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Another one

 
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Sat Dec 26, 2020 8:23 pm    Post subject: Another one Reply with quote

Here is another in my "I told you so" series. Enjoy!

Code:
+-------+-------+-------+
| . . . | . 4 . | 6 3 . |
| . . . | 5 . . | . . 1 |
| 8 . . | 3 9 . | 4 . 7 |
+-------+-------+-------+
| . . 5 | . . . | 9 . 2 |
| . 2 . | 9 . 5 | . 8 . |
| 9 . 4 | . . . | 5 . . |
+-------+-------+-------+
| 5 . 7 | . 6 9 | . . 8 |
| 2 . . | . . 1 | . . . |
| . 1 9 | . 3 . | . . . |
+-------+-------+-------+


Hint: After basics, there is a "simple" one-stepper.

Keith
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ZeroAssoluto



Joined: 05 Feb 2017
Posts: 640
Location: Rimini, Italy

PostPosted: Sun Dec 27, 2020 8:37 am    Post subject: Reply with quote

Hi everyone,

Finned Swordfish with number 7 in r259c567, finned in r9c8 and -7 in r8c7.

Ciao Gianni
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dongrave



Joined: 06 Mar 2014
Posts: 450

PostPosted: Sun Dec 27, 2020 3:45 pm    Post subject: Reply with quote

Code:

+------------+--------------+--------------+
| 7   59  2  | 1   4    8   | 6   3    59  |
| 346 469 36 | 5   27   267 | 8   29   1   |
| 8   56  1  | 3   9    26  | 4   25   7   |
+------------+--------------+--------------+
| 13  78  5  | 467 178  347 | 9   167  2   |
| 136 2   36 | 9   17   5   | 137 8    4   |
| 9   78  4  | 267 1278 237 | 5   167  36  |
+------------+--------------+--------------+
| 5   34  7  | 24  6    9   | 123 14   8   |
| 2   346 8  | 47  5    1   | 37  4679 369 |
| 46  1   9  | 8   3    247 | 27  4567 56  |
+------------+--------------+--------------+

Instead of using a simple Finned Swordfish (that I couldn't find) I used a simple forcing chain. Smile

(6=4)r9c1 - r9c6 = (4-3)r4c6 = r6c6 - (3=6)r6c9 => r9c9 <> 6; stte.
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Sun Dec 27, 2020 10:57 pm    Post subject: Reply with quote

ZeroAssoluto is correct, but I have a way of coming at these things that others may find useful.

After basics:

Code:
+----------------+----------------+----------------+
| 7    59   2    | 1    4    8    | 6    3    59   |
| 346  469  36   | 5    27   267  | 8    29   1    |
| 8    56   1    | 3    9    26   | 4    25   7    |
+----------------+----------------+----------------+
| 13   78   5    | 467  178  347  | 9    167  2    |
| 136  2    36   | 9    17   5    | 137  8    4    |
| 9    78   4    | 267  1278 237  | 5    167  36   |
+----------------+----------------+----------------+
| 5    34   7    | 24   6    9    | 123  14   8    |
| 2    346  8    | 47   5    1    | 37   4679 369  |
| 46   1    9    | 8    3    247  | 27   4567 56   |
+----------------+----------------+----------------+


There is a UR and an xy-Wing (both taking out 7s) which will get you to a kite that makes the single-step elimination, -7 in R8C7.

But, look at the after basics grid above. We are interested in single-digit eliminations like you find with turbots (kites and skyscrapers) or with fish (x-Wings, swordfish, etc.)

For each unsolved digit, look at how its possibilities occur in each 3x3 box. If the possibilities lie in more than one row or column, that box is "interesting".

Look for example, at the candidate 3. In box 1 there are two candidates in row 2. Not interesting. The interesting boxes for 3 are box 4, 6, and 9. So far, so good.

Now, the critical point: If the interesting boxes are to be useful, there must be four of them arranged in a rectangle*. If not, there is no single-digit elimination.

* Full disclosure: Also, there may be six boxes arranged in a swordfish pattern, but let's keep it simple.

Get it? In this grid there is no possibility of a kite or a skyscraper or an x-Wing or ... for digit 3. Don't even bother to look.

Now look at digit 6. There are four interesting boxes: 1, 6, 7, and 9. But they do not lie in a rectangle. Move on.

The only interesting and potentially useful digit is 7. The interesting boxes are 5, 6, 8, and 9. And, they lie in a rectangle.

Now, look for single-digit strong links on 7.

Code:
+----------------+----------------+----------------+
| 7    59   2    | 1    4    8    | 6    3    59   |
| 346  469  36   | 5    27a  267A | 8    29   1    |
| 8    56   1    | 3    9    26   | 4    25   7    |
+----------------+----------------+----------------+
| 13   78   5    | 467  178  347  | 9    167  2    |
| 136  2    36   | 9    17b  5    | 137B 8    4    |
| 9    78   4    | 267  1278 237  | 5    167  36   |
+----------------+----------------+----------------+
| 5    34   7    | 24   6    9    | 123  14   8    |
| 2    346  8    | 47C  5    1    | 3-7  4679 369  |
| 46   1    9    | 8    3    247c | 27D 4567D 56   |
+----------------+----------------+----------------+


Three strong links on 7 are marked: aA, bB, and cC. The logic is:
1. At least one of a and b is not true (not 7).
2. If a is not true, A is true; if b is not true, B is true; if c is not true, C is true.
3. If A is true, c is not true.
4. C and B are thus pincers on 7. (One or both of C and B are 7.)

For extra credit, note the grouped strong link in row 9. If c is not true, one of the cells DD is true. Any cell that sees both B and the two cells DD is not 7, making the same elimination in r8c7.

A few comments:

I hope you find this useful. I do. If not, thank you anyway for reading.

I solve puzzles with pencil and paper in an armchair. I do not use software, except to format puzzles for posts like this. If you do use software in solving puzzles, all this may be not interesting to you.

I find it easy (after some practice) to scan a puzzle for interesting boxes, and thus not waste my time looking for kites and skyscrapers where they do not exist. The exercise is also useful to find basic moves I may have missed.

I apply the logic of strong links as I go. So, I have no need to remember patterns like all the species of turbots and fish, and their finned and kraken variants.

Best wishes,

Keith


Last edited by keith on Mon Dec 28, 2020 8:28 pm; edited 1 time in total
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immpy



Joined: 06 May 2017
Posts: 470

PostPosted: Mon Dec 28, 2020 4:56 pm    Post subject: Reply with quote

Thank you Keith, for the puzzle and the beautiful dissertation on useful strong links. More fuel for us armchair solvers to burn. I will be referring to this one often I'm sure, as it sinks in to the gray matter! Thanks again.

cheers...immp
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dongrave



Joined: 06 Mar 2014
Posts: 450

PostPosted: Mon Dec 28, 2020 7:28 pm    Post subject: Reply with quote

Thanks for the pointers Keith! They're much appreciated!
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Mon Dec 28, 2020 8:32 pm    Post subject: Reply with quote

dongrave and immpy,

Thank you very much for the positive comments. Greatly appreciated.

Keith
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immpy



Joined: 06 May 2017
Posts: 470

PostPosted: Sat Jan 02, 2021 10:32 pm    Post subject: Reply with quote

So useful, this search for "interesting boxes". I see it everywhere now. Previously, I simply wasn't aware of it at all, let alone how it might aid in making eliminations. Brilliant Keith!

cheers...immp
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