Stuck on a puzzle 16/12/2020

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Stuck on a puzzle 16/12/2020

Postby Fortesque92 » Wed Dec 16, 2020 7:22 am

Pretty stumped on this one, any ideas?
Screen Shot 2020-12-16 at 6.21.58 pm.png
Screen Shot 2020-12-16 at 6.21.58 pm.png (139.01 KiB) Viewed 149 times
Fortesque92
 
Posts: 30
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Re: Stuck on a puzzle 16/12/2020

Postby Leren » Wed Dec 16, 2020 7:51 am

Code: Select all
*-------------------------------------------------*
| 67 4   5 | 3678  *267    2378   | 28  1     9   |
| 79 1   3 | 4     *279    2789   | 28  5     6   |
| 8  69  2 | 169    5      19     | 4   3     7   |
|----------+----------------------+---------------|
| 4  289 7 | 689   *69     5      | 1   269   3   |
| 5  289 1 | 6789   3      4789   | 67  24679 248 |
| 39 389 6 | 2      14-79  14789  | 57  479   458 |
|----------+----------------------+---------------|
| 2  5   9 | 37     8      347    | 367 467   1   |
| 1  37  4 | 357   *27     6      | 9   8     25  |
| 36 367 8 | 13579  14-279 123479 | 357 247   245 |
*-------------------------------------------------*

The first part is easy : there is a naked quad (2679) in the 4 cells marked * and you can remove some of these digits from other cells in column 5.

But then things get a bit tricky. I could solve the puzzle in a number of other moves, but that would take up a lot of space, so I've gone for a slightly trickier move that shortens the solution.

Code: Select all
*-------------------------------------------------*
| 67  4   5 | 3678    267 2378    | 28  1     9   |
| 79  1   3 | 4       279 2789    | 28  5     6   |
| 8   69  2 | 169     5   19      | 4   3     7   |
|-----------+---------------------+---------------|
| 4   289 7 | 689     69  5       | 1   269   3   |
| 5   289 1 | 6789    3   4789    | 67  24679 248 |
| 39  389 6 | 2       14  14789   | 57  479   458 |
|-----------+---------------------+---------------|
| 2   5   9 |a37      8   4-37    | 367 467   1   |
| 1  c37  4 |b357    b27  6       | 9   8     25  |
| 36  367 8 | 159-37  14  1249-37 | 357 247   245 |
*-------------------------------------------------*

(3=7) r7c4 - r8c45 = (7-3) r8c2 = (3) r8c4 loop => - 37 r7c6, r9c46; stte

I've included the notation, but hopefully you can convince yourself the both 3 and 7 must be in the 3 cells that I've marked a & b, so you can remove 3 & 7 from other cells in Box 8.

The puzzle solves in singles from there. If you want help with that last move, I'll try and explain it in words.

Leren
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Re: Stuck on a puzzle 16/12/2020

Postby SpAce » Wed Dec 16, 2020 8:15 pm

Hi Leren,

Leren wrote:
grid: Show
Code: Select all
*-------------------------------------------------*
| 67  4   5 | 3678    267 2378    | 28  1     9   |
| 79  1   3 | 4       279 2789    | 28  5     6   |
| 8   69  2 | 169     5   19      | 4   3     7   |
|-----------+---------------------+---------------|
| 4   289 7 | 689     69  5       | 1   269   3   |
| 5   289 1 | 6789    3   4789    | 67  24679 248 |
| 39  389 6 | 2       14  14789   | 57  479   458 |
|-----------+---------------------+---------------|
| 2   5   9 |a37      8   4-37    | 367 467   1   |
| 1  c37  4 |b357    b27  6       | 9   8     25  |
| 36  367 8 | 159-37  14  1249-37 | 357 247   245 |
*-------------------------------------------------*

(3=7) r7c4 - r8c45 = (7-3) r8c2 = (3) r8c4 loop => - 37 r7c6, r9c46; stte

I've included the notation, but hopefully you can convince yourself the both 3 and 7 must be in the 3 cells that I've marked a & b, so you can remove 3 & 7 from other cells in Box 8.

That's a nice move. I'm not sure, but for a beginner it might be slightly simpler to see the corresponding Sue de Coq:

Code: Select all
.------------.------------------------.------------------.
| 67  4    5 |  3678     267  2378    | 28   1       9   |
| 79  1    3 |  4        279  2789    | 28   5       6   |
| 8   69   2 |  169      5    19      | 4    3       7   |
:------------+------------------------+------------------:
| 4   289  7 |  689      69   5       | 1    269     3   |
| 5   289  1 |  6789     3    4789    | 67   24679   248 |
| 39  389  6 |  2        14   14789   | 57   479     458 |
:------------+------------------------+------------------:
| 2   5    9 | *37       8    4-37    | 367  467     1   |
| 1   37   4 | *357     *27   6       | 9    8      *25  |
| 36  367  8 |  159-37   14   1249-37 | 357  247     245 |
'------------'------------------------'------------------'

Sue de Coq: (37)r7c4--(37'25)r8c45--(25)r8c9 => -37 b8p379

It's pretty much the simplest possible example of a classic SdC, too. (It could be seen and written as a doubly-linked ALS-XZ, or an ALS-Loop, too).

Another way to see the logic in eleven's style: there are four possible digits (2,5,3,7) in the four cells (r7c4, r8c459), and no digit can be twice because of the way they see each other -- thus all four digits must be in those cells (or at least one would be empty). Logically that's kind of a bent quad, though that name has been (mis)used for slightly different patterns, too. Since the only cells (of that group) possible for 3 and 7 are in box 8, those digits can't exist in the other cells of that box. Similarly 2 and 5 are locked into those cells in row 8, but they have nothing to eliminate (no other candidates of 2 or 5 in that row).
-SpAce-: Show
Code: Select all
   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."
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Re: Stuck on a puzzle 16/12/2020

Postby yzfwsf » Wed Dec 16, 2020 9:30 pm

Almost Locked Pair: 37 in r8c45 r8c2 r7c4 => r7c6<>37 r9c4<>37 r9c5<>7 r9c6<>37;stte
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Re: Stuck on a puzzle 16/12/2020

Postby Fortesque92 » Thu Dec 17, 2020 2:38 am

Wow, I think most of the techniques beyond the Naked Quad are a bit out of my current skill level but I really appreciate all the responses!
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Re: Stuck on a puzzle 16/12/2020

Postby Leren » Thu Dec 17, 2020 3:35 am

Oops - mea culpa!!! When I copied your puzzle solved cell status, I left out two solved cells, the 5 and 8 in Row 6. With that fixed, all that you need is the following :

Code: Select all
*---------------------------------------------*
| 67 4   5 | 3678 267  2378 | 28   1      9   |
| 79 1   3 | 4    279  2789 | 28   5      6   |
| 8  69  2 | 169  5    19   | 4    3      7   |
|----------+----------------+-----------------|
| 4  28  7 | 689  69   5    | 1    269    3   |
| 5  28  1 | 6789 3    4789 | 67   24679  24  |
| 39 39  6 | 2    147  147  | 5    47     8   |
|----------+----------------+-----------------|
| 2  5   9 | 37   8    347  | 367  67-4   1   |
| 1  37  4 | 357  27   6    | 9    8     *25  |
| 36 367 8 | 159  1249 1249 | 37  *24    *245 |
*---------------------------------------------*

The naked triple (245) in Box 9 removes the 4 from r7c9 and the puzzle solves with singles from there. Sorry about that.

Leren
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