Analysis of zz-www.sudokuwiki.org-0007-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=7
level: medium
position: ..27.15......3..8..8.9...7..6.1.3.5.5.......8.7.8.5.9..4...9.3..2..6......93.86.. initial
Autosolve
position: ..278156.....3..8..8.9...7..6.1.3.5.5.......8.7.8.5.96.4...9.3..2..6......93.86.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B5: 1 => CTR => B5: 3,9 * DIS # A4: 4,8 => CTR => A4: 2,9 * PRF # E4: 2,4 => SOL * DIS # E5: 2,4 => CTR => E5: 7,9 * DIS # G6: 2,4 => CTR => G6: 1,3 * DIS # E3: 2,4 => CTR => E3: 5 * DIS # A7: 1,7 => CTR => A7: 6,8 * DIS # A8: 1,7 => CTR => A8: 3,8 * DIS # C8: 1,7 => CTR => C8: 3,5,8 * DIS # C7: 1,5 => CTR => C7: 6,7,8 * DIS # B2: 9 => CTR => B2: 1,5 * DIS # E7: 2,5 => CTR => E7: 1,7 * DIS # E9: 2,5 => CTR => E9: 1,4,7 * DIS # D2: 2,5 => CTR => D2: 4,6 * DIS # I8: 4,5 => CTR => I8: 1,7,9 * DIS # G8: 1,4 => CTR => G8: 7,8,9 * DIS # I8: 1,4 => CTR => I8: 5,7,9 * CNT 17 HDP CHAINS / 66 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B5: 1 => CTR => B5: 3,9 * DIS B5: 3,9 # A4: 4,8 => CTR => A4: 2,9 * PRF B5: 3,9 + A4: 2,9 # E4: 2,4 => SOL * STA B5: 3,9 + A4: 2,9 + E4: 2,4 * CNT 3 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..27.15......3..8..8.9...7..6.1.3.5.5.......8.7.8.5.9..4...9.3..2..6......93.86.. | initial |
| ..278156.....3..8..8.9...7..6.1.3.5.5.......8.7.8.5.96.4...9.3..2..6......93.86.. | autosolve |
| 492781563715436289386952471968123754534697128271845396647219835823564917159378642 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) B1: 3,9 C4: 4,8 E6: 2,4 A9: 1,7 B9: 1,5 D7: 2,5 D8: 4,5 F8: 4,7 H8: 1,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E7,E9: 1.. / E7 = 1 => 9 pairs (_) / E9 = 1 => 0 pairs (X) A4,A6: 2.. / A4 = 2 => 13 pairs (_) / A6 = 2 => 16 pairs (_) H5,H9: 2.. / H5 = 2 => 19 pairs (_) / H9 = 2 => 10 pairs (_) I1,I3: 3.. / I1 = 3 => 0 pairs (*) / I3 = 3 => 0 pairs (X) G5,G6: 3.. / G5 = 3 => 12 pairs (_) / G6 = 3 => 13 pairs (_) A8,C8: 3.. / A8 = 3 => 10 pairs (_) / C8 = 3 => 15 pairs (_) B1,B5: 3.. / B1 = 3 => 11 pairs (_) / B5 = 3 => 0 pairs (*) A1,I1: 4.. / A1 = 4 => 10 pairs (_) / I1 = 4 => 14 pairs (_) D2,E3: 5.. / D2 = 5 => 0 pairs (X) / E3 = 5 => 9 pairs (_) C3,E3: 5.. / C3 = 5 => 0 pairs (X) / E3 = 5 => 9 pairs (_) B2,B9: 5.. / B2 = 5 => 14 pairs (_) / B9 = 5 => 9 pairs (_) D5,F5: 6.. / D5 = 6 => 9 pairs (_) / F5 = 6 => 14 pairs (_) A7,C7: 6.. / A7 = 6 => 9 pairs (_) / C7 = 6 => 9 pairs (_) D2,D5: 6.. / D2 = 6 => 14 pairs (_) / D5 = 6 => 9 pairs (_) A2,C2: 7.. / A2 = 7 => 12 pairs (_) / C2 = 7 => 9 pairs (_) F5,F8: 7.. / F5 = 7 => 0 pairs (*) / F8 = 7 => 0 pairs (X) A4,C4: 8.. / A4 = 8 => 0 pairs (X) / C4 = 8 => 8 pairs (_) G7,G8: 8.. / G7 = 8 => 16 pairs (_) / G8 = 8 => 14 pairs (_) A4,B5: 9.. / A4 = 9 => 0 pairs (*) / B5 = 9 => 0 pairs (X) E4,E5: 9.. / E4 = 9 => 11 pairs (_) / E5 = 9 => 0 pairs (*) G8,I8: 9.. / G8 = 9 => 17 pairs (_) / I8 = 9 => 12 pairs (_) A4,E4: 9.. / A4 = 9 => 0 pairs (*) / E4 = 9 => 0 pairs (X) B5,E5: 9.. / B5 = 9 => 11 pairs (_) / E5 = 9 => 0 pairs (*) G2,G8: 9.. / G2 = 9 => 12 pairs (_) / G8 = 9 => 17 pairs (_) * DURATION: 0:00:31.859236 START: 03:27:52.252472 END: 03:28:24.111708 2017-05-01 * CP COUNT: (24) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B1,B9,C4,D7,D8,E6,F8,H8) * ..278156.....3..8..8.9...7..6.1.3.5.5.......8.7.8.5.96.4...9.3..2..6......93.86.. * PAIR B1: 3,9 BLK 1 A1: 3,9,4 # reduction candidate for 3,9 A1: 3,9 # 14 pairs A1: 4 # 10 pairs * PAIR B1: 3,9 ROW 1 I1: 3,9,4 # reduction candidate for 3,9 I1: 4 # 14 pairs I1: 3,9 # 10 pairs * PAIR B1: 3,9 COL B B5: 3,9,1 # reduction candidate for 3,9 B5: 1 => CTR * .3278156..9..3..8..8.9...739681.3.5.51..9...827.845196.4...9.3.32..6......93.86.. B5: 3,9 # 11 pairs * PAIR C4: 4,8 BLK 4 A4: 4,8,2,9 # reduction candidate for 4,8 A4: 4,8 => CTR * 4327815699.7.3..8118695..73864193.5259.....4827.845.9664...9.3.32..6..1...93.8624 A4: 2,9 # 9 pairs * PAIR E6: 2,4 BLK 5 E4: 2,4,7,9 # reduction candidate for 2,4 E4: 2,4 => SOLVED * 492781563715436289386952471968123754534697128271845396647219835823564917159378642 E4: 7,9 # 10 pairs D5: 2,4,6 # reduction candidate for 2,4 D5: 2,4 # 14 pairs E5: 2,4,7,9 # reduction candidate for 2,4 E5: 2,4 => CTR * .3278156....43..81.8.95..73.6.193.5.59.6.7..8.7.8.5.96.4.2.9.3..2.564.1..193786.. E5: 7,9 # 10 pairs F5: 2,4,6,7 # reduction candidate for 2,4 F5: 2,4 # 11 pairs * PAIR E6: 2,4 ROW 6 A6: 2,4,1,3 # reduction candidate for 2,4 A6: 2,4 # 12 pairs G6: 2,4,1,3 # reduction candidate for 2,4 G6: 2,4 => CTR * .3278156.....3..8..8.9...73.6.1.3.5.594...318.7.825496.4.219.3..2.567.4...934862. G6: 1,3 # 10 pairs * PAIR E6: 2,4 COL E E3: 2,4,5 # reduction candidate for 2,4 E3: 2,4 => CTR * ..2781563.1753..893859.6.71.6.1.3.5.53.69.7.8.7.8.5.96146259837.2.4679157593186.. E3: 5 # 9 pairs E9: 2,4,1,5,7 # reduction candidate for 2,4 E9: 2,4 # 11 pairs * PAIR A9: 1,7 BLK 7 A7: 1,7,6,8 # reduction candidate for 1,7 A7: 1,7 => CTR * ..2781563.1753..893859.6.71.6.1.3.5.53.69.7.8.7.8.5.96146259837.2.4679157593186.. A7: 6,8 # 10 pairs C7: 1,7,5,6,8 # reduction candidate for 1,7 C7: 1,7 # 16 pairs A8: 1,7,3,8 # reduction candidate for 1,7 A8: 1,7 => CTR * ..278156.....3.98..8.95..7..6.1.3.5.5.......8.7.8.5.96.4.2.9.3..2356.8.9..93.86.. A8: 3,8 # 10 pairs C8: 1,7,3,5,8 # reduction candidate for 1,7 C8: 1,7 => CTR * 49278156371543698268395247196814325753.6.7..8.7.8.5.96.4.219735327564819159378624 C8: 3,5,8 # 9 pairs * PAIR A9: 1,7 ROW 9 E9: 1,7,2,4,5 # reduction candidate for 1,7 E9: 1,7 # 17 pairs I9: 1,7,2,4,5 # reduction candidate for 1,7 I9: 1,7 # 19 pairs * PAIR A9: 1,7 COL A A2: 1,7,4,6,9 # reduction candidate for 1,7 A2: 1,7 # 12 pairs A2: 4,6,9 # 9 pairs * PAIR B9: 1,5 BLK 7 C7: 1,5,6,7,8 # reduction candidate for 1,5 C7: 1,5 => CTR * ..278156..57.3..8..8695..7.26819375459..7.218.71825396645219837823567...719348625 C7: 6,7,8 # 9 pairs C8: 1,5,3,7,8 # reduction candidate for 1,5 C8: 1,5 # 16 pairs * PAIR B9: 1,5 ROW 9 E9: 1,5,2,4,7 # reduction candidate for 1,5 E9: 1,5 # 17 pairs I9: 1,5,2,4,7 # reduction candidate for 1,5 I9: 1,5 # 14 pairs * PAIR B9: 1,5 COL B B2: 1,5,9 # reduction candidate for 1,5 B2: 9 => CTR * .32781569.9..3..8..8.9...739681.3.5.514.9.328273845196.4...983..2..6.9...593.86.. B2: 1,5 # 11 pairs * PAIR D7: 2,5 BLK 8 E7: 2,5,1,7 # reduction candidate for 2,5 E7: 2,5 => CTR * ..2781563.1753..893859.6.71.6.1.3.5.53.69.7.8.7.8.5.96146259837.2.4679157593186.. E7: 1,7 # 10 pairs E9: 2,5,1,4,7 # reduction candidate for 2,5 E9: 2,5 => CTR * 932781564.57.3.981.8.95.273.6.193457594.7...8.7.845.96.4.519.3..25467.19719328645 E9: 1,4,7 # 9 pairs * PAIR D7: 2,5 ROW 7 I7: 2,5,1,7 # reduction candidate for 2,5 I7: 2,5 # 11 pairs I7: 1,7 # 10 pairs * PAIR D7: 2,5 COL D D2: 2,5,4,6 # reduction candidate for 2,5 D2: 2,5 => CTR * .3278156..5.23..81.8.95.273.6.193.5.59.672.4827.845.96.4.519.32.2.467.1..193.86.. D2: 4,6 # 10 pairs * PAIR D8: 4,5 BLK 8 E9: 4,5,1,2,7 # reduction candidate for 4,5 E9: 4,5 # 13 pairs E9: 1,2,7 # 13 pairs * PAIR D8: 4,5 ROW 8 I8: 4,5,1,7,9 # reduction candidate for 4,5 I8: 4,5 => CTR * 432781569957.3..8118695..73.6419375259..72..8.7.8.5.96645219837.2.567914719348625 I8: 1,7,9 # 9 pairs * PAIR D8: 4,5 COL D D2: 4,5,2,6 # reduction candidate for 4,5 D2: 2,6 # 13 pairs D2: 4,5 # 9 pairs * PAIR F8: 4,7 BLK 8 E9: 4,7,1,2,5 # reduction candidate for 4,7 E9: 1,2,5 # 13 pairs E9: 4,7 # 12 pairs * PAIR F8: 4,7 ROW 8 G8: 4,7,1,8,9 # reduction candidate for 4,7 G8: 4,7 # 27 pairs I8: 4,7,1,5,9 # reduction candidate for 4,7 I8: 4,7 # 30 pairs * PAIR F8: 4,7 COL F F5: 4,7,2,6 # reduction candidate for 4,7 F5: 4,7 # 13 pairs F5: 2,6 # 12 pairs * PAIR H8: 1,4 BLK 9 G8: 1,4,7,8,9 # reduction candidate for 1,4 G8: 1,4 => CTR * ..278156.....3.98..8695..7.26819375459..7.218.7182539664.21983.82.567..9..934862. G8: 7,8,9 # 9 pairs I8: 1,4,5,7,9 # reduction candidate for 1,4 I8: 1,4 => CTR * ..278156.....3..8..8695..7.26819375459..7.218.7182539664.21983.8235679....934862. I8: 5,7,9 # 9 pairs H9: 1,4,2 # reduction candidate for 1,4 H9: 1,4 # 19 pairs I9: 1,4,2,5,7 # reduction candidate for 1,4 I9: 1,4 # 13 pairs * PAIR H8: 1,4 COL H H5: 1,4,2 # reduction candidate for 1,4 H5: 2 # 19 pairs H5: 1,4 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0007-base-pr-000.dot * REASONING * DIS # B5: 1 => CTR => B5: 3,9 * DIS # A4: 4,8 => CTR => A4: 2,9 * PRF # E4: 2,4 => SOL * DIS # E5: 2,4 => CTR => E5: 7,9 * DIS # G6: 2,4 => CTR => G6: 1,3 * DIS # E3: 2,4 => CTR => E3: 5 * DIS # A7: 1,7 => CTR => A7: 6,8 * DIS # A8: 1,7 => CTR => A8: 3,8 * DIS # C8: 1,7 => CTR => C8: 3,5,8 * DIS # C7: 1,5 => CTR => C7: 6,7,8 * DIS # B2: 9 => CTR => B2: 1,5 * DIS # E7: 2,5 => CTR => E7: 1,7 * DIS # E9: 2,5 => CTR => E9: 1,4,7 * DIS # D2: 2,5 => CTR => D2: 4,6 * DIS # I8: 4,5 => CTR => I8: 1,7,9 * DIS # G8: 1,4 => CTR => G8: 7,8,9 * DIS # I8: 1,4 => CTR => I8: 5,7,9 * CNT 17 HDP CHAINS / 66 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B1,B9,C4,D7,D8,E6,F8,H8) * ..278156.....3..8..8.9...7..6.1.3.5.5.......8.7.8.5.96.4...9.3..2..6......93.86.. * PAIR B1: 3,9 BLK 1 A1: 3,9,4 # reduction candidate for 3,9 A1: 3,9 # 14 pairs A1: 4 # 10 pairs * PAIR B1: 3,9 ROW 1 I1: 3,9,4 # reduction candidate for 3,9 I1: 4 # 14 pairs I1: 3,9 # 10 pairs * PAIR B1: 3,9 COL B B5: 3,9,1 # reduction candidate for 3,9 B5: 1 => CTR * .3278156..9..3..8..8.9...739681.3.5.51..9...827.845196.4...9.3.32..6......93.86.. * PAIR RESTART * PAIR B1: 3,9 BLK 1 A1: 3,9,4 # reduction candidate for 3,9 A1: 3,9 # 14 pairs A1: 4 # 12 pairs * PAIR B1: 3,9 ROW 1 I1: 3,9,4 # reduction candidate for 3,9 I1: 4 # 14 pairs I1: 3,9 # 12 pairs * PAIR C4: 4,8 BLK 4 A4: 4,8,2,9 # reduction candidate for 4,8 A4: 4,8 => CTR * 4327815699.7.3..8118695..73864193.5259.....4827.845.9664...9.3.32..6..1...93.8624 * PAIR E6: 2,4 BLK 5 E4: 2,4,7,9 # reduction candidate for 2,4 E4: 2,4 => SOLVED * 492781563715436289386952471968123754534697128271845396647219835823564917159378642 * DURATION: 0:00:09.924071 START: 03:29:11.765959 END: 03:29:21.690030 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0007-base-pr-001.dot * REASONING * DIS # B5: 1 => CTR => B5: 3,9 * DIS B5: 3,9 # A4: 4,8 => CTR => A4: 2,9 * PRF B5: 3,9 + A4: 2,9 # E4: 2,4 => SOL * STA B5: 3,9 + A4: 2,9 + E4: 2,4 * CNT 3 HDP CHAINS / 12 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=7
Solution
position: 492781563715436289386952471968123754534697128271845396647219835823564917159378642 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 # A1: 3,9 => UNS * INC # A1: 4 => UNS * INC # I1: 3,9 => UNS * INC # I1: 4 => UNS * INC # B5: 3,9 => UNS * DIS # B5: 1 => CTR => B5: 3,9 * DIS # A4: 4,8 => CTR => A4: 2,9 * INC # A4: 2,9 => UNS * PRF # E4: 2,4 => SOL * INC # E4: 7,9 => UNS * INC # D5: 2,4 => UNS * DIS # E5: 2,4 => CTR => E5: 7,9 * INC # E5: 7,9 => UNS * INC # F5: 2,4 => UNS * INC # A6: 2,4 => UNS * DIS # G6: 2,4 => CTR => G6: 1,3 * INC # G6: 1,3 => UNS * DIS # E3: 2,4 => CTR => E3: 5 * INC # E3: 5 => UNS * INC # E9: 2,4 => UNS * DIS # A7: 1,7 => CTR => A7: 6,8 * INC # A7: 6,8 => UNS * INC # C7: 1,7 => UNS * DIS # A8: 1,7 => CTR => A8: 3,8 * INC # A8: 3,8 => UNS * DIS # C8: 1,7 => CTR => C8: 3,5,8 * INC # C8: 3,5,8 => UNS * INC # E9: 1,7 => UNS * INC # I9: 1,7 => UNS * INC # A2: 1,7 => UNS * INC # A2: 4,6,9 => UNS * DIS # C7: 1,5 => CTR => C7: 6,7,8 * INC # C7: 6,7,8 => UNS * INC # C8: 1,5 => UNS * INC # E9: 1,5 => UNS * INC # I9: 1,5 => UNS * INC # B2: 1,5 => UNS * DIS # B2: 9 => CTR => B2: 1,5 * DIS # E7: 2,5 => CTR => E7: 1,7 * INC # E7: 1,7 => UNS * DIS # E9: 2,5 => CTR => E9: 1,4,7 * INC # E9: 1,4,7 => UNS * INC # I7: 2,5 => UNS * INC # I7: 1,7 => UNS * DIS # D2: 2,5 => CTR => D2: 4,6 * INC # D2: 4,6 => UNS * INC # E9: 4,5 => UNS * INC # E9: 1,2,7 => UNS * DIS # I8: 4,5 => CTR => I8: 1,7,9 * INC # I8: 1,7,9 => UNS * INC # D2: 4,5 => UNS * INC # D2: 2,6 => UNS * INC # E9: 4,7 => UNS * INC # E9: 1,2,5 => UNS * INC # G8: 4,7 => UNS * INC # I8: 4,7 => UNS * INC # F5: 4,7 => UNS * INC # F5: 2,6 => UNS * DIS # G8: 1,4 => CTR => G8: 7,8,9 * INC # G8: 7,8,9 => UNS * DIS # I8: 1,4 => CTR => I8: 5,7,9 * INC # I8: 5,7,9 => UNS * INC # H9: 1,4 => UNS * INC # I9: 1,4 => UNS * INC # H5: 1,4 => UNS * INC # H5: 2 => UNS * CNT 66 HDP CHAINS / 66 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 3,9 => UNS * INC # A1: 4 => UNS * INC # I1: 3,9 => UNS * INC # I1: 4 => UNS * INC # B5: 3,9 => UNS * DIS # B5: 1 => CTR => B5: 3,9 * INC B5: 3,9 # A1: 3,9 => UNS * INC B5: 3,9 # A1: 4 => UNS * INC B5: 3,9 # I1: 3,9 => UNS * INC B5: 3,9 # I1: 4 => UNS * DIS B5: 3,9 # A4: 4,8 => CTR => A4: 2,9 * PRF B5: 3,9 + A4: 2,9 # E4: 2,4 => SOL * STA B5: 3,9 + A4: 2,9 + E4: 2,4 * CNT 12 HDP CHAINS / 12 HYP OPENED