Analysis of zz-sudoku-de-692870-base.sdk
Contents
Original Sudoku
level: medium
position: ..6....217.3..94....2.8.......39.5..6..5.2..4..8.64.......7.6....18..2.742....3.. initial
Autosolve
position: .9643..217.3.294...42.8.9....43985..6.9512..4..876419...5271649961843257427956318 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 5,8 => CTR => B2: 1 * PRF # B2: 1 => SOL * DIS # B2: 8 => CTR => B2: 1,5 * PRF # I3: 5,6 => SOL * DIS # I3: 3 => CTR => I3: 5,6 * DIS # H5: 8 => CTR => H5: 3,7 * DIS # A6: 3,5 => CTR => A6: 2 * PRF # A6: 2 => SOL * DIS # H3: 6,7 => CTR => H3: 3 * PRF # H3: 3 => SOL * PRF # H5: 7,8 => SOL * DIS # H5: 3 => CTR => H5: 7,8 * DIS # A6: 5 => CTR => A6: 2,3 * CNT 13 HDP CHAINS / 16 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 5,8 => CTR => B2: 1 * PRF B2: 1 => SOL * STA B2: 1 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..6....217.3..94....2.8.......39.5..6..5.2..4..8.64.......7.6....18..2.742....3.. | initial |
| .9643..217.3.294...42.8.9....43985..6.9512..4..876419...5271649961843257427956318 | autosolve |
| 896435721713629485542187936174398562639512874258764193385271649961843257427956318 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) A1: 5,8 A3: 1,5 F1: 5,7 D2: 1,6 D3: 1,6 F3: 5,7 G1: 7,8 H2: 6,8 I2: 5,6 A4: 1,2 B4: 1,7 B5: 3,7 B6: 3,5 H4: 6,7 I4: 2,6 G5: 7,8 I6: 2,3 A7: 3,8 B7: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,A3: 1.. / B2 = 1 => 0 pairs (*) / A3 = 1 => 0 pairs (X) D2,D3: 1.. / D2 = 1 => 0 pairs (X) / D3 = 1 => 0 pairs (_) A4,B4: 1.. / A4 = 1 => 0 pairs (*) / B4 = 1 => 0 pairs (X) B2,D2: 1.. / B2 = 1 => 0 pairs (*) / D2 = 1 => 0 pairs (X) A3,D3: 1.. / A3 = 1 => 0 pairs (X) / D3 = 1 => 0 pairs (_) A3,A4: 1.. / A3 = 1 => 0 pairs (X) / A4 = 1 => 0 pairs (_) B2,B4: 1.. / B2 = 1 => 0 pairs (*) / B4 = 1 => 0 pairs (X) A4,A6: 2.. / A4 = 2 => 0 pairs (X) / A6 = 2 => 0 pairs (_) I4,I6: 2.. / I4 = 2 => 0 pairs (*) / I6 = 2 => 0 pairs (X) A4,I4: 2.. / A4 = 2 => 0 pairs (X) / I4 = 2 => 0 pairs (_) A6,I6: 2.. / A6 = 2 => 0 pairs (*) / I6 = 2 => 0 pairs (X) H3,I3: 3.. / H3 = 3 => 0 pairs (*) / I3 = 3 => 0 pairs (X) H5,I6: 3.. / H5 = 3 => 0 pairs (X) / I6 = 3 => 0 pairs (_) A7,B7: 3.. / A7 = 3 => 15 pairs (_) / B7 = 3 => 0 pairs (X) B5,H5: 3.. / B5 = 3 => 0 pairs (*) / H5 = 3 => 0 pairs (X) A6,A7: 3.. / A6 = 3 => 0 pairs (X) / A7 = 3 => 15 pairs (_) H3,H5: 3.. / H3 = 3 => 0 pairs (*) / H5 = 3 => 0 pairs (X) I3,I6: 3.. / I3 = 3 => 0 pairs (X) / I6 = 3 => 0 pairs (_) F1,F3: 5.. / F1 = 5 => 15 pairs (_) / F3 = 5 => 0 pairs (X) I2,I3: 5.. / I2 = 5 => 20 pairs (_) / I3 = 5 => 0 pairs (X) A6,B6: 5.. / A6 = 5 => 0 pairs (X) / B6 = 5 => 20 pairs (_) A1,F1: 5.. / A1 = 5 => 0 pairs (X) / F1 = 5 => 15 pairs (_) B2,I2: 5.. / B2 = 5 => 0 pairs (X) / I2 = 5 => 20 pairs (_) B2,B6: 5.. / B2 = 5 => 0 pairs (X) / B6 = 5 => 20 pairs (_) D2,D3: 6.. / D2 = 6 => 0 pairs (*) / D3 = 6 => 0 pairs (X) H4,I4: 6.. / H4 = 6 => 0 pairs (*) / I4 = 6 => 0 pairs (X) F1,F3: 7.. / F1 = 7 => 0 pairs (X) / F3 = 7 => 15 pairs (_) G1,H3: 7.. / G1 = 7 => 15 pairs (_) / H3 = 7 => 0 pairs (X) B4,B5: 7.. / B4 = 7 => 0 pairs (*) / B5 = 7 => 0 pairs (X) F1,G1: 7.. / F1 = 7 => 0 pairs (X) / G1 = 7 => 15 pairs (_) F3,H3: 7.. / F3 = 7 => 15 pairs (_) / H3 = 7 => 0 pairs (X) B4,H4: 7.. / B4 = 7 => 0 pairs (*) / H4 = 7 => 0 pairs (X) G1,G5: 7.. / G1 = 7 => 15 pairs (_) / G5 = 7 => 0 pairs (X) A1,B2: 8.. / A1 = 8 => 15 pairs (_) / B2 = 8 => 0 pairs (X) G1,H2: 8.. / G1 = 8 => 0 pairs (X) / H2 = 8 => 15 pairs (_) G5,H5: 8.. / G5 = 8 => 15 pairs (_) / H5 = 8 => 0 pairs (X) A7,B7: 8.. / A7 = 8 => 0 pairs (X) / B7 = 8 => 15 pairs (_) A1,G1: 8.. / A1 = 8 => 15 pairs (_) / G1 = 8 => 0 pairs (X) B2,H2: 8.. / B2 = 8 => 0 pairs (X) / H2 = 8 => 15 pairs (_) A1,A7: 8.. / A1 = 8 => 15 pairs (_) / A7 = 8 => 0 pairs (X) B2,B7: 8.. / B2 = 8 => 0 pairs (X) / B7 = 8 => 15 pairs (_) G1,G5: 8.. / G1 = 8 => 0 pairs (X) / G5 = 8 => 15 pairs (_) H2,H5: 8.. / H2 = 8 => 15 pairs (_) / H5 = 8 => 0 pairs (X) * DURATION: 0:01:11.076271 START: 07:53:26.046948 END: 07:54:37.123219 2017-05-01 * CP COUNT: (43) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A4,A7,B4,B5,B6,B7,D2,D3,F1,F3,G1,G5,H2,H4,I2,I4,I6) * .9643..217.3.294...42.8.9....43985..6.9512..4..876419...5271649961843257427956318 * PAIR A1: 5,8 BLK 1 B2: 5,8,1 # reduction candidate for 5,8 B2: 5,8 => CTR * .9643..217.31294..14268.9..214398576679512834..876419...5271649961843257427956318 B2: 1 => SOLVED * 896435721713629485542187936174398562639512874258764193385271649961843257427956318 * PAIR A3: 1,5 BLK 1 B2: 1,5,8 # reduction candidate for 1,5 B2: 8 => CTR * .9643..2178312946514268597...43985..6.9512..4..876419...5271649961843257427956318 B2: 1,5 # 15 pairs * PAIR I2: 5,6 BLK 3 I3: 5,6,3 # reduction candidate for 5,6 I3: 5,6 => SOLVED * 896435721713629485542187936174398562639512874258764193385271649961843257427956318 I3: 3 => CTR * .9643..21783129465142685973..43985.66.9512.34.58764192.35271649961843257427956318 * PAIR B5: 3,7 ROW 5 H5: 3,7,8 # reduction candidate for 3,7 H5: 8 => CTR * .9643..217.3.294...42.8.93...43985766.9512..4..876419...5271649961843257427956318 H5: 3,7 # 15 pairs * PAIR B6: 3,5 BLK 4 A6: 3,5,2 # reduction candidate for 3,5 A6: 3,5 => CTR * 896435721753.294...42.8.9..214398576679512834..8764192..5271649961843257427956318 A6: 2 => SOLVED * 896435721713629485542187936174398562639512874258764193385271649961843257427956318 * PAIR H4: 6,7 COL H H3: 6,7,3 # reduction candidate for 6,7 H3: 6,7 => CTR * .9643..217.3.29485.42.8.9632143985..6.9512.34..8764192..5271649961843257427956318 H3: 3 => SOLVED * 896435721713629485542187936174398562639512874258764193385271649961843257427956318 * PAIR G5: 7,8 BLK 6 H5: 7,8,3 # reduction candidate for 7,8 H5: 7,8 => SOLVED * 896435721713629485542187936174398562639512874258764193385271649961843257427956318 H5: 3 => CTR * 8964357217.3.2948..42.87963214398576679512834.38764192385271649961843257427956318 * PAIR I6: 2,3 ROW 6 A6: 2,3,5 # reduction candidate for 2,3 A6: 5 => CTR * .9643..217.3.294...42.8.9..214398576679512834538764192385271649961843257427956318 A6: 2,3 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-692870-base-pr-000.dot * REASONING * DIS # B2: 5,8 => CTR => B2: 1 * PRF # B2: 1 => SOL * DIS # B2: 8 => CTR => B2: 1,5 * PRF # I3: 5,6 => SOL * DIS # I3: 3 => CTR => I3: 5,6 * DIS # H5: 8 => CTR => H5: 3,7 * DIS # A6: 3,5 => CTR => A6: 2 * PRF # A6: 2 => SOL * DIS # H3: 6,7 => CTR => H3: 3 * PRF # H3: 3 => SOL * PRF # H5: 7,8 => SOL * DIS # H5: 3 => CTR => H5: 7,8 * DIS # A6: 5 => CTR => A6: 2,3 * CNT 13 HDP CHAINS / 16 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A4,A7,B4,B5,B6,B7,D2,D3,F1,F3,G1,G5,H2,H4,I2,I4,I6) * .9643..217.3.294...42.8.9....43985..6.9512..4..876419...5271649961843257427956318 * PAIR A1: 5,8 BLK 1 B2: 5,8,1 # reduction candidate for 5,8 B2: 5,8 => CTR * .9643..217.31294..14268.9..214398576679512834..876419...5271649961843257427956318 B2: 1 => SOLVED * 896435721713629485542187936174398562639512874258764193385271649961843257427956318 * DURATION: 0:00:02.746510 START: 07:54:54.845467 END: 07:54:57.591977 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-692870-base-pr-001.dot * REASONING * DIS # B2: 5,8 => CTR => B2: 1 * PRF B2: 1 => SOL * STA B2: 1 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokus.de/692870.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: .9643..217.3.294...42.8.9....43985..6.9512..4..876419...5271649961843257427956318 A1: 5,8 B2: 1,5,8 # reduction candidate for 5,8 B2: 5,8 => CTR * .9643..217.31294..14268.9..214398576679512834..876419...5271649961843257427956318 B2: 1 => SOLVED * 896435721713629485542187936174398562639512874258764193385271649961843257427956318 * SOLVED! -------------------------------------------------- -------------------------------------------------- * AUTO .. E2 = 2 # set value C4 = 4 # set value F4 = 8 # set value E5 = 1 # set value D6: 7 # naked single E9: 5 # naked single D6 = 7 # set value D1: 4 # naked single D7 = 2 # set value B8 = 6 # set value C9 = 7 # set value C5: 9 # naked single E9 = 5 # set value F8: 3 # naked single E8: 4.. # hidden single D9: 9.. # hidden single H7: 4.. # hidden single C7: 5.. # hidden single G6: 1.. # hidden single D1 = 4 # set value E1: 3 # naked single E1 = 3 # set value E8: 4 # naked single C5 = 9 # set value C7: 5 # naked single G6 = 1 # set value C7 = 5 # set value H7 = 4 # set value E8 = 4 # set value F8 = 3 # set value F7: 1 # naked single A8: 9 # naked single D9 = 9 # set value I9: 8 # naked single I9 = 8 # set value I7: 9 # naked single H9: 1 # naked single B3: 4.. # hidden single F9: 6.. # hidden single H8: 5.. # hidden single B3 = 4 # set value F7 = 1 # set value F9: 6 # naked single I7 = 9 # set value H8: 5 # naked single A8 = 9 # set value H8 = 5 # set value F9 = 6 # set value H9 = 1 # set value B1: 9.. # hidden single H6: 9.. # hidden single B1 = 9 # set value H6 = 9 # set value G3: 9.. # hidden single G3 = 9 # set value * UNSOLVED! |:step:| 00 -------------------------------------------------- * FORCE VALUE:: I3 = 3 I3 = 3 # set value I6: 2 # naked single I2: 5.. # hidden single H5: 3.. # hidden single => CTR * DISABLE VALUE:: I3 != 3 H3: 3.. # hidden single I6: 3.. # hidden single * SOLVED! |:step:| 01 --------------------------------------------------
Solution
position: 896435721713629485542187936174398562639512874258764193385271649961843257427956318 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:
* DIS # B2: 5,8 => CTR => B2: 1 * PRF # B2: 1 => SOL * INC # B2: 1,5 => UNS * DIS # B2: 8 => CTR => B2: 1,5 * PRF # I3: 5,6 => SOL * DIS # I3: 3 => CTR => I3: 5,6 * INC # H5: 3,7 => UNS * DIS # H5: 8 => CTR => H5: 3,7 * DIS # A6: 3,5 => CTR => A6: 2 * PRF # A6: 2 => SOL * DIS # H3: 6,7 => CTR => H3: 3 * PRF # H3: 3 => SOL * PRF # H5: 7,8 => SOL * DIS # H5: 3 => CTR => H5: 7,8 * INC # A6: 2,3 => UNS * DIS # A6: 5 => CTR => A6: 2,3 * CNT 16 HDP CHAINS / 16 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B2: 5,8 => CTR => B2: 1 * PRF B2: 1 => SOL * STA B2: 1 * CNT 2 HDP CHAINS / 1 HYP OPENED