Analysis of zz-sudoku-de-703274-base.sdk
Contents
Original Sudoku
level: medium
position: .....7..98.1..34...4.....31..8.7...3...6.2...6...1.9..31.....9...65..2.75..8..... initial
Autosolve
position: 2..147..98.19.34...4.2...31..847...3...6.2...6..31.9..31.7...9..8653.2.75..8..3.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B1: 3,5 => SOL * DIS # C5: 3,5 => CTR => C5: 4,7,9 * PRF # C3: 7,9 => SOL * DIS # C3: 5 => CTR => C3: 7,9 * DIS # A5: 7,9 => CTR => A5: 1,4 * PRF # A5: 1,4 => SOL * DIS # E3: 5,6 => CTR => E3: 8 * PRF # B2: 5,6 => SOL * DIS # B2: 7 => CTR => B2: 5,6 * DIS # H2: 5,6 => CTR => H2: 2,7 * DIS # I2: 5,6 => CTR => I2: 2 * PRF # A5: 1,9 => SOL * DIS # A5: 4,7 => CTR => A5: 1,9 * DIS # E5: 8 => CTR => E5: 5,9 * DIS # B4: 5,9 => CTR => B4: 2 * DIS # E5: 5,8 => CTR => E5: 9 * DIS # H6: 5,8 => CTR => H6: 2,4,7 * DIS # I6: 5,8 => CTR => I6: 2,4 * DIS # F3: 5,8 => CTR => F3: 6 * DIS # C9: 2,4 => CTR => C9: 7,9 * DIS # C9: 4,9 => CTR => C9: 2,7 * DIS # F8: 1 => CTR => F8: 4,9 * DIS # A5: 4,9 => CTR => A5: 1,7 * DIS # C9: 2,9 => CTR => C9: 4,7 * DIS # G5: 5,8 => CTR => G5: 1,7 * DIS # I6: 5,8 => CTR => I6: 2,4 * DIS # H9: 6 => CTR => H9: 1,4 * DIS # F8: 1,4 => CTR => F8: 9 * DIS # H9: 1 => CTR => H9: 4,6 * CNT 29 HDP CHAINS / 56 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B1: 3,5 => SOL * STA B1: 3,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....7..98.1..34...4.....31..8.7...3...6.2...6...1.9..31.....9...65..2.75..8..... | initial |
| 2..147..98.19.34...4.2...31..847...3...6.2...6..31.9..31.7...9..8653.2.75..8..3.. | autosolve |
| 253147689861953472749286531928475163134692758675318924312764895486539217597821346 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) C1: 3,5 A3: 7,9 E2: 5,6 A4: 1,9 F4: 5,9 F6: 5,8 C7: 2,4 A8: 4,9 E7: 2,6 F7: 4,6 E9: 2,9 G7: 5,8 I7: 5,8 H8: 1,4 I9: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A4,A5: 1.. / A4 = 1 => 0 pairs (X) / A5 = 1 => 0 pairs (_) G4,G5: 1.. / G4 = 1 => 0 pairs (*) / G5 = 1 => 0 pairs (X) F8,F9: 1.. / F8 = 1 => 0 pairs (X) / F9 = 1 => 16 pairs (_) H8,H9: 1.. / H8 = 1 => 16 pairs (_) / H9 = 1 => 0 pairs (X) A4,G4: 1.. / A4 = 1 => 0 pairs (X) / G4 = 1 => 0 pairs (_) A5,G5: 1.. / A5 = 1 => 0 pairs (*) / G5 = 1 => 0 pairs (X) F8,H8: 1.. / F8 = 1 => 0 pairs (X) / H8 = 1 => 16 pairs (_) F9,H9: 1.. / F9 = 1 => 16 pairs (_) / H9 = 1 => 0 pairs (X) H2,I2: 2.. / H2 = 2 => 0 pairs (X) / I2 = 2 => 15 pairs (_) E7,E9: 2.. / E7 = 2 => 0 pairs (X) / E9 = 2 => 17 pairs (_) B4,H4: 2.. / B4 = 2 => 18 pairs (_) / H4 = 2 => 0 pairs (X) C7,E7: 2.. / C7 = 2 => 17 pairs (_) / E7 = 2 => 0 pairs (X) I2,I6: 2.. / I2 = 2 => 15 pairs (_) / I6 = 2 => 0 pairs (X) B1,C1: 3.. / B1 = 3 => 0 pairs (X) / C1 = 3 => 15 pairs (_) B5,C5: 3.. / B5 = 3 => 15 pairs (_) / C5 = 3 => 0 pairs (X) B1,B5: 3.. / B1 = 3 => 0 pairs (X) / B5 = 3 => 15 pairs (_) C1,C5: 3.. / C1 = 3 => 15 pairs (_) / C5 = 3 => 0 pairs (X) C7,F7: 4.. / C7 = 4 => 0 pairs (X) / F7 = 4 => 17 pairs (_) A5,A8: 4.. / A5 = 4 => 0 pairs (X) / A8 = 4 => 16 pairs (_) G7,I7: 5.. / G7 = 5 => 17 pairs (_) / I7 = 5 => 16 pairs (_) B1,B2: 6.. / B1 = 6 => 21 pairs (_) / B2 = 6 => 0 pairs (*) G4,H4: 6.. / G4 = 6 => 0 pairs (X) / H4 = 6 => 20 pairs (_) E7,F7: 6.. / E7 = 6 => 17 pairs (_) / F7 = 6 => 0 pairs (X) H9,I9: 6.. / H9 = 6 => 0 pairs (X) / I9 = 6 => 16 pairs (_) F3,F7: 6.. / F3 = 6 => 17 pairs (_) / F7 = 6 => 0 pairs (X) I2,I9: 6.. / I2 = 6 => 0 pairs (X) / I9 = 6 => 16 pairs (_) H2,G3: 7.. / H2 = 7 => 0 pairs (*) / G3 = 7 => 0 pairs (X) B9,C9: 7.. / B9 = 7 => 0 pairs (X) / C9 = 7 => 18 pairs (_) B2,H2: 7.. / B2 = 7 => 0 pairs (X) / H2 = 7 => 0 pairs (_) A3,A5: 7.. / A3 = 7 => 0 pairs (*) / A5 = 7 => 0 pairs (X) G3,G5: 7.. / G3 = 7 => 0 pairs (X) / G5 = 7 => 0 pairs (_) E3,F3: 8.. / E3 = 8 => 16 pairs (_) / F3 = 8 => 0 pairs (X) G1,H1: 8.. / G1 = 8 => 18 pairs (_) / H1 = 8 => 16 pairs (_) E5,F6: 8.. / E5 = 8 => 0 pairs (X) / F6 = 8 => 16 pairs (_) G7,I7: 8.. / G7 = 8 => 16 pairs (_) / I7 = 8 => 17 pairs (_) E3,E5: 8.. / E3 = 8 => 16 pairs (_) / E5 = 8 => 0 pairs (X) F3,F6: 8.. / F3 = 8 => 0 pairs (X) / F6 = 8 => 16 pairs (_) A3,C3: 9.. / A3 = 9 => 0 pairs (X) / C3 = 9 => 0 pairs (_) F4,E5: 9.. / F4 = 9 => 0 pairs (X) / E5 = 9 => 17 pairs (_) A8,F8: 9.. / A8 = 9 => 0 pairs (X) / F8 = 9 => 16 pairs (_) E5,E9: 9.. / E5 = 9 => 17 pairs (_) / E9 = 9 => 0 pairs (X) * DURATION: 0:01:08.862814 START: 07:59:59.746575 END: 08:01:08.609389 2017-05-01 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A8,C1,C7,E2,E7,E9,F4,F6,F7,G7,H8,I7,I9) * 2..147..98.19.34...4.2...31..847...3...6.2...6..31.9..31.7...9..8653.2.75..8..3.. * PAIR C1: 3,5 BLK 1 B1: 3,5,6 # reduction candidate for 3,5 B1: 3,5 => SOLVED * 253147689861953472749286531928475163134692758675318924312764895486539217597821346 B1: 6 # 21 pairs * PAIR C1: 3,5 COL C C5: 3,5,4,7,9 # reduction candidate for 3,5 C5: 3,5 => CTR * 2..147..98619534727492865319284751631..69275.6.431.92.312764.9.486539217597821346 C5: 4,7,9 # 15 pairs * PAIR A3: 7,9 BLK 1 C3: 7,9,5 # reduction candidate for 7,9 C3: 7,9 => SOLVED * 253147689861953472749286531928475163134692758675318924312764895486539217597821346 C3: 5 => CTR * 2.3147..98719534..9452..73119847...37..6.21..6..31.97.31.7...9.4865392175.78213.. * PAIR A3: 7,9 COL A A5: 7,9,1,4 # reduction candidate for 7,9 A5: 7,9 => CTR * 2..147..98.19.34...4.2..7311984756237..6921..62.31897.3127...9.4865392175..8213.. A5: 1,4 => SOLVED * 253147689861953472749286531928475163134692758675318924312764895486539217597821346 * PAIR E2: 5,6 BLK 2 E3: 5,6,8 # reduction candidate for 5,6 E3: 5,6 => CTR * 235147..98619534727492685311584796.3.93682...6..3159..314726.9.98653.2.75..89.3.. E3: 8 # 16 pairs F3: 5,6,8 # reduction candidate for 5,6 F3: 5,6 # 16 pairs * PAIR E2: 5,6 ROW 2 B2: 5,6,7 # reduction candidate for 5,6 B2: 5,6 => SOLVED * 253147689861953472749286531928475163134692758675318924312764895486539217597821346 B2: 7 => CTR * 263147..98719534..9452..73119847.6.373.6.21..6..31.97.31.7...9.4865392175.78213.. H2: 5,6,2,7 # reduction candidate for 5,6 H2: 5,6 => CTR * 263147..98719534629452..73119847...37..6.21..6..31.97.31.7...9.4865392175.78213.6 H2: 2,7 # 16 pairs I2: 5,6,2 # reduction candidate for 5,6 I2: 5,6 => CTR * 2..147..98.19.342..4.2..731.2847...37..6.21..654318972312764.9.4865392175.78213.. I2: 2 # 15 pairs * PAIR A4: 1,9 BLK 4 A5: 1,9,4,7 # reduction candidate for 1,9 A5: 1,9 => SOLVED * 253147689861953472749286531928475163134692758675318924312764895486539217597821346 A5: 4,7 => CTR * 2..147..98719.34..9452..73119847...37..6.21..6..31.97.31.7...9.4865392175.78213.. * PAIR F4: 5,9 BLK 5 E5: 5,9,8 # reduction candidate for 5,9 E5: 8 => CTR * 2..147..98.19.34..7492.8.311.8479..34..682...6..3159..31.7...9.98653.2.75..89.3.. E5: 5,9 # 16 pairs * PAIR F4: 5,9 ROW 4 B4: 5,9,2 # reduction candidate for 5,9 B4: 5,9 => CTR * 2..147..98719.34.29452..73119847.6237..6.21..6..31.97.31.7...9.4865392175.7821346 B4: 2 # 18 pairs * PAIR F6: 5,8 BLK 5 E5: 5,8,9 # reduction candidate for 5,8 E5: 5,8 => CTR * 2..147..98.19.34..7492...311.8479..34..6.2...6..31.9..31.7...9.98653.2.75..89.3.. E5: 9 # 17 pairs * PAIR F6: 5,8 ROW 6 H6: 5,8,2,4,7 # reduction candidate for 5,8 H6: 5,8 => CTR * 2..147..98.19.34727492...31..847..23...6.27..6..31.9..31.7...9..8653.2.75..8..3.6 H6: 2,4,7 # 15 pairs I6: 5,8,2,4 # reduction candidate for 5,8 I6: 5,8 => CTR * 2..147.598.19534.2.45286731..8475..3753692..46.43189.53127645984865392175..821346 I6: 2,4 # 16 pairs * PAIR F6: 5,8 COL F F3: 5,8,6 # reduction candidate for 5,8 F3: 5,8 => CTR * 2..147..98.19.34..7492...311.8479..34..6.2...6..31.9..314726.9.98653.2.75..89.3.. F3: 6 # 17 pairs * PAIR C7: 2,4 BLK 7 C9: 2,4,7,9 # reduction candidate for 2,4 C9: 2,4 => CTR * 2..147..98.19.3472.4.2...31..847...3...6.27..6.731.9..31.7...9.98653.2.757.8..3.6 C9: 7,9 # 17 pairs * PAIR C7: 2,4 COL C C6: 2,4,5,7 # reduction candidate for 2,4 C6: 5,7 # 20 pairs C6: 2,4 # 18 pairs * PAIR A8: 4,9 BLK 7 C9: 4,9,2,7 # reduction candidate for 4,9 C9: 4,9 => CTR * 2..147..9861953472749286531.984751.3...6927..6.73189..312764.9..8653.2.757.82.3.6 C9: 2,7 # 16 pairs * PAIR A8: 4,9 ROW 8 F8: 4,9,1 # reduction candidate for 4,9 F8: 1 => CTR * 2..147..98.19.34..7492...311.847...34..6.2...6..31.9..31.7...9.9865312475..8..316 F8: 4,9 # 16 pairs * PAIR A8: 4,9 COL A A5: 4,9,1,7 # reduction candidate for 4,9 A5: 4,9 => CTR * 2..147..98.19.34..7492...311.847...3...6.2...6..31.9..31.7...9..8653.2.75..8..3.. A5: 1,7 # 16 pairs * PAIR E9: 2,9 ROW 9 B9: 2,9,7 # reduction candidate for 2,9 B9: 2,9 # 18 pairs C9: 2,9,4,7 # reduction candidate for 2,9 C9: 2,9 => CTR * 2..147..98.19.34727492...31..847.1631.46.27..6.731.9243127...9..8653.2.757.8..3.6 C9: 4,7 # 16 pairs * PAIR G7: 5,8 COL G G1: 5,8,6 # reduction candidate for 5,8 G1: 5,8 # 19 pairs G5: 5,8,1,7 # reduction candidate for 5,8 G5: 5,8 => CTR * 2..147..98.19.34...4.2..731..847.163...6.2...6..31.9..31.7...9..8653.2.75..8..3.. G5: 1,7 # 16 pairs * PAIR I7: 5,8 COL I I5: 5,8,4 # reduction candidate for 5,8 I5: 5,8 # 18 pairs I6: 5,8,2,4 # reduction candidate for 5,8 I6: 5,8 => CTR * 2..147.598.19534.2.45286731..8475..3753692..46.43189.53127645984865392175..821346 I6: 2,4 # 16 pairs * PAIR H8: 1,4 BLK 9 H9: 1,4,6 # reduction candidate for 1,4 H9: 6 => CTR * 263147..98.1953426.452..7311284796537..6.21..6..31.9.231.7...9..8653.2175..8.1364 H9: 1,4 # 16 pairs * PAIR H8: 1,4 ROW 8 F8: 1,4,9 # reduction candidate for 1,4 F8: 1,4 => CTR * 2..147..98.19.34..7492...311.847...34..6.2...6..31.9..31.7...9.98653.2.75..8..3.. F8: 9 # 16 pairs * PAIR I9: 4,6 BLK 9 H9: 4,6,1 # reduction candidate for 4,6 H9: 1 => CTR * 2..147..98.19.34.27492...311.847...34..6.21..6..31.9.431.7...9.9865312475..8..316 H9: 4,6 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-703274-base-pr-000.dot * REASONING * PRF # B1: 3,5 => SOL * DIS # C5: 3,5 => CTR => C5: 4,7,9 * PRF # C3: 7,9 => SOL * DIS # C3: 5 => CTR => C3: 7,9 * DIS # A5: 7,9 => CTR => A5: 1,4 * PRF # A5: 1,4 => SOL * DIS # E3: 5,6 => CTR => E3: 8 * PRF # B2: 5,6 => SOL * DIS # B2: 7 => CTR => B2: 5,6 * DIS # H2: 5,6 => CTR => H2: 2,7 * DIS # I2: 5,6 => CTR => I2: 2 * PRF # A5: 1,9 => SOL * DIS # A5: 4,7 => CTR => A5: 1,9 * DIS # E5: 8 => CTR => E5: 5,9 * DIS # B4: 5,9 => CTR => B4: 2 * DIS # E5: 5,8 => CTR => E5: 9 * DIS # H6: 5,8 => CTR => H6: 2,4,7 * DIS # I6: 5,8 => CTR => I6: 2,4 * DIS # F3: 5,8 => CTR => F3: 6 * DIS # C9: 2,4 => CTR => C9: 7,9 * DIS # C9: 4,9 => CTR => C9: 2,7 * DIS # F8: 1 => CTR => F8: 4,9 * DIS # A5: 4,9 => CTR => A5: 1,7 * DIS # C9: 2,9 => CTR => C9: 4,7 * DIS # G5: 5,8 => CTR => G5: 1,7 * DIS # I6: 5,8 => CTR => I6: 2,4 * DIS # H9: 6 => CTR => H9: 1,4 * DIS # F8: 1,4 => CTR => F8: 9 * DIS # H9: 1 => CTR => H9: 4,6 * CNT 29 HDP CHAINS / 56 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A8,C1,C7,E2,E7,E9,F4,F6,F7,G7,H8,I7,I9) * 2..147..98.19.34...4.2...31..847...3...6.2...6..31.9..31.7...9..8653.2.75..8..3.. * PAIR C1: 3,5 BLK 1 B1: 3,5,6 # reduction candidate for 3,5 B1: 3,5 => SOLVED * 253147689861953472749286531928475163134692758675318924312764895486539217597821346 * DURATION: 0:00:02.343195 START: 08:02:00.528861 END: 08:02:02.872056 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-703274-base-pr-001.dot * REASONING * PRF # B1: 3,5 => SOL * STA B1: 3,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokus.de/703274.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: 2..147..98.19.34...4.2...31..847...3...6.2...6..31.9..31.7...9..8653.2.75..8..3.. C1: 3,5 B1: 3,5,6 # reduction candidate for 3,5 B1: 3,5 => SOLVED * 253147689861953472749286531928475163134692758675318924312764895486539217597821346 * SOLVED! -------------------------------------------------- * AUTO .. A1 = 2 # set value D1 = 1 # set value D6 = 3 # set value D7 = 7 # set value B8 = 8 # set value E8 = 3 # set value G9 = 3 # set value E1: 4.. # hidden single D4: 4.. # hidden single E1 = 4 # set value D4 = 4 # set value D2: 9 # naked single Q3: 2.. = H2,I2: 2.. => D2,E2 != 2 Q2: 8.. = E3,F3: 8.. => G3 != 8 Q8: 2.. = E7,E9: 2.. => E3 != 2 Q5,Q8: 9.. => E2,E3,F3 != 9 Q9: 1.. = H8,H9: 1.. => H4,H5 != 1 D3: 2.. # hidden single D2 = 9 # set value D3: 2 # naked single D3 = 2 # set value G7,I7: 5,8.. => G7,I7 != 4,6 # hidden pair Q9: 6.. = H9,I9: 6.. => E9,F9 != 6 * UNSOLVED! |:step:| 00 -------------------------------------------------- * DISABLE VALUE:: B1 != 6 B2: 6.. # hidden single |:step:| 01 --------------------------------------------------
Solution
position: 253147689861953472749286531928475163134692758675318924312764895486539217597821346 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 # B1: 3,5 => SOL * INC # B1: 6 => UNS * DIS # C5: 3,5 => CTR => C5: 4,7,9 * INC # C5: 4,7,9 => UNS * PRF # C3: 7,9 => SOL * DIS # C3: 5 => CTR => C3: 7,9 * DIS # A5: 7,9 => CTR => A5: 1,4 * PRF # A5: 1,4 => SOL * DIS # E3: 5,6 => CTR => E3: 8 * INC # E3: 8 => UNS * INC # F3: 5,6 => UNS * PRF # B2: 5,6 => SOL * DIS # B2: 7 => CTR => B2: 5,6 * DIS # H2: 5,6 => CTR => H2: 2,7 * INC # H2: 2,7 => UNS * DIS # I2: 5,6 => CTR => I2: 2 * INC # I2: 2 => UNS * PRF # A5: 1,9 => SOL * DIS # A5: 4,7 => CTR => A5: 1,9 * INC # E5: 5,9 => UNS * DIS # E5: 8 => CTR => E5: 5,9 * DIS # B4: 5,9 => CTR => B4: 2 * INC # B4: 2 => UNS * DIS # E5: 5,8 => CTR => E5: 9 * INC # E5: 9 => UNS * DIS # H6: 5,8 => CTR => H6: 2,4,7 * INC # H6: 2,4,7 => UNS * DIS # I6: 5,8 => CTR => I6: 2,4 * INC # I6: 2,4 => UNS * DIS # F3: 5,8 => CTR => F3: 6 * INC # F3: 6 => UNS * DIS # C9: 2,4 => CTR => C9: 7,9 * INC # C9: 7,9 => UNS * INC # C6: 2,4 => UNS * INC # C6: 5,7 => UNS * DIS # C9: 4,9 => CTR => C9: 2,7 * INC # C9: 2,7 => UNS * INC # F8: 4,9 => UNS * DIS # F8: 1 => CTR => F8: 4,9 * DIS # A5: 4,9 => CTR => A5: 1,7 * INC # A5: 1,7 => UNS * INC # B9: 2,9 => UNS * DIS # C9: 2,9 => CTR => C9: 4,7 * INC # C9: 4,7 => UNS * INC # G1: 5,8 => UNS * DIS # G5: 5,8 => CTR => G5: 1,7 * INC # G5: 1,7 => UNS * INC # I5: 5,8 => UNS * DIS # I6: 5,8 => CTR => I6: 2,4 * INC # I6: 2,4 => UNS * INC # H9: 1,4 => UNS * DIS # H9: 6 => CTR => H9: 1,4 * DIS # F8: 1,4 => CTR => F8: 9 * INC # F8: 9 => UNS * INC # H9: 4,6 => UNS * DIS # H9: 1 => CTR => H9: 4,6 * CNT 56 HDP CHAINS / 56 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # B1: 3,5 => SOL * STA B1: 3,5 * CNT 1 HDP CHAINS / 1 HYP OPENED