Analysis of zz-sudoku-de-652632-base.sdk
Contents
Original Sudoku
level: medium
position: .4...197...8....15....7.3.4...51...8.9.....3.8...63...6.3.2....52....4...793...2. initial
Autosolve
position: .45..197.7.8....1591..75384...51...819....53.85..631..683124759521...463479356821 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C5: 4,7 => CTR => C5: 2,6 * DIS # D2: 2,9 => CTR => D2: 4,6 * PRF # D1: 2,6 => SOL * DIS # D1: 8 => CTR => D1: 2,6 * DIS # D2: 2,6 => CTR => D2: 4,9 * PRF # D1: 2,6 => SOL * DIS # D1: 8 => CTR => D1: 2,6 * PRF # I5: 7 => SOL * DIS # D2: 2,6 => CTR => D2: 4,9 * DIS # C5: 4,7 => CTR => C5: 2,6 * DIS # D6: 2,4 => CTR => D6: 7,9 * DIS # F8: 7,9 => CTR => F8: 8 * PRF # I5: 7 => SOL * DIS # D6: 2,7 => CTR => D6: 4,9 * PRF # I5: 2,7 => SOL * DIS # I5: 6 => CTR => I5: 2,7 * DIS # D6: 2,7 => CTR => D6: 4,9 * DIS # D8: 8,9 => CTR => D8: 7 * CNT 18 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C5: 4,7 => CTR => C5: 2,6 * DIS C5: 2,6 # D2: 2,9 => CTR => D2: 4,6 * PRF C5: 2,6 + D2: 4,6 # D1: 2,6 => SOL * STA C5: 2,6 + D2: 4,6 + D1: 2,6 * CNT 3 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .4...197...8....15....7.3.4...51...8.9.....3.8...63...6.3.2....52....4...793...2. | initial |
| .45..197.7.8....1591..75384...51...819....53.85..631..683124759521...463479356821 | autosolve |
| 345281976768439215912675384234517698196842537857963142683124759521798463479356821 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) A1: 2,3 B2: 3,6 C3: 2,6 E1: 3,8 F2: 2,9 D3: 2,6 I1: 2,6 G2: 2,6 A4: 2,3 B4: 3,6 C4: 4,7 F4: 7,9 E5: 4,8 G4: 2,6 H4: 4,9 H6: 4,9 I6: 2,7 E8: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,C3: 2.. / A1 = 2 => 0 pairs (X) / C3 = 2 => 0 pairs (_) I1,G2: 2.. / I1 = 2 => 0 pairs (X) / G2 = 2 => 0 pairs (_) C3,D3: 2.. / C3 = 2 => 0 pairs (*) / D3 = 2 => 0 pairs (X) A4,G4: 2.. / A4 = 2 => 0 pairs (*) / G4 = 2 => 0 pairs (X) A1,A4: 2.. / A1 = 2 => 0 pairs (X) / A4 = 2 => 0 pairs (_) F2,F5: 2.. / F2 = 2 => 0 pairs (X) / F5 = 2 => 17 pairs (_) G2,G4: 2.. / G2 = 2 => 0 pairs (*) / G4 = 2 => 0 pairs (X) A1,B2: 3.. / A1 = 3 => 0 pairs (*) / B2 = 3 => 0 pairs (X) E1,E2: 3.. / E1 = 3 => 0 pairs (X) / E2 = 3 => 0 pairs (_) A4,B4: 3.. / A4 = 3 => 0 pairs (X) / B4 = 3 => 0 pairs (_) A1,E1: 3.. / A1 = 3 => 0 pairs (*) / E1 = 3 => 0 pairs (X) B2,E2: 3.. / B2 = 3 => 0 pairs (X) / E2 = 3 => 0 pairs (_) A1,A4: 3.. / A1 = 3 => 0 pairs (*) / A4 = 3 => 0 pairs (X) B2,B4: 3.. / B2 = 3 => 0 pairs (X) / B4 = 3 => 0 pairs (_) D2,E2: 4.. / D2 = 4 => 18 pairs (_) / E2 = 4 => 0 pairs (X) H4,H6: 4.. / H4 = 4 => 0 pairs (X) / H6 = 4 => 19 pairs (_) C4,H4: 4.. / C4 = 4 => 19 pairs (_) / H4 = 4 => 0 pairs (X) E2,E5: 4.. / E2 = 4 => 0 pairs (X) / E5 = 4 => 18 pairs (_) B2,C3: 6.. / B2 = 6 => 0 pairs (*) / C3 = 6 => 0 pairs (X) I1,G2: 6.. / I1 = 6 => 0 pairs (*) / G2 = 6 => 0 pairs (X) B4,C5: 6.. / B4 = 6 => 0 pairs (X) / C5 = 6 => 0 pairs (_) G4,I5: 6.. / G4 = 6 => 0 pairs (*) / I5 = 6 => 0 pairs (X) D1,I1: 6.. / D1 = 6 => 0 pairs (X) / I1 = 6 => 0 pairs (_) C3,D3: 6.. / C3 = 6 => 0 pairs (X) / D3 = 6 => 0 pairs (_) B4,G4: 6.. / B4 = 6 => 0 pairs (X) / G4 = 6 => 0 pairs (_) C5,I5: 6.. / C5 = 6 => 0 pairs (*) / I5 = 6 => 0 pairs (X) B2,B4: 6.. / B2 = 6 => 0 pairs (*) / B4 = 6 => 0 pairs (X) C3,C5: 6.. / C3 = 6 => 0 pairs (X) / C5 = 6 => 0 pairs (_) G2,G4: 6.. / G2 = 6 => 0 pairs (X) / G4 = 6 => 0 pairs (_) I1,I5: 6.. / I1 = 6 => 0 pairs (*) / I5 = 6 => 0 pairs (X) I5,I6: 7.. / I5 = 7 => 0 pairs (*) / I6 = 7 => 0 pairs (X) D8,F8: 7.. / D8 = 7 => 19 pairs (_) / F8 = 7 => 0 pairs (X) C4,F4: 7.. / C4 = 7 => 0 pairs (X) / F4 = 7 => 19 pairs (_) D1,E1: 8.. / D1 = 8 => 0 pairs (X) / E1 = 8 => 0 pairs (_) F5,F8: 8.. / F5 = 8 => 0 pairs (X) / F8 = 8 => 19 pairs (_) F4,D6: 9.. / F4 = 9 => 0 pairs (X) / D6 = 9 => 19 pairs (_) H4,H6: 9.. / H4 = 9 => 19 pairs (_) / H6 = 9 => 0 pairs (X) F4,H4: 9.. / F4 = 9 => 0 pairs (X) / H4 = 9 => 19 pairs (_) D6,H6: 9.. / D6 = 9 => 19 pairs (_) / H6 = 9 => 0 pairs (X) E2,E8: 9.. / E2 = 9 => 0 pairs (X) / E8 = 9 => 20 pairs (_) * DURATION: 0:01:06.709378 START: 07:38:08.700769 END: 07:39:15.410147 2017-05-01 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B2,B4,C3,C4,D3,E1,E5,E8,F2,F4,G2,G4,H4,H6,I1,I6) * .45..197.7.8....1591..75384...51...819....53.85..631..683124759521...463479356821 * PAIR C3: 2,6 COL C C5: 2,6,4,7 # reduction candidate for 2,6 C5: 4,7 => CTR * .45..197.7.8....15916275384.6.51.2.819....53.85..631..683124759521...463479356821 C5: 2,6 # 20 pairs * PAIR F2: 2,9 BLK 2 D2: 2,9,4,6 # reduction candidate for 2,9 D2: 2,9 => CTR * .458319767.8.4..1591..75384...51...819..8.53.85..631..683124759521.98463479356821 D2: 4,6 # 19 pairs * PAIR D3: 2,6 BLK 2 D1: 2,6,8 # reduction candidate for 2,6 D1: 2,6 => SOLVED * 345281976768439215912675384234517698196842537857963142683124759521798463479356821 D1: 8 => CTR * .45831976738649215916275384...51...819....53.85..631..683124759521...463479356821 D2: 2,6,4,9 # reduction candidate for 2,6 D2: 2,6 => CTR * .45831976738649215916275384...517.9819..8253.85.96314.683124759521798463479356821 D2: 4,9 # 19 pairs * PAIR I1: 2,6 ROW 1 D1: 2,6,8 # reduction candidate for 2,6 D1: 2,6 => SOLVED * 345281976768439215912675384234517698196842537857963142683124759521798463479356821 D1: 8 => CTR * .45831976738649215916275384...51...819....53.85..631..683124759521...463479356821 * PAIR I1: 2,6 COL I I5: 2,6,7 # reduction candidate for 2,6 I5: 7 => SOLVED * 345281976768439215912675384234517698196842537857963142683124759521798463479356821 I5: 2,6 # 19 pairs * PAIR G2: 2,6 ROW 2 D2: 2,6,4,9 # reduction candidate for 2,6 D2: 2,6 => CTR * .45831976738649215916275384...517.9819..8253.85.96314.683124759521798463479356821 D2: 4,9 # 19 pairs * PAIR C4: 4,7 BLK 4 C5: 4,7,2,6 # reduction candidate for 4,7 C5: 4,7 => CTR * .45..197.7.8....15916275384.6.51.2.819....53.85..631..683124759521...463479356821 C5: 2,6 # 20 pairs C6: 4,7,2 # reduction candidate for 4,7 C6: 4,7 # 20 pairs * PAIR F4: 7,9 BLK 5 D6: 7,9,2,4 # reduction candidate for 7,9 D6: 2,4 => CTR * .45..197.7.8..261591..75384...519.4819....53.85..6319.683124759521...463479356821 D6: 7,9 # 22 pairs * PAIR F4: 7,9 COL F F8: 7,9,8 # reduction candidate for 7,9 F8: 7,9 => CTR * .45..197.7.8..261591..75384...51...819...853.85..631..683124759521...463479356821 F8: 8 # 19 pairs * PAIR E5: 4,8 BLK 5 D5: 4,8,2,7 # reduction candidate for 4,8 D5: 4,8 # 21 pairs D5: 2,7 # 19 pairs * PAIR G4: 2,6 BLK 6 I5: 2,6,7 # reduction candidate for 2,6 I5: 7 => SOLVED * 345281976768439215912675384234517698196842537857963142683124759521798463479356821 I5: 2,6 # 19 pairs * PAIR H6: 4,9 ROW 6 D6: 4,9,2,7 # reduction candidate for 4,9 D6: 2,7 => CTR * .45..197.7.8..261591..75384...519.4819....53.854.6319.683124759521...463479356821 D6: 4,9 # 21 pairs * PAIR I6: 2,7 BLK 6 I5: 2,7,6 # reduction candidate for 2,7 I5: 2,7 => SOLVED * 345281976768439215912675384234517698196842537857963142683124759521798463479356821 I5: 6 => CTR * .456819727.8.3.61591..75384...51...819....53685..631.7683124759521...463479356821 * PAIR I6: 2,7 ROW 6 C6: 2,7,4 # reduction candidate for 2,7 C6: 2,7 # 21 pairs D6: 2,7,4,9 # reduction candidate for 2,7 D6: 2,7 => CTR * .45..197.7.8..261591..75384...519.4819....53.854.6319.683124759521...463479356821 D6: 4,9 # 21 pairs * PAIR E8: 8,9 BLK 8 D8: 8,9,7 # reduction candidate for 8,9 D8: 8,9 => CTR * .45..197.7.8..261591..75384..7519.4819...853.85..6319.683124759521..7463479356821 D8: 7 # 19 pairs F8: 8,9,7 # reduction candidate for 8,9 F8: 8,9 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-652632-base-pr-000.dot * REASONING * DIS # C5: 4,7 => CTR => C5: 2,6 * DIS # D2: 2,9 => CTR => D2: 4,6 * PRF # D1: 2,6 => SOL * DIS # D1: 8 => CTR => D1: 2,6 * DIS # D2: 2,6 => CTR => D2: 4,9 * PRF # D1: 2,6 => SOL * DIS # D1: 8 => CTR => D1: 2,6 * PRF # I5: 7 => SOL * DIS # D2: 2,6 => CTR => D2: 4,9 * DIS # C5: 4,7 => CTR => C5: 2,6 * DIS # D6: 2,4 => CTR => D6: 7,9 * DIS # F8: 7,9 => CTR => F8: 8 * PRF # I5: 7 => SOL * DIS # D6: 2,7 => CTR => D6: 4,9 * PRF # I5: 2,7 => SOL * DIS # I5: 6 => CTR => I5: 2,7 * DIS # D6: 2,7 => CTR => D6: 4,9 * DIS # D8: 8,9 => CTR => D8: 7 * CNT 18 HDP CHAINS / 35 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B2,B4,C3,C4,D3,E1,E5,E8,F2,F4,G2,G4,H4,H6,I1,I6) * .45..197.7.8....1591..75384...51...819....53.85..631..683124759521...463479356821 * PAIR C3: 2,6 COL C C5: 2,6,4,7 # reduction candidate for 2,6 C5: 4,7 => CTR * .45..197.7.8....15916275384.6.51.2.819....53.85..631..683124759521...463479356821 * PAIR RESTART * PAIR F2: 2,9 BLK 2 D2: 2,9,4,6 # reduction candidate for 2,9 D2: 2,9 => CTR * .458319767.8.4..1591..75384...51...819.48.53.85..631..683124759521.98463479356821 * PAIR D3: 2,6 BLK 2 D1: 2,6,8 # reduction candidate for 2,6 D1: 2,6 => SOLVED * 345281976768439215912675384234517698196842537857963142683124759521798463479356821 * DURATION: 0:00:06.012108 START: 07:39:49.674298 END: 07:39:55.686406 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-652632-base-pr-001.dot * REASONING * DIS # C5: 4,7 => CTR => C5: 2,6 * DIS C5: 2,6 # D2: 2,9 => CTR => D2: 4,6 * PRF C5: 2,6 + D2: 4,6 # D1: 2,6 => SOL * STA C5: 2,6 + D2: 4,6 + D1: 2,6 * CNT 3 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.sudokus.de/652632.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: .45..197.7.8....1591..75384...51...819....53.85..631..683124759521...463479356821 A1: 2,3 B2: 3,6 C3: 2,6 C5: 2,4,6,7 # reduction candidate for 2,6 C5: 4,7 => CTR * .45..197.7.8....15916275384.6.51.2.819....53.85..631..683124759521...463479356821 E1: 3,8 F2: 2,9 D2: 2,4,6,9 # reduction candidate for 2,9 D2: 2,9 => CTR * .458319767.8.4..1591..75384...51...819.48.53.85..631..683124759521.98463479356821 D3: 2,6 D1: 2,6,8 # reduction candidate for 2,6 D1: 2,6 => SOLVED * 345281976768439215912675384234517698196842537857963142683124759521798463479356821 * SOLVED! -------------------------------------------------- * AUTO .. A2 = 7 # set value H3 = 8 # set value B7 = 8 # set value C8 = 1 # set value A9: 4 # naked single I8 = 3 # set value A9 = 4 # set value A3: 9.. # hidden single D7: 1.. # hidden single G9: 8.. # hidden single A3 = 9 # set value D7 = 1 # set value G9 = 8 # set value E9: 5 # naked single B3: 1.. # hidden single F7: 4.. # hidden single I9: 1.. # hidden single A5: 1.. # hidden single B3 = 1 # set value B6: 5 # naked single A5 = 1 # set value B6 = 5 # set value F7 = 4 # set value E9 = 5 # set value F9: 6 # naked single F9 = 6 # set value I9: 1 # naked single I9 = 1 # set value F3: 5.. # hidden single G6: 1.. # hidden single G5: 5.. # hidden single H8: 6.. # hidden single C1: 5.. # hidden single H7: 5.. # hidden single C1 = 5 # set value F3 = 5 # set value G5 = 5 # set value G7: 7 # naked single G6 = 1 # set value G7 = 7 # set value I7: 9 # naked single H7 = 5 # set value I7 = 9 # set value H8: 6 # naked single H8 = 6 # set value C4,F4,H4: 4,7,9.. => C4,F4 != 2,6 # hidden triple * UNSOLVED! |:step:| 00 -------------------------------------------------- highlight 6 xwing B2: 3,6 G2: 2,6 B4: 3,6 G4: 2,6 * DISABLE VALUE:: D2 != 6 |:step:| 01 -------------------------------------------------- highlight 3 A1: 2,3 E2: 3,4,9 B4: 3,6 E1: 3,8 B2: 3,6 A4: 2,3 A1,E2,B4 = 3 => E1,B2,A4 != 3 # forced chain E1 = 3 => E2 = 4,9 & ... => A1 = 2 => D1,I1 != 2 => I1 = 6 => D1 = 8 & G2 = 2 => D2,F2 != 2 => F2 = 9 => D2,E2 != 9 => D2,E2 = 4 => CTR * CTR! => E1 != 3 & ... * AUTO .. * SOLVED! |:step:| 02 --------------------------------------------------
Solution
position: 345281976768439215912675384234517698196842537857963142683124759521798463479356821 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 # C5: 2,6 => UNS * DIS # C5: 4,7 => CTR => C5: 2,6 * DIS # D2: 2,9 => CTR => D2: 4,6 * INC # D2: 4,6 => UNS * PRF # D1: 2,6 => SOL * DIS # D1: 8 => CTR => D1: 2,6 * DIS # D2: 2,6 => CTR => D2: 4,9 * INC # D2: 4,9 => UNS * PRF # D1: 2,6 => SOL * DIS # D1: 8 => CTR => D1: 2,6 * INC # I5: 2,6 => UNS * PRF # I5: 7 => SOL * DIS # D2: 2,6 => CTR => D2: 4,9 * INC # D2: 4,9 => UNS * DIS # C5: 4,7 => CTR => C5: 2,6 * INC # C5: 2,6 => UNS * INC # C6: 4,7 => UNS * INC # D6: 7,9 => UNS * DIS # D6: 2,4 => CTR => D6: 7,9 * DIS # F8: 7,9 => CTR => F8: 8 * INC # F8: 8 => UNS * INC # D5: 4,8 => UNS * INC # D5: 2,7 => UNS * INC # I5: 2,6 => UNS * PRF # I5: 7 => SOL * INC # D6: 4,9 => UNS * DIS # D6: 2,7 => CTR => D6: 4,9 * PRF # I5: 2,7 => SOL * DIS # I5: 6 => CTR => I5: 2,7 * INC # C6: 2,7 => UNS * DIS # D6: 2,7 => CTR => D6: 4,9 * INC # D6: 4,9 => UNS * DIS # D8: 8,9 => CTR => D8: 7 * INC # D8: 7 => UNS * INC # F8: 8,9 => UNS * CNT 35 HDP CHAINS / 35 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C5: 2,6 => UNS * DIS # C5: 4,7 => CTR => C5: 2,6 * DIS C5: 2,6 # D2: 2,9 => CTR => D2: 4,6 * PRF C5: 2,6 + D2: 4,6 # D1: 2,6 => SOL * STA C5: 2,6 + D2: 4,6 + D1: 2,6 * CNT 4 HDP CHAINS / 4 HYP OPENED