Analysis of zz-sudoku-de-707313-base.sdk
Contents
Original Sudoku
level: medium
position: 93...54..7..41...3.....61....9.6...4.7.....3.5...8.6....86.....4...28..6..39...25 initial
Autosolve
position: 9318754627..41..838....61..389.6...4.7.....385...8.6..2.86...4.4.7.28..6..3947825 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C2: 2,6 => SOL * DIS # C2: 5 => CTR => C2: 2,6 * DIS # C3: 2,4 => CTR => C3: 5 * PRF # C3: 5 => SOL * DIS # B6: 1 => CTR => B6: 2,4 * DIS # F5: 2,9 => CTR => F5: 1,4 * DIS # F6: 2,9 => CTR => F6: 1,3,4 * PRF # D6: 1,7 => SOL * PRF # H3: 7 => SOL * DIS # G5: 5,9 => CTR => G5: 2 * PRF # H3: 7,9 => SOL * DIS # H3: 5 => CTR => H3: 7,9 * DIS # I6: 7,9 => CTR => I6: 1 * PRF # I6: 1 => SOL * PRF # I7: 7,9 => SOL * DIS # I7: 1 => CTR => I7: 7,9 * DIS # C5: 2,4 => CTR => C5: 6 * DIS # F6: 2,4 => CTR => F6: 1,3,9 * DIS # C3: 2,4 => CTR => C3: 5 * PRF # C3: 5 => SOL * PRF # D4: 1,2 => SOL * DIS # F5: 1,2 => CTR => F5: 4,9 * DIS # D6: 1,2 => CTR => D6: 3,7 * DIS # F6: 1,2 => CTR => F6: 3,4,9 * DIS # G5: 5,9 => CTR => G5: 2 * PRF # D8: 3,5 => SOL * DIS # D8: 1 => CTR => D8: 3,5 * PRF # D8: 1,3 => SOL * DIS # D8: 5 => CTR => D8: 1,3 * PRF # F6: 1,3 => SOL * DIS # F6: 2,4,9 => CTR => F6: 1,3 * PRF # G7: 3,9 => SOL * PRF # I7: 7 => SOL * CNT 33 HDP CHAINS / 52 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C2: 2,6 => SOL * STA C2: 2,6 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 93...54..7..41...3.....61....9.6...4.7.....3.5...8.6....86.....4...28..6..39...25 | initial |
| 9318754627..41..838....61..389.6...4.7.....385...8.6..2.86...4.4.7.28..6..3947825 | autosolve |
| 931875462762419583845236179389162754176594238524783691298651347457328916613947825 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) B2: 2,6 B3: 2,4 F2: 2,9 D3: 2,3 E3: 3,9 G2: 5,9 I3: 7,9 A5: 1,6 C6: 2,4 F4: 1,2 E5: 5,9 B7: 5,9 B8: 5,9 A9: 1,6 B9: 1,6 E7: 3,5 F7: 1,3 G8: 3,9 H8: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A5,B6: 1.. / A5 = 1 => 18 pairs (_) / B6 = 1 => 0 pairs (X) A9,B9: 1.. / A9 = 1 => 0 pairs (X) / B9 = 1 => 18 pairs (_) F7,D8: 1.. / F7 = 1 => 0 pairs (*) / D8 = 1 => 0 pairs (X) I7,H8: 1.. / I7 = 1 => 0 pairs (X) / H8 = 1 => 0 pairs (_) F7,I7: 1.. / F7 = 1 => 0 pairs (*) / I7 = 1 => 0 pairs (X) D8,H8: 1.. / D8 = 1 => 0 pairs (X) / H8 = 1 => 0 pairs (_) A5,A9: 1.. / A5 = 1 => 18 pairs (_) / A9 = 1 => 0 pairs (X) B6,B9: 1.. / B6 = 1 => 0 pairs (X) / B9 = 1 => 18 pairs (_) I6,I7: 1.. / I6 = 1 => 0 pairs (*) / I7 = 1 => 0 pairs (X) F2,D3: 2.. / F2 = 2 => 0 pairs (X) / D3 = 2 => 0 pairs (_) G4,G5: 2.. / G4 = 2 => 0 pairs (X) / G5 = 2 => 22 pairs (_) D3,E3: 3.. / D3 = 3 => 0 pairs (X) / E3 = 3 => 0 pairs (_) D6,F6: 3.. / D6 = 3 => 0 pairs (X) / F6 = 3 => 0 pairs (_) G7,G8: 3.. / G7 = 3 => 0 pairs (*) / G8 = 3 => 0 pairs (X) D8,G8: 3.. / D8 = 3 => 0 pairs (*) / G8 = 3 => 0 pairs (X) E3,E7: 3.. / E3 = 3 => 0 pairs (*) / E7 = 3 => 0 pairs (X) F6,F7: 3.. / F6 = 3 => 0 pairs (*) / F7 = 3 => 0 pairs (X) B3,C3: 4.. / B3 = 4 => 20 pairs (_) / C3 = 4 => 0 pairs (X) F5,F6: 4.. / F5 = 4 => 20 pairs (_) / F6 = 4 => 0 pairs (X) C5,F5: 4.. / C5 = 4 => 0 pairs (X) / F5 = 4 => 20 pairs (_) B3,B6: 4.. / B3 = 4 => 20 pairs (_) / B6 = 4 => 0 pairs (X) C2,C3: 5.. / C2 = 5 => 0 pairs (X) / C3 = 5 => 0 pairs (_) G2,H3: 5.. / G2 = 5 => 0 pairs (*) / H3 = 5 => 0 pairs (X) B7,B8: 5.. / B7 = 5 => 0 pairs (X) / B8 = 5 => 0 pairs (_) E7,D8: 5.. / E7 = 5 => 0 pairs (*) / D8 = 5 => 0 pairs (X) C2,G2: 5.. / C2 = 5 => 0 pairs (X) / G2 = 5 => 0 pairs (_) C3,H3: 5.. / C3 = 5 => 0 pairs (*) / H3 = 5 => 0 pairs (X) B7,E7: 5.. / B7 = 5 => 0 pairs (X) / E7 = 5 => 0 pairs (_) B8,D8: 5.. / B8 = 5 => 0 pairs (*) / D8 = 5 => 0 pairs (X) E5,E7: 5.. / E5 = 5 => 0 pairs (X) / E7 = 5 => 0 pairs (_) H3,H4: 5.. / H3 = 5 => 0 pairs (X) / H4 = 5 => 0 pairs (_) B2,C2: 6.. / B2 = 6 => 18 pairs (_) / C2 = 6 => 0 pairs (X) A5,C5: 6.. / A5 = 6 => 0 pairs (X) / C5 = 6 => 18 pairs (_) A9,B9: 6.. / A9 = 6 => 18 pairs (_) / B9 = 6 => 0 pairs (X) A5,A9: 6.. / A5 = 6 => 0 pairs (X) / A9 = 6 => 18 pairs (_) B2,B9: 6.. / B2 = 6 => 18 pairs (_) / B9 = 6 => 0 pairs (X) C2,C5: 6.. / C2 = 6 => 0 pairs (X) / C5 = 6 => 18 pairs (_) H3,I3: 7.. / H3 = 7 => 0 pairs (*) / I3 = 7 => 0 pairs (X) D4,D6: 7.. / D4 = 7 => 23 pairs (_) / D6 = 7 => 0 pairs (*) G7,I7: 7.. / G7 = 7 => 21 pairs (_) / I7 = 7 => 0 pairs (*) G4,G7: 7.. / G4 = 7 => 0 pairs (*) / G7 = 7 => 0 pairs (X) F2,E3: 9.. / F2 = 9 => 0 pairs (*) / E3 = 9 => 0 pairs (X) B7,B8: 9.. / B7 = 9 => 0 pairs (*) / B8 = 9 => 0 pairs (X) F2,G2: 9.. / F2 = 9 => 0 pairs (*) / G2 = 9 => 0 pairs (X) E3,E5: 9.. / E3 = 9 => 0 pairs (X) / E5 = 9 => 0 pairs (_) * DURATION: 0:01:15.552426 START: 08:05:58.030092 END: 08:07:13.582518 2017-05-01 * CP COUNT: (45) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A9,B2,B3,B7,B8,B9,C6,D3,E3,E5,E7,F2,F4,F7,G2,G8,H8,I3) * 9318754627..41..838....61..389.6...4.7.....385...8.6..2.86...4.4.7.28..6..3947825 * PAIR B2: 2,6 BLK 1 C2: 2,6,5 # reduction candidate for 2,6 C2: 2,6 => SOLVED * 931875462762419583845236179389162754176594238524783691298651347457328916613947825 C2: 5 => CTR * 9318754627654129838..396157389.61.74176.5..385...8.6..2.86...4.4.7.28..6..3947825 * PAIR B3: 2,4 BLK 1 C3: 2,4,5 # reduction candidate for 2,4 C3: 2,4 => CTR * 9318754627.541.9838...96157389.6...4.76.5..385...8.6..2.86...4.4.7.28..6..3947825 C3: 5 => SOLVED * 931875462762419583845236179389162754176594238524783691298651347457328916613947825 * PAIR B3: 2,4 COL B B6: 2,4,1 # reduction candidate for 2,4 B6: 1 => CTR * 93187546272641958384523617.389.6...4.7.....3851..8.6..2.86...414.7128396163947825 B6: 2,4 # 18 pairs * PAIR F2: 2,9 COL F F5: 2,9,1,4 # reduction candidate for 2,9 F5: 2,9 => CTR * 9318754627..41..838....61..389.6...4.74....385.2.846..2.86.3.414.7128396..3947825 F5: 1,4 # 20 pairs F6: 2,9,1,3,4 # reduction candidate for 2,9 F6: 2,9 => CTR * 9318754627..41..838..2361.938976125417...4.385..38.6..2.86.3.414.7128396..3947825 F6: 1,3,4 # 20 pairs * PAIR D3: 2,3 COL D D6: 2,3,1,7 # reduction candidate for 2,3 D6: 1,7 => SOLVED * 931875462762419583845236179389162754176594238524783691298651347457328916613947825 D6: 2,3 # 25 pairs * PAIR G2: 5,9 BLK 3 H3: 5,9,7 # reduction candidate for 5,9 H3: 7 => SOLVED * 931875462762419583845236179389162754176594238524783691298651347457328916613947825 H3: 5,9 # 22 pairs * PAIR G2: 5,9 COL G G5: 5,9,2 # reduction candidate for 5,9 G5: 5,9 => CTR * 93187546276.41..838...361.9389.612.41762.4.385...8.6..2.86.37414.7128396613947825 G5: 2 # 22 pairs * PAIR I3: 7,9 BLK 3 H3: 7,9,5 # reduction candidate for 7,9 H3: 7,9 => SOLVED * 931875462762419583845236179389162754176594238524783691298651347457328916613947825 H3: 5 => CTR * 9318754627.541.9838...96157389.6...4.76.5..385...8.6..2.86..74.4.7.283.6..3947825 * PAIR I3: 7,9 COL I I6: 7,9,1 # reduction candidate for 7,9 I6: 7,9 => CTR * 9318754627..41..838...361.9389.6...4.7..9..385..38.6.7298653741457128396..3947825 I6: 1 => SOLVED * 931875462762419583845236179389162754176594238524783691298651347457328916613947825 I7: 7,9,1 # reduction candidate for 7,9 I7: 7,9 => SOLVED * 931875462762419583845236179389162754176594238524783691298651347457328916613947825 I7: 1 => CTR * 9318754627..41..838...361.9389.6...4.7..9..385..38.6.7298653741457128396..3947825 * PAIR C6: 2,4 BLK 4 C5: 2,4,6 # reduction candidate for 2,4 C5: 2,4 => CTR * 9318754627.641.5838.5..61..389.6..5467.....3851..8.6..2.86...414.7128396163947825 C5: 6 # 18 pairs B6: 2,4,1 # reduction candidate for 2,4 B6: 2,4 # 18 pairs * PAIR C6: 2,4 ROW 6 F6: 2,4,1,3,9 # reduction candidate for 2,4 F6: 2,4 => CTR * 9318754627..41..838..2361.938976...4.7.59.2385..38.6.7298653741457128396..3947825 F6: 1,3,9 # 20 pairs * PAIR C6: 2,4 COL C C3: 2,4,5 # reduction candidate for 2,4 C3: 2,4 => CTR * 9318754627.541.9838...96157389.6...4.76.5..385...8.6..2.86...4.4.7.28..6..3947825 C3: 5 => SOLVED * 931875462762419583845236179389162754176594238524783691298651347457328916613947825 * PAIR F4: 1,2 BLK 5 D4: 1,2,5,7 # reduction candidate for 1,2 D4: 1,2 => SOLVED * 931875462762419583845236179389162754176594238524783691298651347457328916613947825 D4: 5,7 # 20 pairs D5: 1,2,5 # reduction candidate for 1,2 D5: 1,2 # 24 pairs F5: 1,2,4,9 # reduction candidate for 1,2 F5: 1,2 => CTR * 9318754627.6419583845236179389.6...4.74....385.2.846..2.86.3.414.7128396..3947825 F5: 4,9 # 20 pairs D6: 1,2,3,7 # reduction candidate for 1,2 D6: 1,2 => CTR * 9318754627..41..838....61..38976...4.7.....385...836..2.86.1749497528316..3947825 D6: 3,7 # 20 pairs F6: 1,2,3,4,9 # reduction candidate for 1,2 F6: 1,2 => CTR * 9318754627..4195838.5236179389.6...4.7...4.385..38.6..2.86.3.414.7128396..3947825 F6: 3,4,9 # 19 pairs * PAIR E5: 5,9 ROW 5 G5: 5,9,2 # reduction candidate for 5,9 G5: 5,9 => CTR * 93187546276.41..838...361.9389.612.41762.4.385...8.6..2.86.37414.7128396613947825 G5: 2 # 22 pairs * PAIR E7: 3,5 BLK 8 D8: 3,5,1 # reduction candidate for 3,5 D8: 3,5 => SOLVED * 931875462762419583845236179389162754176594238524783691298651347457328916613947825 D8: 1 => CTR * 9318754627..41..838...361.9389.6...4.7..9..385..38.6.7298653741457128396..3947825 * PAIR F7: 1,3 BLK 8 D8: 1,3,5 # reduction candidate for 1,3 D8: 1,3 => SOLVED * 931875462762419583845236179389162754176594238524783691298651347457328916613947825 D8: 5 => CTR * 9318754627..41..838....61..389162..4.7.....385...8.6..2.86.1.4.4.7528316..3947825 * PAIR F7: 1,3 COL F F6: 1,3,2,4,9 # reduction candidate for 1,3 F6: 1,3 => SOLVED * 931875462762419583845236179389162754176594238524783691298651347457328916613947825 F6: 2,4,9 => CTR * 9318754627..41..838..2361.938976...4.7.59.2385..38.6.7298653741457128396..3947825 * PAIR G8: 3,9 BLK 9 G7: 3,9,7 # reduction candidate for 3,9 G7: 3,9 => SOLVED * 931875462762419583845236179389162754176594238524783691298651347457328916613947825 G7: 7 # 21 pairs * PAIR H8: 1,9 BLK 9 I7: 1,9,7 # reduction candidate for 1,9 I7: 7 => SOLVED * 931875462762419583845236179389162754176594238524783691298651347457328916613947825 I7: 1,9 # 21 pairs * PAIR H8: 1,9 COL H H6: 1,9,7 # reduction candidate for 1,9 H6: 7 # 24 pairs H6: 1,9 # 23 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-707313-base-pr-000.dot * REASONING * PRF # C2: 2,6 => SOL * DIS # C2: 5 => CTR => C2: 2,6 * DIS # C3: 2,4 => CTR => C3: 5 * PRF # C3: 5 => SOL * DIS # B6: 1 => CTR => B6: 2,4 * DIS # F5: 2,9 => CTR => F5: 1,4 * DIS # F6: 2,9 => CTR => F6: 1,3,4 * PRF # D6: 1,7 => SOL * PRF # H3: 7 => SOL * DIS # G5: 5,9 => CTR => G5: 2 * PRF # H3: 7,9 => SOL * DIS # H3: 5 => CTR => H3: 7,9 * DIS # I6: 7,9 => CTR => I6: 1 * PRF # I6: 1 => SOL * PRF # I7: 7,9 => SOL * DIS # I7: 1 => CTR => I7: 7,9 * DIS # C5: 2,4 => CTR => C5: 6 * DIS # F6: 2,4 => CTR => F6: 1,3,9 * DIS # C3: 2,4 => CTR => C3: 5 * PRF # C3: 5 => SOL * PRF # D4: 1,2 => SOL * DIS # F5: 1,2 => CTR => F5: 4,9 * DIS # D6: 1,2 => CTR => D6: 3,7 * DIS # F6: 1,2 => CTR => F6: 3,4,9 * DIS # G5: 5,9 => CTR => G5: 2 * PRF # D8: 3,5 => SOL * DIS # D8: 1 => CTR => D8: 3,5 * PRF # D8: 1,3 => SOL * DIS # D8: 5 => CTR => D8: 1,3 * PRF # F6: 1,3 => SOL * DIS # F6: 2,4,9 => CTR => F6: 1,3 * PRF # G7: 3,9 => SOL * PRF # I7: 7 => SOL * CNT 33 HDP CHAINS / 52 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A9,B2,B3,B7,B8,B9,C6,D3,E3,E5,E7,F2,F4,F7,G2,G8,H8,I3) * 9318754627..41..838....61..389.6...4.7.....385...8.6..2.86...4.4.7.28..6..3947825 * PAIR B2: 2,6 BLK 1 C2: 2,6,5 # reduction candidate for 2,6 C2: 2,6 => SOLVED * 931875462762419583845236179389162754176594238524783691298651347457328916613947825 * DURATION: 0:00:02.237609 START: 08:08:04.802055 END: 08:08:07.039664 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-707313-base-pr-001.dot * REASONING * PRF # C2: 2,6 => SOL * STA C2: 2,6 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokus.de/707313.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: 9318754627..41..838....61..389.6...4.7.....385...8.6..2.86...4.4.7.28..6..3947825 B2: 2,6 C2: 2,5,6 # reduction candidate for 2,6 C2: 2,6 => SOLVED * 931875462762419583845236179389162754176594238524783691298651347457328916613947825 * SOLVED! -------------------------------------------------- |:step:| 00 -------------------------------------------------- * DISABLE VALUE:: H3 != 5 |:step:| 01 --------------------------------------------------
Solution
position: 931875462762419583845236179389162754176594238524783691298651347457328916613947825 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:
* PRF # C2: 2,6 => SOL * DIS # C2: 5 => CTR => C2: 2,6 * DIS # C3: 2,4 => CTR => C3: 5 * PRF # C3: 5 => SOL * INC # B6: 2,4 => UNS * DIS # B6: 1 => CTR => B6: 2,4 * DIS # F5: 2,9 => CTR => F5: 1,4 * INC # F5: 1,4 => UNS * DIS # F6: 2,9 => CTR => F6: 1,3,4 * INC # F6: 1,3,4 => UNS * INC # D6: 2,3 => UNS * PRF # D6: 1,7 => SOL * INC # H3: 5,9 => UNS * PRF # H3: 7 => SOL * DIS # G5: 5,9 => CTR => G5: 2 * INC # G5: 2 => UNS * PRF # H3: 7,9 => SOL * DIS # H3: 5 => CTR => H3: 7,9 * DIS # I6: 7,9 => CTR => I6: 1 * PRF # I6: 1 => SOL * PRF # I7: 7,9 => SOL * DIS # I7: 1 => CTR => I7: 7,9 * DIS # C5: 2,4 => CTR => C5: 6 * INC # C5: 6 => UNS * INC # B6: 2,4 => UNS * DIS # F6: 2,4 => CTR => F6: 1,3,9 * INC # F6: 1,3,9 => UNS * DIS # C3: 2,4 => CTR => C3: 5 * PRF # C3: 5 => SOL * PRF # D4: 1,2 => SOL * INC # D4: 5,7 => UNS * INC # D5: 1,2 => UNS * DIS # F5: 1,2 => CTR => F5: 4,9 * INC # F5: 4,9 => UNS * DIS # D6: 1,2 => CTR => D6: 3,7 * INC # D6: 3,7 => UNS * DIS # F6: 1,2 => CTR => F6: 3,4,9 * INC # F6: 3,4,9 => UNS * DIS # G5: 5,9 => CTR => G5: 2 * INC # G5: 2 => UNS * PRF # D8: 3,5 => SOL * DIS # D8: 1 => CTR => D8: 3,5 * PRF # D8: 1,3 => SOL * DIS # D8: 5 => CTR => D8: 1,3 * PRF # F6: 1,3 => SOL * DIS # F6: 2,4,9 => CTR => F6: 1,3 * PRF # G7: 3,9 => SOL * INC # G7: 7 => UNS * INC # I7: 1,9 => UNS * PRF # I7: 7 => SOL * INC # H6: 1,9 => UNS * INC # H6: 7 => UNS * CNT 52 HDP CHAINS / 52 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C2: 2,6 => SOL * STA C2: 2,6 * CNT 1 HDP CHAINS / 1 HYP OPENED