The New Sudoku Players' Forum

[polydigm]

I've studied many advanced techniques and just can't get any further on this one. For instance I've tried looking for x-wings, unique rectangles, conjugate chain contradictions on all available numbers and so on. Any help would be appreciated.

[Leren]

The puzzle solved cell status in line format : ..8237..5....8427..276..834.8.172..9...468..22.1395.6886...3.27.3472..8.7.28....3

Ignoring basic moves like pointing pairs/triples and naked tuples, which I assume you are familiar with, all that is required is three Skyscrapers.

The first one is slightly trickier than normal because one of the Strong links in it is a grouped link.

Code: Select all

*-----------------------------------------------*
|a146   14   8    | 2  3   7   | 169   19    5  |
|a13569 59-1 3569 | 59 8   4   | 2     7    d16 |
| 59    2    7    | 6  15  19  | 8     3     4  |
|-----------------+------------+----------------|
| 3456  8    356  | 1  7   2   | 345   45    9  |
| 359   579  359  | 4  6   8   | 1357  15    2  |
| 2     47   1    | 3  9   5   | 47    6     8  |
|-----------------+------------+----------------|
| 8     6    59   | 59 14  3   | 14    2     7  |
|b159   3    4    | 7  2   169 | 1569  8    c16 |
| 7     159  2    | 8  145 169 | 14569 1459  3  |
*-----------------------------------------------*

At least one of the three cells marked a and d must be 1, and since r2c2 can see all of these it can't be 1. Then a naked pair (59) in r2c24 gets you to here :

Code: Select all

*----------------------------------------------*
| 146   14    8   | 2  3   7   | 169   19   5  |
| 136  a59    36  |b59 8   4   | 2     7    16 |
| 59    2     7   | 6  15  19  | 8     3    4  |
|-----------------+------------+---------------|
| 3456  8     356 | 1  7   2   | 345   45   9  |
| 359   579   359 | 4  6   8   | 1357  15   2  |
| 2     47    1   | 3  9   5   | 47    6    8  |
|-----------------+------------+---------------|
| 8     6    d59  |c59 14  3   | 14    2    7  |
| 159   3     4   | 7  2   169 | 1569  8    16 |
| 7     1-59  2   | 8  145 169 | 14569 1459 3  |
*----------------------------------------------*

Here you have two Skyscrapers on 5 and 9 in the same 4 cells. At least one of cells a and d must be 5 or 9, so one must be 5 and the other 9. Therefore r9c2 can't be 5 or 9, so it's 1 and the puzzle solves with singles from there.

If you are unfamiliar with the Skyscraper technique it is described nicely here.

Leren

[polydigm]

Thanks @Leren. I hadn't come across Skyscrapers before so I'm adding those to my arsenal. Your solution highlighted a solution I could have used with what I know already. R28C19 is a finned X-Wing with fin R1C1 so R2C2 cannot be 1.

Code: Select all

*-----------------------------------------------*
|f146   14   8    | 2  3   7   | 169   19    5  |
|x13569 59-1 3569 | 59 8   4   | 2     7    x16 |
| 59    2    7    | 6  15  19  | 8     3     4  |
|-----------------+------------+----------------|
| 3456  8    356  | 1  7   2   | 345   45    9  |
| 359   579  359  | 4  6   8   | 1357  15    2  |
| 2     47   1    | 3  9   5   | 47    6     8  |
|-----------------+------------+----------------|
| 8     6    59   | 59 14  3   | 14    2     7  |
|x159   3    4    | 7  2   169 | 1569  8    x16 |
| 7     159  2    | 8  145 169 | 14569 1459  3  |
*-----------------------------------------------*

Then we have the following. What I know as a Remote Pair is in cells a and d, linked by cells b and c, an even number chain of equal bi-valued cells. The ends must alternate so any cells that see both cannot be either number. Here R9C2 sees a and d so it can only be 1. After this it all falls out.

Code: Select all

*-----------------------------------------------*
| 146   14   8    | 2  3   7   | 169   19    5  |
| 13569 a59  3569 |b59 8   4   | 2     7    x16 |
| 59    2    7    | 6  15  19  | 8     3     4  |
|-----------------+------------+----------------|
| 3456  8    356  | 1  7   2   | 345   45    9  |
| 359   579  359  | 4  6   8   | 1357  15    2  |
| 2     47   1    | 3  9   5   | 47    6     8  |
|-----------------+------------+----------------|
| 8     6   d59   |c59 14  3   | 14    2     7  |
|x159   3    4    | 7  2   169 | 1569  8    x16 |
| 7   1-5-9  2    | 8  145 169 | 14569 1459  3  |
*-----------------------------------------------*