Analysis of zz-sudoku-de-709857-base.sdk
Contents
Original Sudoku
level: medium
position: ..57..61.6.....3.9.2..6...4.7...24.....6.8.....69...5.4...7..3.9.1.....8.63..12.. initial
Autosolve
position: ..57..6126....53.9.2..6.5.4.7...24.....6.8.272.69.785.48257..3.951...7.8763..12.5 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A3: 3,8 => SOL * PRF # E1: 3,8 => SOL * DIS # E1: 9 => CTR => E1: 3,8 * PRF # A4: 1,5 => SOL * DIS # D2: 1,4 => CTR => D2: 2,8 * DIS # B5: 1,4 => CTR => B5: 3,9 * PRF # E1: 3,9 => SOL * DIS # E1: 8 => CTR => E1: 3,9 * DIS # F1: 3,9 => CTR => F1: 4 * PRF # C2: 4 => SOL * PRF # C3: 7,8 => SOL * DIS # C3: 9 => CTR => C3: 7,8 * PRF # C3: 7 => SOL * DIS # B5: 4,9 => CTR => B5: 1,3 * PRF # B5: 1,3 => SOL * DIS # E4: 1,3 => CTR => E4: 5 * PRF # E6: 1,3 => SOL * PRF # A4: 1,3 => SOL * DIS # I4: 1,3 => CTR => I4: 6 * PRF # I4: 6 => SOL * DIS # D3: 8 => CTR => D3: 1,3 * PRF # B5: 3,4 => SOL * DIS # I4: 1,3 => CTR => I4: 6 * PRF # I4: 6 => SOL * PRF # E6: 1,3 => SOL * PRF # D8: 4 => SOL * DIS # D2: 4,8 => CTR => D2: 1,2 * PRF # E1: 3 => SOL * DIS # I4: 3 => CTR => I4: 1,6 * PRF # F8: 3 => SOL * CNT 30 HDP CHAINS / 51 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A3: 3,8 => SOL * STA A3: 3,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..57..61.6.....3.9.2..6...4.7...24.....6.8.....69...5.4...7..3.9.1.....8.63..12.. | initial |
| ..57..6126....53.9.2..6.5.4.7...24.....6.8.272.69.785.48257..3.951...7.8763..12.5 | autosolve |
| 895734612614285379327169584178352496539648127246917853482576931951423768763891245 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) A1: 3,8 B2: 1,4 F3: 3,9 H2: 7,8 H3: 7,8 C4: 8,9 C5: 4,9 D4: 1,3 H4: 6,9 G5: 1,9 I6: 1,3 F7: 6,9 E8: 2,3 D9: 4,8 E9: 8,9 G7: 1,9 I7: 1,6 H8: 4,6 H9: 4,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,A3: 1.. / B2 = 1 => 0 pairs (*) / A3 = 1 => 0 pairs (X) G7,I7: 1.. / G7 = 1 => 0 pairs (X) / I7 = 1 => 0 pairs (_) A3,D3: 1.. / A3 = 1 => 26 pairs (_) / D3 = 1 => 0 pairs (*) G5,G7: 1.. / G5 = 1 => 0 pairs (*) / G7 = 1 => 0 pairs (X) D2,E2: 2.. / D2 = 2 => 22 pairs (_) / E2 = 2 => 0 pairs (X) D8,E8: 2.. / D8 = 2 => 0 pairs (X) / E8 = 2 => 22 pairs (_) D2,D8: 2.. / D2 = 2 => 22 pairs (_) / D8 = 2 => 0 pairs (X) E2,E8: 2.. / E2 = 2 => 0 pairs (X) / E8 = 2 => 22 pairs (_) I4,I6: 3.. / I4 = 3 => 0 pairs (X) / I6 = 3 => 24 pairs (_) F1,D2: 4.. / F1 = 4 => 21 pairs (_) / D2 = 4 => 0 pairs (X) E5,E6: 4.. / E5 = 4 => 0 pairs (*) / E6 = 4 => 0 pairs (X) H8,H9: 4.. / H8 = 4 => 0 pairs (X) / H9 = 4 => 0 pairs (_) B1,F1: 4.. / B1 = 4 => 0 pairs (X) / F1 = 4 => 21 pairs (_) B6,E6: 4.. / B6 = 4 => 0 pairs (*) / E6 = 4 => 0 pairs (X) D9,H9: 4.. / D9 = 4 => 0 pairs (X) / H9 = 4 => 0 pairs (_) C2,C5: 4.. / C2 = 4 => 0 pairs (*) / C5 = 4 => 0 pairs (X) F1,F8: 4.. / F1 = 4 => 21 pairs (_) / F8 = 4 => 0 pairs (X) A4,A5: 5.. / A4 = 5 => 0 pairs (X) / A5 = 5 => 19 pairs (_) E4,E5: 5.. / E4 = 5 => 19 pairs (_) / E5 = 5 => 0 pairs (X) A4,E4: 5.. / A4 = 5 => 0 pairs (X) / E4 = 5 => 19 pairs (_) A5,E5: 5.. / A5 = 5 => 19 pairs (_) / E5 = 5 => 0 pairs (X) H4,I4: 6.. / H4 = 6 => 0 pairs (X) / I4 = 6 => 0 pairs (_) F7,F8: 6.. / F7 = 6 => 0 pairs (*) / F8 = 6 => 0 pairs (X) I7,H8: 6.. / I7 = 6 => 0 pairs (X) / H8 = 6 => 0 pairs (_) F7,I7: 6.. / F7 = 6 => 0 pairs (*) / I7 = 6 => 0 pairs (X) F8,H8: 6.. / F8 = 6 => 0 pairs (X) / H8 = 6 => 0 pairs (_) H4,H8: 6.. / H4 = 6 => 0 pairs (X) / H8 = 6 => 0 pairs (_) I4,I7: 6.. / I4 = 6 => 0 pairs (*) / I7 = 6 => 0 pairs (X) C2,C3: 7.. / C2 = 7 => 20 pairs (_) / C3 = 7 => 0 pairs (*) H2,H3: 7.. / H2 = 7 => 0 pairs (*) / H3 = 7 => 0 pairs (X) C2,H2: 7.. / C2 = 7 => 20 pairs (_) / H2 = 7 => 0 pairs (*) C3,H3: 7.. / C3 = 7 => 0 pairs (*) / H3 = 7 => 0 pairs (X) H2,H3: 8.. / H2 = 8 => 20 pairs (_) / H3 = 8 => 0 pairs (*) A4,C4: 8.. / A4 = 8 => 0 pairs (X) / C4 = 8 => 0 pairs (_) D9,E9: 8.. / D9 = 8 => 0 pairs (*) / E9 = 8 => 0 pairs (X) A1,E1: 8.. / A1 = 8 => 0 pairs (*) / E1 = 8 => 0 pairs (X) B1,C3: 9.. / B1 = 9 => 0 pairs (*) / C3 = 9 => 0 pairs (X) H4,G5: 9.. / H4 = 9 => 0 pairs (*) / G5 = 9 => 0 pairs (X) F7,E9: 9.. / F7 = 9 => 0 pairs (X) / E9 = 9 => 0 pairs (_) G7,H9: 9.. / G7 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) C3,F3: 9.. / C3 = 9 => 0 pairs (X) / F3 = 9 => 0 pairs (_) C4,H4: 9.. / C4 = 9 => 0 pairs (X) / H4 = 9 => 0 pairs (_) F7,G7: 9.. / F7 = 9 => 0 pairs (X) / G7 = 9 => 0 pairs (_) E9,H9: 9.. / E9 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) B1,B5: 9.. / B1 = 9 => 0 pairs (*) / B5 = 9 => 0 pairs (X) E1,E9: 9.. / E1 = 9 => 0 pairs (X) / E9 = 9 => 0 pairs (_) G5,G7: 9.. / G5 = 9 => 0 pairs (X) / G7 = 9 => 0 pairs (_) H4,H9: 9.. / H4 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) * DURATION: 0:01:19.533961 START: 08:08:21.648776 END: 08:09:41.182737 2017-05-01 * CP COUNT: (48) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B2,C4,C5,D4,D9,E8,E9,F3,F7,G5,G7,H2,H3,H4,H8,H9,I6,I7) * ..57..6126....53.9.2..6.5.4.7...24.....6.8.272.69.785.48257..3.951...7.8763..12.5 * PAIR A1: 3,8 BLK 1 A3: 3,8,1 # reduction candidate for 3,8 A3: 3,8 => SOLVED * 895734612614285379327169584178352496539648127246917853482576931951423768763891245 A3: 1 # 26 pairs * PAIR A1: 3,8 ROW 1 E1: 3,8,9 # reduction candidate for 3,8 E1: 3,8 => SOLVED * 895734612614285379327169584178352496539648127246917853482576931951423768763891245 E1: 9 => CTR * 8.579.6126....53.9.29.63574.78..2496.946.81272.694785348257..3.951...7.8763..12.5 * PAIR A1: 3,8 COL A A4: 3,8,1,5 # reduction candidate for 3,8 A4: 1,5 => SOLVED * 895734612614285379327169584178352496539648127246917853482576931951423768763891245 A4: 3,8 # 27 pairs * PAIR B2: 1,4 ROW 2 D2: 1,4,2,8 # reduction candidate for 1,4 D2: 1,4 => CTR * 8357946126471253.912.863574.7.3.24....46.8.27216947853482579136951236748763481295 D2: 2,8 # 22 pairs * PAIR B2: 1,4 COL B B5: 1,4,3,9 # reduction candidate for 1,4 B5: 1,4 => CTR * .957.46126....53.9.2..695.4.7...24.....6.8.27236947851482576.3.951...7.8763..12.5 B5: 3,9 # 20 pairs B6: 1,4,3 # reduction candidate for 1,4 B6: 1,4 # 23 pairs * PAIR F3: 3,9 BLK 2 E1: 3,9,8 # reduction candidate for 3,9 E1: 3,9 => SOLVED * 895734612614285379327169584178352496539648127246917853482576931951423768763891245 E1: 8 => CTR * 3957846126142.53.9.2..6.5.4.78..2496539648127246917853482576931951...768763891245 F1: 3,9,4 # reduction candidate for 3,9 F1: 3,9 => CTR * .457..61261.4253.9.29163574.783.2496.946.81272369.785.48257..3.951...7.8763..12.5 F1: 4 # 21 pairs * PAIR H2: 7,8 ROW 2 C2: 7,8,4 # reduction candidate for 7,8 C2: 4 => SOLVED * 895734612614285379327169584178352496539648127246917853482576931951423768763891245 C2: 7,8 # 22 pairs * PAIR H3: 7,8 ROW 3 C3: 7,8,9 # reduction candidate for 7,8 C3: 7,8 => SOLVED * 895734612614285379327169584178352496539648127246917853482576931951423768763891245 C3: 9 => CTR * ..57..6126.7..5389.29.63574.78..2496.946.81272.6947853482576931951..4768763891245 * PAIR C4: 8,9 COL C C3: 8,9,7 # reduction candidate for 8,9 C3: 7 => SOLVED * 895734612614285379327169584178352496539648127246917853482576931951423768763891245 C3: 8,9 # 20 pairs * PAIR C5: 4,9 BLK 4 B5: 4,9,1,3 # reduction candidate for 4,9 B5: 4,9 => CTR * .3578.6126....53.9.2..6.5.4.78..2496...6.8127216947853482576931951...768763.91245 B5: 1,3 => SOLVED * 895734612614285379327169584178352496539648127246917853482576931951423768763891245 * PAIR D4: 1,3 BLK 5 E4: 1,3,5 # reduction candidate for 1,3 E4: 1,3 => CTR * ..57..612647..538912986.5.4578..2496...658127216947853482576931951...768763.91245 E4: 5 # 19 pairs E5: 1,3,4,5 # reduction candidate for 1,3 E5: 1,3 # 21 pairs E6: 1,3,4 # reduction candidate for 1,3 E6: 1,3 => SOLVED * 895734612614285379327169584178352496539648127246917853482576931951423768763891245 E6: 4 # 20 pairs * PAIR D4: 1,3 ROW 4 A4: 1,3,5,8 # reduction candidate for 1,3 A4: 1,3 => SOLVED * 895734612614285379327169584178352496539648127246917853482576931951423768763891245 A4: 5,8 # 20 pairs I4: 1,3,6 # reduction candidate for 1,3 I4: 1,3 => CTR * 89573.6126....53.9.2..6.5.4.7...246....6.89272.69.785.482579136951..6748763481295 I4: 6 => SOLVED * 895734612614285379327169584178352496539648127246917853482576931951423768763891245 * PAIR D4: 1,3 COL D D3: 1,3,8 # reduction candidate for 1,3 D3: 8 => CTR * 835794612647..53.912.863574.7...24.....6.8.272.69.785.48257..3.951...7.8763481295 D3: 1,3 # 21 pairs * PAIR G5: 1,9 ROW 5 B5: 1,9,3,4 # reduction candidate for 1,9 B5: 3,4 => SOLVED * 895734612614285379327169584178352496539648127246917853482576931951423768763891245 B5: 1,9 # 29 pairs * PAIR I6: 1,3 BLK 6 I4: 1,3,6 # reduction candidate for 1,3 I4: 1,3 => CTR * 89573.6126....53.9.2..6.5.4.7...246....6.89272.69.785.482579136951..6748763481295 I4: 6 => SOLVED * 895734612614285379327169584178352496539648127246917853482576931951423768763891245 * PAIR I6: 1,3 ROW 6 B6: 1,3,4 # reduction candidate for 1,3 B6: 1,3 # 20 pairs E6: 1,3,4 # reduction candidate for 1,3 E6: 1,3 => SOLVED * 895734612614285379327169584178352496539648127246917853482576931951423768763891245 E6: 4 # 20 pairs * PAIR E8: 2,3 BLK 8 D8: 2,3,4 # reduction candidate for 2,3 D8: 4 => SOLVED * 895734612614285379327169584178352496539648127246917853482576931951423768763891245 D8: 2,3 # 24 pairs * PAIR D9: 4,8 COL D D2: 4,8,1,2 # reduction candidate for 4,8 D2: 4,8 => CTR * ..57.4612614825379.2716.5.4.7.3.24.....6.8.2724691785348257..3.95123.7.8763..12.5 D2: 1,2 # 22 pairs * PAIR E9: 8,9 COL E E1: 8,9,3 # reduction candidate for 8,9 E1: 3 => SOLVED * 895734612614285379327169584178352496539648127246917853482576931951423768763891245 E1: 8,9 # 21 pairs * PAIR I7: 1,6 COL I I4: 1,6,3 # reduction candidate for 1,6 I4: 3 => CTR * 89573.6126....53.9.2..6.5.4.7...2463...6.89272.69.7851482579136951..6748763481295 I4: 1,6 # 24 pairs * PAIR H8: 4,6 ROW 8 F8: 4,6,3 # reduction candidate for 4,6 F8: 3 => SOLVED * 895734612614285379327169584178352496539648127246917853482576931951423768763891245 F8: 4,6 # 24 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-709857-base-pr-000.dot * REASONING * PRF # A3: 3,8 => SOL * PRF # E1: 3,8 => SOL * DIS # E1: 9 => CTR => E1: 3,8 * PRF # A4: 1,5 => SOL * DIS # D2: 1,4 => CTR => D2: 2,8 * DIS # B5: 1,4 => CTR => B5: 3,9 * PRF # E1: 3,9 => SOL * DIS # E1: 8 => CTR => E1: 3,9 * DIS # F1: 3,9 => CTR => F1: 4 * PRF # C2: 4 => SOL * PRF # C3: 7,8 => SOL * DIS # C3: 9 => CTR => C3: 7,8 * PRF # C3: 7 => SOL * DIS # B5: 4,9 => CTR => B5: 1,3 * PRF # B5: 1,3 => SOL * DIS # E4: 1,3 => CTR => E4: 5 * PRF # E6: 1,3 => SOL * PRF # A4: 1,3 => SOL * DIS # I4: 1,3 => CTR => I4: 6 * PRF # I4: 6 => SOL * DIS # D3: 8 => CTR => D3: 1,3 * PRF # B5: 3,4 => SOL * DIS # I4: 1,3 => CTR => I4: 6 * PRF # I4: 6 => SOL * PRF # E6: 1,3 => SOL * PRF # D8: 4 => SOL * DIS # D2: 4,8 => CTR => D2: 1,2 * PRF # E1: 3 => SOL * DIS # I4: 3 => CTR => I4: 1,6 * PRF # F8: 3 => SOL * CNT 30 HDP CHAINS / 51 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B2,C4,C5,D4,D9,E8,E9,F3,F7,G5,G7,H2,H3,H4,H8,H9,I6,I7) * ..57..6126....53.9.2..6.5.4.7...24.....6.8.272.69.785.48257..3.951...7.8763..12.5 * PAIR A1: 3,8 BLK 1 A3: 3,8,1 # reduction candidate for 3,8 A3: 3,8 => SOLVED * 895734612614285379327169584178352496539648127246917853482576931951423768763891245 * DURATION: 0:00:02.353791 START: 08:10:32.089100 END: 08:10:34.442891 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-709857-base-pr-001.dot * REASONING * PRF # A3: 3,8 => SOL * STA A3: 3,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokus.de/709857.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: ..57..6126....53.9.2..6.5.4.7...24.....6.8.272.69.785.48257..3.951...7.8763..12.5 A1: 3,8 A3: 1,3,8 # reduction candidate for 3,8 A3: 3,8 => SOLVED * 895734612614285379327169584178352496539648127246917853482576931951423768763891245 * SOLVED! -------------------------------------------------- |:step:| 00 -------------------------------------------------- pair quad |:guess:| highlight 7,8 H2,H3,C3,C2: 7,8.. => C3 = 9 or C2 = 4 # pair quad C3 != 9 |:step:| 01 -------------------------------------------------- * AUTO .. B1: 9.. # hidden single F3: 9.. # hidden single C3,H3: 7,8.. => A3,D3 != 7,8 # naked pair D3,D4: 1,3.. => D2,D8 != 1,3 # naked pair B1 = 9 # set value F3 = 9 # set value F7: 6 # naked single F7 = 6 # set value I7: 1 # naked single I7 = 1 # set value G7: 9 # naked single I6: 3 # naked single G5: 1.. # hidden single E9: 9.. # hidden single H8: 6.. # hidden single F1: 4.. # hidden single I4: 6.. # hidden single F1 = 4 # set value F8: 3 # naked single I4 = 6 # set value H4: 9 # naked single G5 = 1 # set value I6 = 3 # set value G7 = 9 # set value H9: 4 # naked single F8 = 3 # set value E8: 2 # naked single H8 = 6 # set value E9 = 9 # set value H9 = 4 # set value D9: 8 # naked single D8: 4.. # hidden single C5: 9.. # hidden single B5: 3.. # hidden single H4 = 9 # set value C4: 8 # naked single B5 = 3 # set value A5: 5 # naked single C5 = 9 # set value D8 = 4 # set value E8 = 2 # set value D9 = 8 # set value D2: 2 # naked single B6: 4.. # hidden single E5: 4.. # hidden single C2: 4.. # hidden single C2 = 4 # set value B2: 1 # naked single D2 = 2 # set value C4 = 8 # set value C3: 7 # naked single A5 = 5 # set value A4: 1 # naked single E5: 4 # naked single E5 = 4 # set value E6: 1 # naked single B6 = 4 # set value E6 = 1 # set value D4: 3 # naked single E2: 8 # naked single A1: 8.. # hidden single D3: 1.. # hidden single E4: 5.. # hidden single H2: 7.. # hidden single H3: 8.. # hidden single A1 = 8 # set value E1: 3 # naked single E1 = 3 # set value D3: 1 # naked single E4: 5 # naked single B2 = 1 # set value A3: 3 # naked single E2 = 8 # set value H2: 7 # naked single H2 = 7 # set value H3: 8 # naked single A3 = 3 # set value C3 = 7 # set value D3 = 1 # set value H3 = 8 # set value A4 = 1 # set value D4 = 3 # set value E4 = 5 # set value * SOLVED!
Solution
position: 895734612614285379327169584178352496539648127246917853482576931951423768763891245 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 # A3: 3,8 => SOL * INC # A3: 1 => UNS * PRF # E1: 3,8 => SOL * DIS # E1: 9 => CTR => E1: 3,8 * INC # A4: 3,8 => UNS * PRF # A4: 1,5 => SOL * DIS # D2: 1,4 => CTR => D2: 2,8 * INC # D2: 2,8 => UNS * DIS # B5: 1,4 => CTR => B5: 3,9 * INC # B5: 3,9 => UNS * INC # B6: 1,4 => UNS * PRF # E1: 3,9 => SOL * DIS # E1: 8 => CTR => E1: 3,9 * DIS # F1: 3,9 => CTR => F1: 4 * INC # F1: 4 => UNS * INC # C2: 7,8 => UNS * PRF # C2: 4 => SOL * PRF # C3: 7,8 => SOL * DIS # C3: 9 => CTR => C3: 7,8 * INC # C3: 8,9 => UNS * PRF # C3: 7 => SOL * DIS # B5: 4,9 => CTR => B5: 1,3 * PRF # B5: 1,3 => SOL * DIS # E4: 1,3 => CTR => E4: 5 * INC # E4: 5 => UNS * INC # E5: 1,3 => UNS * PRF # E6: 1,3 => SOL * INC # E6: 4 => UNS * PRF # A4: 1,3 => SOL * INC # A4: 5,8 => UNS * DIS # I4: 1,3 => CTR => I4: 6 * PRF # I4: 6 => SOL * INC # D3: 1,3 => UNS * DIS # D3: 8 => CTR => D3: 1,3 * INC # B5: 1,9 => UNS * PRF # B5: 3,4 => SOL * DIS # I4: 1,3 => CTR => I4: 6 * PRF # I4: 6 => SOL * INC # B6: 1,3 => UNS * PRF # E6: 1,3 => SOL * INC # E6: 4 => UNS * INC # D8: 2,3 => UNS * PRF # D8: 4 => SOL * DIS # D2: 4,8 => CTR => D2: 1,2 * INC # D2: 1,2 => UNS * INC # E1: 8,9 => UNS * PRF # E1: 3 => SOL * INC # I4: 1,6 => UNS * DIS # I4: 3 => CTR => I4: 1,6 * INC # F8: 4,6 => UNS * PRF # F8: 3 => SOL * CNT 51 HDP CHAINS / 51 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A3: 3,8 => SOL * STA A3: 3,8 * CNT 1 HDP CHAINS / 1 HYP OPENED