If we have Double Pointers, do we have Double Fitters? Absolutely yes, this post is the Expert level of Fitting In technique, Angel's Wings with Double Fitters.
See the board below, angel's two wings are at 41 and 67. Click the board to see how it works.
See the board below, angel's two wings are at 41 and 67. Click the board to see how it works.
As you can see, number 6 in 66 can fit in two cells of box 4: 41 and 49, and number 8 can fit in two cells of row 6: 49 and 67. Cell 41, 47 and 67 form a chain that linked the two wings. Think of the two possibilities of number 6:
- If 6 goes to 41 then 61 must be 9 in row 4;
- If 6 goes to 47 then 8 goes to 67 then 61 must be 9 in box 6.
Try number 8 you have the same result, either way leads to solution 619.
If you find a chain that can link the two wings - you find the angel!
The chain can be longer, in the board below, Double Fitters of 4, 1 and 5 form a chain 89, 87, 27 and 28, linked the two wings of the angel 89 and 28, the angel is 298.
- If 6 goes to 41 then 61 must be 9 in row 4;
- If 6 goes to 47 then 8 goes to 67 then 61 must be 9 in box 6.
Try number 8 you have the same result, either way leads to solution 619.
If you find a chain that can link the two wings - you find the angel!
The chain can be longer, in the board below, Double Fitters of 4, 1 and 5 form a chain 89, 87, 27 and 28, linked the two wings of the angel 89 and 28, the angel is 298.
The chain can be formed by same number Double Fitters, in the board below, Double Fitter of 7 in box 7 and box 8 form a chain 76, 71, 83 and 89, linked the two wings of the angel 76 and 89, revealing the angel 6 at 85. Note here that since it's the same number chain, 71 and 83 are linked by 'seeing each other'.
Double Pointing Out and Double Fitting In can work together. In the board below, one of the wing, 85, is pointed out by Double Pointer of 7 in 76 and 43, then Double Fitter of 9 fits into 43 and 43 and 51, finally Double Fitter of 8 fits into 51 and the other wing, 59, reveal the angel 7 at 58.
There you have it, exclusively from Touch Sudoku, the Angel's Wings technique, so beautiful so powerful yet easy to spot, it will downgrade puzzles used to be considered diabolical.
Enjoy.
Sudoku Rules and Terminologies
Technique No.1 Pointing Out - Easy Level
Technique No.2 Pointing Out - Medium Level
Technique No.3 Fitting In - Medium Level
Technique No.4 Fitting In - Hard Level
Technique No.5 Pointing Out - Hard Level
Technique No.6 Pointing Out - Expert Level
Technique No.7 Fitting In - Expert Level
The puzzles in this post are from http://school.maths.uwa.edu.au/~gordon/sudokumin.php The work is licensed under a Creative Commons Attribution 2.5 License. Attribution goes to Gordon Royle and The University of Western Australia.
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