Analysis of zz-menneske-no-06913596-base.sdk
Contents
Original Sudoku
level: medium
position: ....8.......1.4.2..5.9..36.6.....8..9...41..21..5....4..37.6....2..............4. initial
Autosolve
position: 2...8.4..3..1.4.2..5.9..36.6.....8..9...41..21..5....4..37.6....2.4............4. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # D5: 8 => SOL * PRF # F6: 2,7 => SOL * DIS # F6: 2,3 => CTR => F6: 7,8,9 * PRF # D9: 2,3 => SOL * DIS # I8: 5,9 => CTR => I8: 3,6,7 * DIS # I2: 5,9 => CTR => I2: 7,8 * CNT 6 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # D5: 8 => SOL * STA D5: 8 * CNT 1 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....8.......1.4.2..5.9..36.6.....8..9...41..21..5....4..37.6....2..............4. | initial |
| 2...8.4..3..1.4.2..5.9..36.6.....8..9...41..21..5....4..37.6....2.4............4. | autosolve |
| 271683495369154728854972361645239817937841652182567934413726589526498173798315246 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) A3: 4,8 D1: 3,6 F1: 3,5 E2: 5,6 E3: 2,7 F3: 2,7 I3: 1,8 D4: 2,3 I7: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H4,I4: 1.. / H4 = 1 => 9 pairs (_) / I4 = 1 => 23 pairs (_) C3,I3: 1.. / C3 = 1 => 22 pairs (_) / I3 = 1 => 9 pairs (_) H1,H4: 1.. / H1 = 1 => 23 pairs (_) / H4 = 1 => 9 pairs (_) E3,F3: 2.. / E3 = 2 => 7 pairs (_) / F3 = 2 => 7 pairs (_) C4,C6: 2.. / C4 = 2 => 0 pairs (X) / C6 = 2 => 9 pairs (_) G7,G9: 2.. / G7 = 2 => 9 pairs (_) / G9 = 2 => 8 pairs (_) E7,G7: 2.. / E7 = 2 => 8 pairs (_) / G7 = 2 => 9 pairs (_) D4,D9: 2.. / D4 = 2 => 9 pairs (_) / D9 = 2 => 0 pairs (X) D1,F1: 3.. / D1 = 3 => 9 pairs (_) / F1 = 3 => 14 pairs (_) A3,C3: 4.. / A3 = 4 => 23 pairs (_) / C3 = 4 => 9 pairs (_) B4,C4: 4.. / B4 = 4 => 9 pairs (_) / C4 = 4 => 23 pairs (_) A7,B7: 4.. / A7 = 4 => 9 pairs (_) / B7 = 4 => 23 pairs (_) A3,A7: 4.. / A3 = 4 => 23 pairs (_) / A7 = 4 => 9 pairs (_) B4,B7: 4.. / B4 = 4 => 9 pairs (_) / B7 = 4 => 23 pairs (_) C3,C4: 4.. / C3 = 4 => 9 pairs (_) / C4 = 4 => 23 pairs (_) F1,E2: 5.. / F1 = 5 => 9 pairs (_) / E2 = 5 => 14 pairs (_) C4,C5: 5.. / C4 = 5 => 10 pairs (_) / C5 = 5 => 16 pairs (_) D1,E2: 6.. / D1 = 6 => 14 pairs (_) / E2 = 6 => 9 pairs (_) D5,E6: 6.. / D5 = 6 => 9 pairs (_) / E6 = 6 => 14 pairs (_) G5,G6: 6.. / G5 = 6 => 14 pairs (_) / G6 = 6 => 9 pairs (_) I8,I9: 6.. / I8 = 6 => 9 pairs (_) / I9 = 6 => 9 pairs (_) D5,G5: 6.. / D5 = 6 => 9 pairs (_) / G5 = 6 => 14 pairs (_) E6,G6: 6.. / E6 = 6 => 14 pairs (_) / G6 = 6 => 9 pairs (_) C8,I8: 6.. / C8 = 6 => 9 pairs (_) / I8 = 6 => 9 pairs (_) D1,D5: 6.. / D1 = 6 => 14 pairs (_) / D5 = 6 => 9 pairs (_) E2,E6: 6.. / E2 = 6 => 9 pairs (_) / E6 = 6 => 14 pairs (_) E3,F3: 7.. / E3 = 7 => 7 pairs (_) / F3 = 7 => 7 pairs (_) A8,A9: 7.. / A8 = 7 => 10 pairs (_) / A9 = 7 => 10 pairs (_) I2,I3: 8.. / I2 = 8 => 9 pairs (_) / I3 = 8 => 22 pairs (_) D5,F6: 8.. / D5 = 8 => 0 pairs (*) / F6 = 8 => 0 pairs (X) H7,H8: 8.. / H7 = 8 => 10 pairs (_) / H8 = 8 => 27 pairs (_) D5,D9: 8.. / D5 = 8 => 0 pairs (*) / D9 = 8 => 0 pairs (X) * DURATION: 0:00:49.872658 START: 07:09:35.487460 END: 07:10:25.360118 2017-05-01 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,D1,D4,E2,E3,F1,F3,I3,I7) * 2...8.4..3..1.4.2..5.9..36.6.....8..9...41..21..5....4..37.6....2.4............4. * PAIR A3: 4,8 BLK 1 C3: 4,8,1 # reduction candidate for 4,8 C3: 1 # 22 pairs C3: 4,8 # 9 pairs * PAIR A3: 4,8 COL A A7: 4,8,5 # reduction candidate for 4,8 A7: 5 # 24 pairs A7: 4,8 # 12 pairs * PAIR D1: 3,6 COL D D5: 3,6,8 # reduction candidate for 3,6 D5: 8 => SOLVED * 271683495369154728854972361645239817937841652182567934413726589526498173798315246 D5: 3,6 # 11 pairs * PAIR F1: 3,5 COL F F8: 3,5,8,9 # reduction candidate for 3,5 F8: 3,5 # 11 pairs F9: 3,5,2,8,9 # reduction candidate for 3,5 F9: 3,5 # 11 pairs * PAIR E3: 2,7 COL E E4: 2,7,3,9 # reduction candidate for 2,7 E4: 2,7 # 10 pairs E6: 2,7,3,6,9 # reduction candidate for 2,7 E6: 2,7 # 14 pairs * PAIR F3: 2,7 COL F F4: 2,7,3,9 # reduction candidate for 2,7 F4: 2,7 # 10 pairs F6: 2,7,3,8,9 # reduction candidate for 2,7 F6: 2,7 => SOLVED * 271683495369154728854972361645239817937841652182567934413726589526498173798315246 F6: 3,8,9 # 9 pairs * PAIR I3: 1,8 ROW 3 C3: 1,8,4 # reduction candidate for 1,8 C3: 1,8 # 23 pairs C3: 4 # 9 pairs * PAIR D4: 2,3 BLK 5 E4: 2,3,7,9 # reduction candidate for 2,3 E4: 2,3 # 15 pairs F4: 2,3,7,9 # reduction candidate for 2,3 F4: 2,3 # 16 pairs E6: 2,3,6,7,9 # reduction candidate for 2,3 E6: 2,3 # 17 pairs F6: 2,3,7,8,9 # reduction candidate for 2,3 F6: 2,3 => CTR * 2..6834..3..154.2..549273616423798159.58416.21..562..44.37.6259.2.4...8....2.8.4. F6: 7,8,9 # 9 pairs * PAIR D4: 2,3 COL D D9: 2,3,8 # reduction candidate for 2,3 D9: 2,3 => SOLVED * 271683495369154728854972361645239817937841652182567934413726589526498173798315246 D9: 8 # 11 pairs * PAIR I7: 5,9 BLK 9 G7: 5,9,1,2 # reduction candidate for 5,9 G7: 5,9 # 11 pairs H7: 5,9,8 # reduction candidate for 5,9 H7: 5,9 # 27 pairs G8: 5,9,1,7 # reduction candidate for 5,9 G8: 5,9 # 14 pairs H8: 5,9,3,7,8 # reduction candidate for 5,9 H8: 5,9 # 18 pairs I8: 5,9,3,6,7 # reduction candidate for 5,9 I8: 5,9 => CTR * 2..6834.7367154.288549..3616452..8139...41..21.25....44.37.6.8..264.8.3....3...46 I8: 3,6,7 # 9 pairs G9: 5,9,1,2,7 # reduction candidate for 5,9 G9: 5,9 # 12 pairs I9: 5,9,3,6,7 # reduction candidate for 5,9 I9: 5,9 # 24 pairs * PAIR I7: 5,9 ROW 7 E7: 5,9,1,2 # reduction candidate for 5,9 E7: 5,9 # 10 pairs E7: 1,2 # 10 pairs * PAIR I7: 5,9 COL I I1: 5,9,1,7 # reduction candidate for 5,9 I1: 5,9 # 11 pairs I2: 5,9,7,8 # reduction candidate for 5,9 I2: 5,9 => CTR * 2.76834..3681547294519..3686.4...8..9.5.416.21.256.9.4.437.6..5.2.4..1...1....24. I2: 7,8 # 10 pairs I4: 5,9,1,3,7 # reduction candidate for 5,9 I4: 5,9 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-menneske-no-06913596-base-pr-000.dot * REASONING * PRF # D5: 8 => SOL * PRF # F6: 2,7 => SOL * DIS # F6: 2,3 => CTR => F6: 7,8,9 * PRF # D9: 2,3 => SOL * DIS # I8: 5,9 => CTR => I8: 3,6,7 * DIS # I2: 5,9 => CTR => I2: 7,8 * CNT 6 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,D1,D4,E2,E3,F1,F3,I3,I7) * 2...8.4..3..1.4.2..5.9..36.6.....8..9...41..21..5....4..37.6....2.4............4. * PAIR A3: 4,8 BLK 1 C3: 4,8,1 # reduction candidate for 4,8 C3: 1 # 22 pairs C3: 4,8 # 9 pairs * PAIR A3: 4,8 COL A A7: 4,8,5 # reduction candidate for 4,8 A7: 5 # 24 pairs A7: 4,8 # 12 pairs * PAIR D1: 3,6 COL D D5: 3,6,8 # reduction candidate for 3,6 D5: 8 => SOLVED * 271683495369154728854972361645239817937841652182567934413726589526498173798315246 * DURATION: 0:00:06.990407 START: 07:10:58.701821 END: 07:11:05.692228 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-menneske-no-06913596-base-pr-001.dot * REASONING * PRF # D5: 8 => SOL * STA D5: 8 * CNT 1 HDP CHAINS / 6 HYP OPENED
Header Info
http://www.menneske.no/sudoku/utskrift.html?number=6913596 umulig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1 * 2...8.4..3..1.4.2..5.9..36.6.....8..9...41..21..5....4..37.6....2.4............4. A3: 4,8 # * reduce to pair C3: 4,8,1 # reduction candidate for 4,8 C3: 1 # 22 pairs C3: 4,8 # 9 pairs A7: 4,8,5 # reduction candidate for 4,8 A7: 5 # 24 pairs A7: 4,8 # 12 pairs D1: 3,6 # * reduce to pair D5: 3,6,8 # reduction candidate for 3,6 D5: 8 => SOLVED * 271683495369154728854972361645239817937841652182567934413726589526498173798315246 * SOLVED!
Solution
position: 271683495369154728854972361645239817937841652182567934413726589526498173798315246 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 # C3: 4,8 => UNS * INC # C3: 1 => UNS * INC # A7: 4,8 => UNS * INC # A7: 5 => UNS * INC # D5: 3,6 => UNS * PRF # D5: 8 => SOL * INC # F8: 3,5 => UNS * INC # F9: 3,5 => UNS * INC # E4: 2,7 => UNS * INC # E6: 2,7 => UNS * INC # F4: 2,7 => UNS * PRF # F6: 2,7 => SOL * INC # F6: 3,8,9 => UNS * INC # C3: 1,8 => UNS * INC # C3: 4 => UNS * INC # E4: 2,3 => UNS * INC # F4: 2,3 => UNS * INC # E6: 2,3 => UNS * DIS # F6: 2,3 => CTR => F6: 7,8,9 * INC # F6: 7,8,9 => UNS * PRF # D9: 2,3 => SOL * INC # D9: 8 => UNS * INC # G7: 5,9 => UNS * INC # H7: 5,9 => UNS * INC # G8: 5,9 => UNS * INC # H8: 5,9 => UNS * DIS # I8: 5,9 => CTR => I8: 3,6,7 * INC # I8: 3,6,7 => UNS * INC # G9: 5,9 => UNS * INC # I9: 5,9 => UNS * INC # E7: 5,9 => UNS * INC # E7: 1,2 => UNS * INC # I1: 5,9 => UNS * DIS # I2: 5,9 => CTR => I2: 7,8 * INC # I2: 7,8 => UNS * INC # I4: 5,9 => UNS * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C3: 4,8 => UNS * INC # C3: 1 => UNS * INC # A7: 4,8 => UNS * INC # A7: 5 => UNS * INC # D5: 3,6 => UNS * PRF # D5: 8 => SOL * STA D5: 8 * CNT 6 HDP CHAINS / 6 HYP OPENED