Post the puzzle or solving technique that's causing you trouble and someone will help

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.
polydigm

Posts: 2
Joined: 06 January 2018

### Re: Tried various advanced techniques

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.

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`*-----------------------------------------------*|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
Leren

Posts: 4007
Joined: 03 June 2012

### Re: Tried various advanced techniques

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  |*-----------------------------------------------*`
polydigm

Posts: 2
Joined: 06 January 2018