Analysis of zz-google-000-base.sdk
Contents
Original Sudoku
level: medium
position: ....8.7.2.6..129......4..8.6.5.....4.9.......2..7..5.11.....6.9..25.....78....... initial
Autosolve
position: 419685732867312945523947186675...3.4391.5....2487..5.1154...6.99325...1.786....53 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # D9: 2,4 => SOL * DIS # D9: 1 => CTR => D9: 2,4 * PRF # H5: 2,7 => SOL * DIS # H5: 6 => CTR => H5: 2,7 * PRF # D9: 2,4 => SOL * DIS # D9: 1 => CTR => D9: 2,4 * CNT 6 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # D9: 2,4 => SOL * STA D9: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....8.7.2.6..129......4..8.6.5.....4.9.......2..7..5.11.....6.9..25.....78....... | initial |
| 419685732867312945523947186675...3.4391.5....2487..5.1154...6.99325...1.786....53 | autosolve |
| 419685732867312945523947186675128394391456278248739561154873629932564817786291453 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (22) D4: 1,8 E4: 2,9 F4: 1,8 D5: 2,4 F5: 4,6 E6: 3,6 F6: 3,9 H4: 2,9 G5: 2,8 I5: 7,8 H6: 6,9 D7: 2,8 E7: 3,7 F7: 3,8 E8: 6,7 F8: 4,6 E9: 2,9 F9: 1,9 H7: 2,7 G8: 4,8 I8: 7,8 G9: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D4,F4: 1.. / D4 = 1 => 0 pairs (*) / F4 = 1 => 0 pairs (X) D9,F9: 1.. / D9 = 1 => 0 pairs (X) / F9 = 1 => 0 pairs (_) D4,D9: 1.. / D4 = 1 => 0 pairs (*) / D9 = 1 => 0 pairs (X) F4,F9: 1.. / F4 = 1 => 0 pairs (X) / F9 = 1 => 0 pairs (_) E4,D5: 2.. / E4 = 2 => 0 pairs (*) / D5 = 2 => 0 pairs (X) H7,G9: 2.. / H7 = 2 => 0 pairs (*) / G9 = 2 => 0 pairs (X) E4,H4: 2.. / E4 = 2 => 0 pairs (*) / H4 = 2 => 0 pairs (X) D7,H7: 2.. / D7 = 2 => 0 pairs (X) / H7 = 2 => 0 pairs (_) E4,E9: 2.. / E4 = 2 => 0 pairs (*) / E9 = 2 => 0 pairs (X) G5,G9: 2.. / G5 = 2 => 0 pairs (*) / G9 = 2 => 0 pairs (X) E6,F6: 3.. / E6 = 3 => 0 pairs (*) / F6 = 3 => 0 pairs (X) E7,F7: 3.. / E7 = 3 => 0 pairs (X) / F7 = 3 => 0 pairs (_) E6,E7: 3.. / E6 = 3 => 0 pairs (*) / E7 = 3 => 0 pairs (X) F6,F7: 3.. / F6 = 3 => 0 pairs (X) / F7 = 3 => 0 pairs (_) D5,F5: 4.. / D5 = 4 => 0 pairs (*) / F5 = 4 => 0 pairs (X) F8,D9: 4.. / F8 = 4 => 0 pairs (*) / D9 = 4 => 0 pairs (X) G8,G9: 4.. / G8 = 4 => 0 pairs (X) / G9 = 4 => 0 pairs (_) F8,G8: 4.. / F8 = 4 => 0 pairs (*) / G8 = 4 => 0 pairs (X) D9,G9: 4.. / D9 = 4 => 0 pairs (X) / G9 = 4 => 0 pairs (_) D5,D9: 4.. / D5 = 4 => 0 pairs (*) / D9 = 4 => 0 pairs (X) F5,F8: 4.. / F5 = 4 => 0 pairs (X) / F8 = 4 => 0 pairs (_) F5,E6: 6.. / F5 = 6 => 0 pairs (*) / E6 = 6 => 0 pairs (X) H5,H6: 6.. / H5 = 6 => 0 pairs (X) / H6 = 6 => 0 pairs (_) E8,F8: 6.. / E8 = 6 => 0 pairs (*) / F8 = 6 => 0 pairs (X) F5,H5: 6.. / F5 = 6 => 0 pairs (*) / H5 = 6 => 0 pairs (X) E6,H6: 6.. / E6 = 6 => 0 pairs (X) / H6 = 6 => 0 pairs (_) E6,E8: 6.. / E6 = 6 => 0 pairs (X) / E8 = 6 => 0 pairs (_) F5,F8: 6.. / F5 = 6 => 0 pairs (*) / F8 = 6 => 0 pairs (X) H5,I5: 7.. / H5 = 7 => 0 pairs (*) / I5 = 7 => 0 pairs (X) E7,E8: 7.. / E7 = 7 => 0 pairs (*) / E8 = 7 => 0 pairs (X) H7,I8: 7.. / H7 = 7 => 0 pairs (X) / I8 = 7 => 0 pairs (_) E7,H7: 7.. / E7 = 7 => 0 pairs (*) / H7 = 7 => 0 pairs (X) E8,I8: 7.. / E8 = 7 => 0 pairs (X) / I8 = 7 => 0 pairs (_) H5,H7: 7.. / H5 = 7 => 0 pairs (*) / H7 = 7 => 0 pairs (X) I5,I8: 7.. / I5 = 7 => 0 pairs (X) / I8 = 7 => 0 pairs (_) D4,F4: 8.. / D4 = 8 => 0 pairs (X) / F4 = 8 => 0 pairs (_) G5,I5: 8.. / G5 = 8 => 0 pairs (X) / I5 = 8 => 0 pairs (_) D7,F7: 8.. / D7 = 8 => 0 pairs (*) / F7 = 8 => 0 pairs (X) G8,I8: 8.. / G8 = 8 => 0 pairs (*) / I8 = 8 => 0 pairs (X) D4,D7: 8.. / D4 = 8 => 0 pairs (X) / D7 = 8 => 0 pairs (_) F4,F7: 8.. / F4 = 8 => 0 pairs (*) / F7 = 8 => 0 pairs (X) G5,G8: 8.. / G5 = 8 => 0 pairs (X) / G8 = 8 => 0 pairs (_) I5,I8: 8.. / I5 = 8 => 0 pairs (*) / I8 = 8 => 0 pairs (X) E4,F6: 9.. / E4 = 9 => 0 pairs (X) / F6 = 9 => 0 pairs (_) H4,H6: 9.. / H4 = 9 => 0 pairs (*) / H6 = 9 => 0 pairs (X) E9,F9: 9.. / E9 = 9 => 0 pairs (*) / F9 = 9 => 0 pairs (X) E4,H4: 9.. / E4 = 9 => 0 pairs (X) / H4 = 9 => 0 pairs (_) F6,H6: 9.. / F6 = 9 => 0 pairs (*) / H6 = 9 => 0 pairs (X) E4,E9: 9.. / E4 = 9 => 0 pairs (X) / E9 = 9 => 0 pairs (_) F6,F9: 9.. / F6 = 9 => 0 pairs (*) / F9 = 9 => 0 pairs (X) * DURATION: 0:01:26.970310 START: 06:21:07.081017 END: 06:22:34.051327 2017-05-01 * CP COUNT: (50) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D4,D5,D7,E4,E6,E7,E8,E9,F4,F5,F6,F7,F8,F9,G5,G8,G9,H4,H6,H7,I5,I8) * 419685732867312945523947186675...3.4391.5....2487..5.1154...6.99325...1.786....53 * PAIR D5: 2,4 COL D D9: 2,4,1 # reduction candidate for 2,4 D9: 2,4 => SOLVED * 419685732867312945523947186675128394391456278248739561154873629932564817786291453 D9: 1 => CTR * 419685732867312945523947186675...3.4391456...24873956115427.6.99325...1.786....53 * PAIR H7: 2,7 COL H H5: 2,7,6 # reduction candidate for 2,7 H5: 2,7 => SOLVED * 419685732867312945523947186675128394391456278248739561154873629932564817786291453 H5: 6 => CTR * 419685732867312945523947186675...3.4391.5..67248763591154.386799325764187864...53 * PAIR G9: 2,4 ROW 9 D9: 2,4,1 # reduction candidate for 2,4 D9: 2,4 => SOLVED * 419685732867312945523947186675128394391456278248739561154873629932564817786291453 D9: 1 => CTR * 419685732867312945523947186675...3.4391456...24873956115427.6.99325...1.786....53 * INCONCLUSIVE * SAVE PR GRAPH zz-google-000-base-pr-000.dot * REASONING * PRF # D9: 2,4 => SOL * DIS # D9: 1 => CTR => D9: 2,4 * PRF # H5: 2,7 => SOL * DIS # H5: 6 => CTR => H5: 2,7 * PRF # D9: 2,4 => SOL * DIS # D9: 1 => CTR => D9: 2,4 * CNT 6 HDP CHAINS / 6 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D4,D5,D7,E4,E6,E7,E8,E9,F4,F5,F6,F7,F8,F9,G5,G8,G9,H4,H6,H7,I5,I8) * 419685732867312945523947186675...3.4391.5....2487..5.1154...6.99325...1.786....53 * PAIR D5: 2,4 COL D D9: 2,4,1 # reduction candidate for 2,4 D9: 2,4 => SOLVED * 419685732867312945523947186675128394391456278248739561154873629932564817786291453 * DURATION: 0:00:02.527109 START: 06:22:42.910942 END: 06:22:45.438051 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-google-000-base-pr-001.dot * REASONING * PRF # D9: 2,4 => SOL * STA D9: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
* PAIR REDUCTION .. * ROUND 1: 419685732867312945523947186675...3.4391.5....2487..5.1154...6.99325...1.786....53 D4: 1,8 E4: 2,9 F4: 1,8 D5: 2,4 D9: 1,2,4 # reduction candidate for 2,4 D9: 2,4 => SOLVED * 419685732867312945523947186675128394391456278248739561154873629932564817786291453 * SOLVED! -------------------------------------------------- -------------------------------------------------- Pairs F5: 4,6 F8: 4,6 * DISABLE VALUE:: F6 != 6 * DISABLE VALUE:: F9 != 4 E4: 2,9 E9: 2,9 * DISABLE VALUE:: E6 != 9 * DISABLE VALUE:: E7 != 2 E4: 2,9 H4: 2,9 * DISABLE VALUE:: D4 != 2 * DISABLE VALUE:: F4 != 9 |:step:| 00 -------------------------------------------------- D5: 2,4 D9: 1,2,4 G9: 2,4 * DISABLE VALUE:: D9 != 1 => D5,D9: 2,4 => D5,G9: 2,4 * DISABLE VALUE:: D7 != 2 D7: 8 # naked single * DISABLE VALUE:: E9 != 2 E9: 9 # naked single * ANALYZE .. * SOLVED! F9: 1.. # hidden single D9: 2.. # hidden single H7: 2.. # hidden single D4: 1.. # hidden single E4: 2.. # hidden single D4: 1 # naked single E4: 2 # naked single H7: 2 # naked single D9: 2 # naked single F9: 1 # naked single F4: 8.. # hidden single F6: 9.. # hidden single F8: 4.. # hidden single I8: 7.. # hidden single H4: 9.. # hidden single E7: 7.. # hidden single G9: 4.. # hidden single D5: 4.. # hidden single H5: 7.. # hidden single F4: 8 # naked single H4: 9 # naked single D5: 4 # naked single H5: 7 # naked single F6: 9 # naked single E7: 7 # naked single F8: 4 # naked single I8: 7 # naked single G9: 4 # naked single E6: 3.. # hidden single G5: 2.. # hidden single H6: 6.. # hidden single F7: 3.. # hidden single E8: 6.. # hidden single G8: 8.. # hidden single F5: 6.. # hidden single I5: 8.. # hidden single F5: 6 # naked single G5: 2 # naked single I5: 8 # naked single E6: 3 # naked single H6: 6 # naked single F7: 3 # naked single E8: 6 # naked single G8: 8 # naked single |:step:| 01 -------------------------------------------------- |:step:| OOPS -------------------------------------------------- Quad with common value: 2 # |:check:||:info:| this is wrong! D5: 2,4 G5: 2, 8 D9: 1,2,4 G9: 2,4 => D,G,5,9 is covered for value 2 D7: 2,8 H5: 2,6,7 E9: 2,9 * DISABLE VALUE:: D7 != 2 D7: 8 # naked single * DISABLE VALUE:: H5 != 2 * DISABLE VALUE:: E9 != 2 E9: 9 # naked single * ANALYZE .. * SOLVED! |:step:| 01 -------------------------------------------------- D9: 2.. # hidden single H7: 2.. # hidden single E4: 2.. # hidden single E4: 2 # naked single H7: 2 # naked single D9: 2 # naked single F6: 9.. # hidden single F9: 1.. # hidden single F8: 4.. # hidden single I8: 7.. # hidden single H4: 9.. # hidden single E7: 7.. # hidden single G9: 4.. # hidden single D4: 1.. # hidden single D5: 4.. # hidden single H5: 7.. # hidden single D4: 1 # naked single H4: 9 # naked single D5: 4 # naked single H5: 7 # naked single F6: 9 # naked single E7: 7 # naked single F8: 4 # naked single I8: 7 # naked single F9: 1 # naked single G9: 4 # naked single E6: 3.. # hidden single F4: 8.. # hidden single G5: 2.. # hidden single H6: 6.. # hidden single F7: 3.. # hidden single E8: 6.. # hidden single G8: 8.. # hidden single F5: 6.. # hidden single I5: 8.. # hidden single F4: 8 # naked single F5: 6 # naked single G5: 2 # naked single I5: 8 # naked single E6: 3 # naked single H6: 6 # naked single F7: 3 # naked single E8: 6 # naked single G8: 8 # naked single
Solution
position: 419685732867312945523947186675128394391456278248739561154873629932564817786291453 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 # D9: 2,4 => SOL * DIS # D9: 1 => CTR => D9: 2,4 * PRF # H5: 2,7 => SOL * DIS # H5: 6 => CTR => H5: 2,7 * PRF # D9: 2,4 => SOL * DIS # D9: 1 => CTR => D9: 2,4 * CNT 6 HDP CHAINS / 6 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # D9: 2,4 => SOL * STA D9: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED