8,1,4,7,9 # reduction candidate for 3,8 G1: 3,8 # 12 pairs G1: 1,4,7,9 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0057-base-pr-000.dot * REASONING * DIS # A1: 5,6 => CTR => A1: 9 * DIS # B1: 5,6 => CTR => B1: 2,9 * DIS # C5: 5,6 => CTR => C5: 3,7 * DIS # D1: 1,9 => CTR => D1: 4,5,6,7 * DIS # I1: 2,4 => CTR => I1: 1,3,8 * DIS # A4: 4,5 => CTR => A4: 6,7 * DIS # H4: 3,4 => CTR => H4: 1,5,7 * DIS # D9: 5,6 => CTR => D9: 2,7,9 * DIS # F9: 5,6 => CTR => F9: 2,3,8,9 * CNT 9 HDP CHAINS / 55 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B8,C1,D3,D7,G7,I2,I5) * .........8.13.....374.2..65..98..2...1..9..8..82..76.924..1..97.....45.6......... * PAIR C1: 5,6 BLK 1 A1: 5,6,9 # reduction candidate for 5,6 A1: 5,6 => CTR * .2.47....8913..47237412..657.98412.3.1329678448253761924.6138971379845269.8752341 B1: 5,6,2 # reduction candidate for 5,6 B1: 5,6 => CTR * 9........8213..97437492..657398..2.1.1..92783.821376.924..1389719...4536..3.89412 * RESTART * PAIR C1: 5,6 ROW 1 D1: 5,6,1,4,7 # reduction candidate for 5,6 D1: 5,6 # 21 pairs E1: 5,6,4,7,8 # reduction candidate for 5,6 E1: 5,6 # 16 pairs F1: 5,6,1,8 # reduction candidate for 5,6 F1: 5,6 # 11 pairs * PAIR C1: 5,6 COL C C5: 5,6,3,7 # reduction candidate for 5,6 C5: 5,6 => CTR * 92.7..3418.134.9.237412..65.398.1254.1..92783.82.3761924..1..9719.2.4536...9.3.2. C7: 5,6,3,8 # reduction candidate for 5,6 C7: 5,6 # 15 pairs C9: 5,6,3,7,8 # reduction candidate for 5,6 C9: 5,6 # 16 pairs * PAIR RESTART * PAIR C1: 5,6 ROW 1 D1: 5,6,1,4,7 # reduction candidate for 5,6 D1: 5,6 => CTR * 92.......8.13.....37412..654.98.12...1..9..8..824.761924..1..971....45.6......... E1: 5,6,4,7,8 # reduction candidate for 5,6 E1: 5,6 # 19 pairs F1: 5,6,1,8 # reduction candidate for 5,6 F1: 5,6 # 14 pairs * PAIR C1: 5,6 COL C C7: 5,6,3,8 # reduction candidate for 5,6 C7: 5,6 # 15 pairs C9: 5,6,3,7,8 # reduction candidate for 5,6 C9: 5,6 # 16 pairs * PAIR RESTART * PAIR C1: 5,6 ROW 1 E1: 5,6,4,7,8 # reduction candidate for 5,6 E1: 5,6 # 19 pairs F1: 5,6,1,8 # reduction candidate for 5,6 F1: 5,6 # 14 pairs * PAIR C1: 5,6 COL C C7: 5,6,3,8 # reduction candidate for 5,6 C7: 5,6 # 15 pairs C9: 5,6,3,7,8 # reduction candidate for 5,6 C9: 5,6 # 16 pairs * PAIR D3: 1,9 BLK 2 F3: 1,9,8 # reduction candidate for 1,9 F3: 1,9 => CTR * 92.......8.13..9.2374.2.8657.984.25..1369278448215763924.51.3971....45266.527...8 * PAIR I2: 2,4 BLK 3 H2: 2,4,7 # reduction candidate for 2,4 H2: 7 => SOLVED * 926475138851369472374128965769841253513296784482537619245613897137984526698752341 * DURATION: 0:00:17.202300 START: 04:27:51.603247 END: 04:28:08.805547 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0057-base-pr-001.dot * REASONING * DIS # A1: 5,6 => CTR => A1: 9 * DIS A1: 9 # B1: 5,6 => CTR => B1: 2 * DIS A1: 9 + B1: 2 # C5: 5,6 => CTR => C5: 3,7 * DIS A1: 9 + B1: 2 + C5: 3,7 # D1: 5,6 => CTR => D1: 1,4,7 * DIS A1: 9 + B1: 2 + C5: 3,7 + D1: 1,4,7 # F3: 1,9 => CTR => F3: 8 * PRF A1: 9 + B1: 2 + C5: 3,7 + D1: 1,4,7 + F3: 8 # H2: 7 => SOL * STA A1: 9 + B1: 2 + C5: 3,7 + D1: 1,4,7 + F3: 8 + H2: 7 * CNT 6 HDP CHAINS / 20 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=57
Solution
position: 926475138851369472374128965769841253513296784482537619245613897137984526698752341 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 # A1: 5,6 => CTR => A1: 9 * INC # A1: 9 => UNS * DIS # B1: 5,6 => CTR => B1: 2,9 * INC # B1: 2,9 => UNS * INC # B2: 5,6 => UNS * INC # D1: 5,6 => UNS * INC # E1: 5,6 => UNS * INC # F1: 5,6 => UNS * DIS # C5: 5,6 => CTR => C5: 3,7 * INC # C5: 3,7 => UNS * INC # C7: 5,6 => UNS * INC # C9: 5,6 => UNS * DIS # D1: 1,9 => CTR => D1: 4,5,6,7 * INC # D1: 4,5,6,7 => UNS * INC # F1: 1,9 => UNS * INC # F3: 1,9 => UNS * INC # G3: 1,9 => UNS * INC # G3: 8 => UNS * INC # H1: 2,4 => UNS * DIS # I1: 2,4 => CTR => I1: 1,3,8 * INC # I1: 1,3,8 => UNS * INC # H2: 2,4 => UNS * INC # I9: 2,4 => UNS * INC # I9: 1,3,8 => UNS * DIS # A4: 4,5 => CTR => A4: 6,7 * INC # A4: 6,7 => UNS * INC # A5: 4,5 => UNS * INC # D6: 4,5 => UNS * INC # E6: 4,5 => UNS * INC # H6: 4,5 => UNS * DIS # H4: 3,4 => CTR => H4: 1,5,7 * INC # H4: 1,5,7 => UNS * INC # I4: 3,4 => UNS * INC # G5: 3,4 => UNS * INC # H6: 3,4 => UNS * INC # I1: 3,4 => UNS * INC # I9: 3,4 => UNS * INC # B9: 3,9 => UNS * INC # B9: 5,6 => UNS * INC # F7: 5,6 => UNS * DIS # D9: 5,6 => CTR => D9: 2,7,9 * INC # D9: 2,7,9 => UNS * INC # E9: 5,6 => UNS * DIS # F9: 5,6 => CTR => F9: 2,3,8,9 * INC # F9: 2,3,8,9 => UNS * INC # C7: 5,6 => UNS * INC # C7: 3,8 => UNS * INC # D1: 5,6 => UNS * INC # D5: 5,6 => UNS * INC # G9: 3,8 => UNS * INC # I9: 3,8 => UNS * INC # C7: 3,8 => UNS * INC # F7: 3,8 => UNS * INC # G1: 3,8 => UNS * INC # G1: 1,4,7,9 => UNS * CNT 55 HDP CHAINS / 55 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 5,6 => CTR => A1: 9 * DIS A1: 9 # B1: 5,6 => CTR => B1: 2 * INC A1: 9 + B1: 2 # D1: 5,6 => UNS * INC A1: 9 + B1: 2 # E1: 5,6 => UNS * INC A1: 9 + B1: 2 # F1: 5,6 => UNS * DIS A1: 9 + B1: 2 # C5: 5,6 => CTR => C5: 3,7 * INC A1: 9 + B1: 2 + C5: 3,7 # C7: 5,6 => UNS * INC A1: 9 + B1: 2 + C5: 3,7 # C9: 5,6 => UNS * DIS A1: 9 + B1: 2 + C5: 3,7 # D1: 5,6 => CTR => D1: 1,4,7 * INC A1: 9 + B1: 2 + C5: 3,7 + D1: 1,4,7 # E1: 5,6 => UNS * INC A1: 9 + B1: 2 + C5: 3,7 + D1: 1,4,7 # F1: 5,6 => UNS * INC A1: 9 + B1: 2 + C5: 3,7 + D1: 1,4,7 # C7: 5,6 => UNS * INC A1: 9 + B1: 2 + C5: 3,7 + D1: 1,4,7 # C9: 5,6 => UNS * INC A1: 9 + B1: 2 + C5: 3,7 + D1: 1,4,7 # E1: 5,6 => UNS * INC A1: 9 + B1: 2 + C5: 3,7 + D1: 1,4,7 # F1: 5,6 => UNS * INC A1: 9 + B1: 2 + C5: 3,7 + D1: 1,4,7 # C7: 5,6 => UNS * INC A1: 9 + B1: 2 + C5: 3,7 + D1: 1,4,7 # C9: 5,6 => UNS * DIS A1: 9 + B1: 2 + C5: 3,7 + D1: 1,4,7 # F3: 1,9 => CTR => F3: 8 * INC A1: 9 + B1: 2 + C5: 3,7 + D1: 1,4,7 + F3: 8 # H2: 2,4 => UNS * PRF A1: 9 + B1: 2 + C5: 3,7 + D1: 1,4,7 + F3: 8 # H2: 7 => SOL * STA A1: 9 + B1: 2 + C5: 3,7 + D1: 1,4,7 + F3: 8 + H2: 7 * CNT 20 HDP CHAINS / 20 HYP OPENED