Analysis of zz-sudoku-de-697744-base.sdk
Contents
Original Sudoku
level: medium
position: .6.2.4.7.3..9.7..8.4..1..5...5...8..63.....91..7...3...7..9..8.8..4.2..6.1.5.6.3. initial
Autosolve
position: .682.417.3.19.7..874..1..5...5...8..63.....91.87...3...76.9..8.8.3472.16.1.586.3. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # G3: 2,9 => SOL * DIS # G3: 6 => CTR => G3: 2,9 * DIS # I3: 2,9 => CTR => I3: 3 * PRF # I3: 3 => SOL * DIS # C9: 4 => CTR => C9: 2,9 * DIS # D3: 3,8 => CTR => D3: 6 * PRF # D3: 6 => SOL * DIS # I3: 2 => CTR => I3: 3,9 * DIS # G2: 2,4 => CTR => G2: 6 * PRF # G2: 6 => SOL * DIS # A4: 2,9 => CTR => A4: 1,4 * DIS # A4: 2,4 => CTR => A4: 1,9 * PRF # A6: 2,4 => SOL * PRF # C9: 2,4 => SOL * DIS # C9: 9 => CTR => C9: 2,4 * DIS # E4: 2,4 => CTR => E4: 3,6 * DIS # D4: 1,6 => CTR => D4: 3,7 * DIS # D4: 1,3 => CTR => D4: 6,7 * DIS # F4: 9 => CTR => F4: 1,3 * CNT 19 HDP CHAINS / 32 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # G3: 2,9 => SOL * STA G3: 2,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .6.2.4.7.3..9.7..8.4..1..5...5...8..63.....91..7...3...7..9..8.8..4.2..6.1.5.6.3. | initial |
| .682.417.3.19.7..874..1..5...5...8..63.....91.87...3...76.9..8.8.3472.16.1.586.3. | autosolve |
| 568234179321957648749618253195763824634825791287149365476391582853472916912586437 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) A1: 5,9 B2: 2,5 C3: 2,9 E1: 3,5 E2: 5,6 F3: 3,8 I1: 3,9 H2: 2,4 B4: 2,9 C5: 2,4 D5: 7,8 E5: 2,4 F5: 5,8 D6: 1,6 G5: 5,7 B8: 5,9 D7: 1,3 F7: 1,3 G8: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A4,A6: 1.. / A4 = 1 => 20 pairs (_) / A6 = 1 => 0 pairs (X) D7,F7: 1.. / D7 = 1 => 0 pairs (X) / F7 = 1 => 20 pairs (_) B2,C3: 2.. / B2 = 2 => 0 pairs (*) / C3 = 2 => 0 pairs (X) C5,E5: 2.. / C5 = 2 => 0 pairs (X) / E5 = 2 => 19 pairs (_) B2,B4: 2.. / B2 = 2 => 0 pairs (*) / B4 = 2 => 0 pairs (X) I1,I3: 3.. / I1 = 3 => 0 pairs (X) / I3 = 3 => 0 pairs (_) D7,F7: 3.. / D7 = 3 => 20 pairs (_) / F7 = 3 => 0 pairs (X) E1,I1: 3.. / E1 = 3 => 0 pairs (*) / I1 = 3 => 0 pairs (X) E1,E4: 3.. / E1 = 3 => 0 pairs (*) / E4 = 3 => 0 pairs (X) G2,H2: 4.. / G2 = 4 => 0 pairs (X) / H2 = 4 => 24 pairs (_) C5,E5: 4.. / C5 = 4 => 19 pairs (_) / E5 = 4 => 0 pairs (X) C5,C9: 4.. / C5 = 4 => 19 pairs (_) / C9 = 4 => 0 pairs (X) A1,B2: 5.. / A1 = 5 => 0 pairs (*) / B2 = 5 => 0 pairs (X) E1,E2: 5.. / E1 = 5 => 0 pairs (X) / E2 = 5 => 0 pairs (_) F5,F6: 5.. / F5 = 5 => 21 pairs (_) / F6 = 5 => 0 pairs (X) G5,I6: 5.. / G5 = 5 => 0 pairs (X) / I6 = 5 => 21 pairs (_) A7,B8: 5.. / A7 = 5 => 0 pairs (X) / B8 = 5 => 0 pairs (_) A1,E1: 5.. / A1 = 5 => 0 pairs (*) / E1 = 5 => 0 pairs (X) B2,E2: 5.. / B2 = 5 => 0 pairs (X) / E2 = 5 => 0 pairs (_) F5,G5: 5.. / F5 = 5 => 21 pairs (_) / G5 = 5 => 0 pairs (X) F6,I6: 5.. / F6 = 5 => 0 pairs (X) / I6 = 5 => 21 pairs (_) B8,G8: 5.. / B8 = 5 => 0 pairs (*) / G8 = 5 => 0 pairs (X) A1,A7: 5.. / A1 = 5 => 0 pairs (*) / A7 = 5 => 0 pairs (X) B2,B8: 5.. / B2 = 5 => 0 pairs (X) / B8 = 5 => 0 pairs (_) I6,I7: 5.. / I6 = 5 => 21 pairs (_) / I7 = 5 => 0 pairs (X) E2,D3: 6.. / E2 = 6 => 0 pairs (X) / D3 = 6 => 0 pairs (_) G2,G3: 6.. / G2 = 6 => 0 pairs (*) / G3 = 6 => 0 pairs (X) H4,H6: 6.. / H4 = 6 => 20 pairs (_) / H6 = 6 => 24 pairs (_) E2,G2: 6.. / E2 = 6 => 0 pairs (X) / G2 = 6 => 0 pairs (_) D3,G3: 6.. / D3 = 6 => 0 pairs (*) / G3 = 6 => 0 pairs (X) D4,D5: 7.. / D4 = 7 => 21 pairs (_) / D5 = 7 => 0 pairs (X) I4,G5: 7.. / I4 = 7 => 0 pairs (X) / G5 = 7 => 21 pairs (_) G9,I9: 7.. / G9 = 7 => 0 pairs (X) / I9 = 7 => 21 pairs (_) D4,I4: 7.. / D4 = 7 => 21 pairs (_) / I4 = 7 => 0 pairs (X) D5,G5: 7.. / D5 = 7 => 0 pairs (X) / G5 = 7 => 21 pairs (_) G5,G9: 7.. / G5 = 7 => 21 pairs (_) / G9 = 7 => 0 pairs (X) I4,I9: 7.. / I4 = 7 => 0 pairs (X) / I9 = 7 => 21 pairs (_) D3,F3: 8.. / D3 = 8 => 0 pairs (X) / F3 = 8 => 21 pairs (_) D5,F5: 8.. / D5 = 8 => 21 pairs (_) / F5 = 8 => 0 pairs (X) D3,D5: 8.. / D3 = 8 => 0 pairs (X) / D5 = 8 => 21 pairs (_) F3,F5: 8.. / F3 = 8 => 21 pairs (_) / F5 = 8 => 0 pairs (X) A1,C3: 9.. / A1 = 9 => 0 pairs (X) / C3 = 9 => 0 pairs (_) F4,F6: 9.. / F4 = 9 => 0 pairs (X) / F6 = 9 => 21 pairs (_) A1,I1: 9.. / A1 = 9 => 0 pairs (X) / I1 = 9 => 0 pairs (_) A6,F6: 9.. / A6 = 9 => 0 pairs (X) / F6 = 9 => 21 pairs (_) B8,G8: 9.. / B8 = 9 => 0 pairs (X) / G8 = 9 => 0 pairs (_) B4,B8: 9.. / B4 = 9 => 0 pairs (*) / B8 = 9 => 0 pairs (X) C3,C9: 9.. / C3 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) * DURATION: 0:01:16.012117 START: 07:55:12.155782 END: 07:56:28.167899 2017-05-01 * CP COUNT: (48) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B2,B4,B8,C3,C5,D5,D6,D7,E1,E2,E5,F3,F5,F7,G5,G8,H2,I1) * .682.417.3.19.7..874..1..5...5...8..63.....91.87...3...76.9..8.8.3472.16.1.586.3. * PAIR C3: 2,9 ROW 3 G3: 2,9,6 # reduction candidate for 2,9 G3: 2,9 => SOLVED * 568234179321957648749618253195763824634825791287149365476391582853472916912586437 G3: 6 => CTR * .68254173351967..8742.1.659.25.3.8..634.2..91.87.4.3..576.9..8.893472.16.1.586.3. I3: 2,9,3 # reduction candidate for 2,9 I3: 2,9 => CTR * 968254173351967..8742.1.659..5.3.8..63.....91.87...3...76.9..8.8.3472.16.1.586.3. I3: 3 => SOLVED * 568234179321957648749618253195763824634825791287149365476391582853472916912586437 * PAIR C3: 2,9 COL C C9: 2,9,4 # reduction candidate for 2,9 C9: 4 => CTR * 568234179321957648749618253.95...8..632845791.871.93.5276.9..8.8.3472.16.14586.3. C9: 2,9 # 19 pairs * PAIR F3: 3,8 BLK 2 D3: 3,8,6 # reduction candidate for 3,8 D3: 3,8 => CTR * .68254173351967..8742.1.659.25.3.8..634.2..91.87.4.3..576.9..8.893472.16.1.586.3. D3: 6 => SOLVED * 568234179321957648749618253195763824634825791287149365476391582853472916912586437 * PAIR I1: 3,9 BLK 3 I3: 3,9,2 # reduction candidate for 3,9 I3: 2 => CTR * .682.41733.19.7..874..1.952..5...8..63.....91.87...3...76.9..8.8.3472.16.1.586.3. I3: 3,9 # 21 pairs * PAIR H2: 2,4 BLK 3 G2: 2,4,6 # reduction candidate for 2,4 G2: 2,4 => CTR * .68254173351967..8742.1.659.25.3.8..634.2..91.87.4.3..576.9..8.893472.16.1.586.3. G2: 6 => SOLVED * 568234179321957648749618253195763824634825791287149365476391582853472916912586437 * PAIR H2: 2,4 COL H H4: 2,4,6 # reduction candidate for 2,4 H4: 2,4 # 24 pairs H6: 2,4,6 # reduction candidate for 2,4 H6: 2,4 # 20 pairs * PAIR B4: 2,9 BLK 4 A4: 2,9,1,4 # reduction candidate for 2,9 A4: 2,9 => CTR * .68254173351967248742.18659.25731864634825791187649325576193482893472.16.1.586.37 A4: 1,4 # 20 pairs A6: 2,9,1,4 # reduction candidate for 2,9 A6: 2,9 # 21 pairs * PAIR C5: 2,4 BLK 4 A4: 2,4,1,9 # reduction candidate for 2,4 A4: 2,4 => CTR * .682.417.3.1967..874..1.65..95...86.63...57911876.93.5.76.9..8.853472.16.1.586.3. A4: 1,9 # 20 pairs A6: 2,4,1,9 # reduction candidate for 2,4 A6: 2,4 => SOLVED * 568234179321957648749618253195763824634825791287149365476391582853472916912586437 A6: 1,9 # 20 pairs * PAIR C5: 2,4 COL C C9: 2,4,9 # reduction candidate for 2,4 C9: 2,4 => SOLVED * 568234179321957648749618253195763824634825791287149365476391582853472916912586437 C9: 9 => CTR * 9682541733519.7..874..1..5...5...8..634.2..91.87...3...76.9..8.8.3472.16.19586.3. * PAIR E5: 2,4 BLK 5 E4: 2,4,3,6 # reduction candidate for 2,4 E4: 2,4 => CTR * 568234179321957648749618253195...86.63.8.5791.87169325.76391.8.85347291691.586437 E4: 3,6 # 21 pairs E6: 2,4,6 # reduction candidate for 2,4 E6: 2,4 # 21 pairs * PAIR D6: 1,6 BLK 5 D4: 1,6,3,7 # reduction candidate for 1,6 D4: 1,6 => CTR * 56823417.3.19.7..874..1..5...5...8.763.7.8591.87..53...76.9..85853472916.1.58673. D4: 3,7 # 20 pairs * PAIR D7: 1,3 COL D D4: 1,3,6,7 # reduction candidate for 1,3 D4: 1,3 => CTR * 56823417.3.19.7..874..1..5...5...8.763.7.8591.87..53...76.9..85853472916.1.58673. D4: 6,7 # 20 pairs * PAIR F7: 1,3 COL F F4: 1,3,9 # reduction candidate for 1,3 F4: 9 => CTR * 5682341793219.7..874..1..5...5..98..63.....91987...3...76.9..8.893472516.1.586.3. F4: 1,3 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-697744-base-pr-000.dot * REASONING * PRF # G3: 2,9 => SOL * DIS # G3: 6 => CTR => G3: 2,9 * DIS # I3: 2,9 => CTR => I3: 3 * PRF # I3: 3 => SOL * DIS # C9: 4 => CTR => C9: 2,9 * DIS # D3: 3,8 => CTR => D3: 6 * PRF # D3: 6 => SOL * DIS # I3: 2 => CTR => I3: 3,9 * DIS # G2: 2,4 => CTR => G2: 6 * PRF # G2: 6 => SOL * DIS # A4: 2,9 => CTR => A4: 1,4 * DIS # A4: 2,4 => CTR => A4: 1,9 * PRF # A6: 2,4 => SOL * PRF # C9: 2,4 => SOL * DIS # C9: 9 => CTR => C9: 2,4 * DIS # E4: 2,4 => CTR => E4: 3,6 * DIS # D4: 1,6 => CTR => D4: 3,7 * DIS # D4: 1,3 => CTR => D4: 6,7 * DIS # F4: 9 => CTR => F4: 1,3 * CNT 19 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B2,B4,B8,C3,C5,D5,D6,D7,E1,E2,E5,F3,F5,F7,G5,G8,H2,I1) * .682.417.3.19.7..874..1..5...5...8..63.....91.87...3...76.9..8.8.3472.16.1.586.3. * PAIR C3: 2,9 ROW 3 G3: 2,9,6 # reduction candidate for 2,9 G3: 2,9 => SOLVED * 568234179321957648749618253195763824634825791287149365476391582853472916912586437 * DURATION: 0:00:02.307301 START: 07:56:59.589552 END: 07:57:01.896853 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-697744-base-pr-001.dot * REASONING * PRF # G3: 2,9 => SOL * STA G3: 2,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokus.de/697744.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: .682.417.3.19.7..874..1..5...5...8..63.....91.87...3...76.9..8.8.3472.16.1.586.3. A1: 5,9 B2: 2,5 C3: 2,9 G3: 2,6,9 # reduction candidate for 2,9 G3: 2,9 => SOLVED * 568234179321957648749618253195763824634825791287149365476391582853472916912586437 * SOLVED! -------------------------------------------------- -------------------------------------------------- * AUTO .. A3 = 7 # set value B6 = 8 # set value C7 = 6 # set value H8 = 1 # set value E9 = 8 # set value C8: 3.. # hidden single E8: 7.. # hidden single C1: 8.. # hidden single C1 = 8 # set value C8 = 3 # set value E8: 7 # naked single E8 = 7 # set value C2: 1.. # hidden single C2 = 1 # set value G1: 1.. # hidden single G1 = 1 # set value Q2: 5.. = E1,E2: 5.. => E5,E6 != 5 Q6: 6.. = H4,H6: 6.. => H2 != 6 C5,E5: 2,4.. => G5 != 2,4 # naked pair * UNSOLVED! |:step:| 00 -------------------------------------------------- good |:guess:| -------------------------------------------------- highlight 1,3 D7,F7,D4,F4: 1,3.. => D4 = 6,7 or F4 = 9 # pair quad D4 != 6,7 => CTR => F4 != 9 * DISABLE VALUE:: F4 != 9 |:step:| 01 -------------------------------------------------- * AUTO .. A3 = 7 # set value B6 = 8 # set value C7 = 6 # set value H8 = 1 # set value E9 = 8 # set value F6: 9.. # hidden single C8: 3.. # hidden single E8: 7.. # hidden single C1: 8.. # hidden single C1 = 8 # set value F6 = 9 # set value C8 = 3 # set value E8: 7 # naked single E8 = 7 # set value F5: 5.. # hidden single I6: 5.. # hidden single C2: 1.. # hidden single C2 = 1 # set value F5 = 5 # set value G5: 7 # naked single G5 = 7 # set value D5: 8 # naked single I6 = 5 # set value G1: 1.. # hidden single D4: 7.. # hidden single I9: 7.. # hidden single F3: 8.. # hidden single G1 = 1 # set value F3 = 8 # set value D4 = 7 # set value D5 = 8 # set value I9 = 7 # set value Q9: 9.. = G8,G9: 9.. => G3 != 9 I1,I3: 3,9.. => I3 != 2 # hidden pair |:step:| 02 --------------------------------------------------
Solution
position: 568234179321957648749618253195763824634825791287149365476391582853472916912586437 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 # G3: 2,9 => SOL * DIS # G3: 6 => CTR => G3: 2,9 * DIS # I3: 2,9 => CTR => I3: 3 * PRF # I3: 3 => SOL * INC # C9: 2,9 => UNS * DIS # C9: 4 => CTR => C9: 2,9 * DIS # D3: 3,8 => CTR => D3: 6 * PRF # D3: 6 => SOL * INC # I3: 3,9 => UNS * DIS # I3: 2 => CTR => I3: 3,9 * DIS # G2: 2,4 => CTR => G2: 6 * PRF # G2: 6 => SOL * INC # H4: 2,4 => UNS * INC # H6: 2,4 => UNS * DIS # A4: 2,9 => CTR => A4: 1,4 * INC # A4: 1,4 => UNS * INC # A6: 2,9 => UNS * DIS # A4: 2,4 => CTR => A4: 1,9 * INC # A4: 1,9 => UNS * PRF # A6: 2,4 => SOL * INC # A6: 1,9 => UNS * PRF # C9: 2,4 => SOL * DIS # C9: 9 => CTR => C9: 2,4 * DIS # E4: 2,4 => CTR => E4: 3,6 * INC # E4: 3,6 => UNS * INC # E6: 2,4 => UNS * DIS # D4: 1,6 => CTR => D4: 3,7 * INC # D4: 3,7 => UNS * DIS # D4: 1,3 => CTR => D4: 6,7 * INC # D4: 6,7 => UNS * INC # F4: 1,3 => UNS * DIS # F4: 9 => CTR => F4: 1,3 * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # G3: 2,9 => SOL * STA G3: 2,9 * CNT 1 HDP CHAINS / 1 HYP OPENED