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chicago tribune 1/26/18 DS grade too hard

 
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mtharp



Joined: 19 Jun 2006
Posts: 30

PostPosted: Wed Jan 31, 2018 3:58 am    Post subject: chicago tribune 1/26/18 DS grade too hard Reply with quote

Folks, I am stuck again. Your help appreciated.

Gianni, I always admire your approach.

Keith, your conjugal pair help got me this far:

Code:

+---------+---------+-----------+
| 5  7  3 | 1 2  4  | 9  8   6  |
| 4  9  1 | 5 8  6  | 7  2   3  |
| 6  8  2 | 3 9  7  | 15 4   15 |
+---------+---------+-----------+
| 13 4  9 | 7 16 35 | 8  56  2  |
| 2  6  5 | 9 4  8  | 3  1   7  |
| 8  13 7 | 2 16 35 | 4  569 59 |
+---------+---------+-----------+
| 13 2  6 | 8 7  9  | 15 35  4  |
| 7  13 8 | 4 5  2  | 6  39  19 |
| 9  5  4 | 6 3  1  | 2  7   8  |
+---------+---------+-----------+

Play this puzzle online at the Daily Sudoku site

I hope I am not missing something simple.

Mike
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keith



Joined: 19 Sep 2005
Posts: 3340
Location: near Detroit, Michigan, USA

PostPosted: Wed Jan 31, 2018 5:46 am    Post subject: Reply with quote

Mike,

There are two things:

1. This is a BUG+1

A BUG is a pattern that is not unique. It occurs when each cell has two candidates, and each candidate occurs only twice in each house (row, column, or box).
In this case the BUG is:
Code:
+-------------+-------------+-------------+
| 5   7   3   | 1   2   4   | 9   8   6   |
| 4   9   1   | 5   8   6   | 7   2   3   |
| 6   8   2   | 3   9   7   | 15  4   15  |
+-------------+-------------+-------------+
| 13  4   9   | 7   16  35  | 8   56  2   |
| 2   6   5   | 9   4   8   | 3   1   7   |
| 8   13  7   | 2   16  35  | 4   69  59  |
+-------------+-------------+-------------+
| 13  2   6   | 8   7   9   | 15  35  4   |
| 7   13  8   | 4   5   2   | 6   39  19  |
| 9   5   4   | 6   3   1   | 2   7   8   |
+-------------+-------------+-------------+

In any cell that has two candidates, pick one of the candidates. You will get a solution. Pick the other candidate, you will also get a solution. So, what I have posted above has two solutions.

But, the rule is there is only one valid solution. Let's go back to what you posted:
Code:
+-------------+-------------+-------------+
| 5   7   3   | 1   2   4   | 9   8   6   |
| 4   9   1   | 5   8   6   | 7   2   3   |
| 6   8   2   | 3   9   7   | 15  4   15  |
+-------------+-------------+-------------+
| 13  4   9   | 7   16  35  | 8   56  2   |
| 2   6   5   | 9   4   8   | 3   1   7   |
| 8   13  7   | 2   16  35  | 4  *569 59  |
+-------------+-------------+-------------+
| 13  2   6   | 8   7   9   | 15  35  4   |
| 7   13  8   | 4   5   2   | 6   39  19  |
| 9   5   4   | 6   3   1   | 2   7   8   |
+-------------+-------------+-------------+
R6C8 cannot be 69, it must be 5.

2. There is a short chain that solves it:
Code:
+-------------+-------------+-------------+
| 5   7   3   | 1   2   4   | 9   8   6   |
| 4   9   1   | 5   8   6   | 7   2   3   |
| 6   8   2   | 3   9   7   | 15  4   15  |
+-------------+-------------+-------------+
|-13  4   9   | 7  a16  35  | 8  b56  2   |
| 2   6   5   | 9   4   8   | 3   1   7   |
| 8   13  7   | 2   16  35  | 4   569 59  |
+-------------+-------------+-------------+
|d13  2   6   | 8   7   9   | 15 c35  4   |
| 7   13  8   | 4   5   2   | 6   39  19  |
| 9   5   4   | 6   3   1   | 2   7   8   |
+-------------+-------------+-------------+
a and d are pincers on 1, via b and c. There are other similar chains.

I solve using pencil and paper in an armchair. So, I rarely use chains. I prefer to recognize patterns, like the BUG+1.

If someone posts a complex chain, you can bet they are using software to solve the puzzle. Just not my cup of tea.

Keith
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immpy



Joined: 06 May 2017
Posts: 199

PostPosted: Wed Jan 31, 2018 8:17 am    Post subject: Reply with quote

Thank you for explaining the BUG+1 Keith. A beautiful solving technique it is, indeed, when it presents itself.

Keith (or anyone here), if you can enlighten us. I have a question. Can a Skyscraper have extensions (like some wings do) on the pincers? I am curious. Can a Kite have extensions on their pincers??

Any knowledge in this regard is very appreciated. Thank you.

I am enjoying looking for strong links Keith, and I'm beginning to do it before making some pencil marks. Great tool, thanks again.

cheers...immp
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keith



Joined: 19 Sep 2005
Posts: 3340
Location: near Detroit, Michigan, USA

PostPosted: Wed Jan 31, 2018 8:47 am    Post subject: Reply with quote

Quote:
Can a Skyscraper have extensions (like some wings do) on the pincers?


immpy, absolutely! That's part of the beauty of strong links, you can string them together.

What is a swordfish? It is three strong links that line up in a certain way. (Yes, I know there are more general definitions.)

This is often called coloring, or multi-coloring.

I think my contribution here is to show you the Type C cells, so you can quickly decide if there might be worthwhile strong links (in a single digit) or not.

Which reminds me, there is a fourth thing you need to know: What is a cycle? I'll get to that. You'll be doing franken jellyfish in no time at all!

Which also reminds me, if you figure out this strong link thing, there is an entire Chinese Restaurant menu list of patterns you can forget about.

(Have you noticed on a Chinese Menu, that they have 200 choices comprising the same 15 ingredients?)

Keith
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keith



Joined: 19 Sep 2005
Posts: 3340
Location: near Detroit, Michigan, USA

PostPosted: Wed Jan 31, 2018 9:15 am    Post subject: Reply with quote

I should also remark that these single-digit strong-link patterns are difficult to program, so most published puzzles are not screened for them. That gives us pencil and paper solvers a small advantage.

immpy makes an important point: Once you learn how these single-digit strong links work, you will be able to look at a puzzle without pencil marks and decide where to search and which digits to look at.

My own solving has evolved to doing basics and then looking for useful single-digit strong links. Only after that do I look for XY- and XYZ-wings, URs, and the like. Chains are an absolute last resort.

Keith
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immpy



Joined: 06 May 2017
Posts: 199

PostPosted: Wed Jan 31, 2018 7:22 pm    Post subject: Reply with quote

Thank you Keith for all of your shared wisdom. Happy puzzle solving!

cheers...immp
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mtharp



Joined: 19 Jun 2006
Posts: 30

PostPosted: Thu Feb 01, 2018 2:14 am    Post subject: Reply with quote

Keith, thank you.

To be sure I understand, you posted:

1. This is a BUG+1

A BUG is a pattern that is not unique. It occurs when each cell has two candidates, and each candidate occurs only twice in each house (row, column, or box).
In this case the BUG is:
Code:
+-------------+-------------+-------------+
| 5 7 3 | 1 2 4 | 9 8 6 |
| 4 9 1 | 5 8 6 | 7 2 3 |
| 6 8 2 | 3 9 7 | 15 4 15 |
+-------------+-------------+-------------+
| 13 4 9 | 7 16 35 | 8 56 2 |
| 2 6 5 | 9 4 8 | 3 1 7 |
| 8 13 7 | 2 16 35 | 4 69 59 |
+-------------+-------------+-------------+
| 13 2 6 | 8 7 9 | 15 35 4 |
| 7 13 8 | 4 5 2 | 6 39 19 |
| 9 5 4 | 6 3 1 | 2 7 8 |
+-------------+-------------+-------------+

In any cell that has two candidates, pick one of the candidates. You will get a solution. Pick the other candidate, you will also get a solution. So, what I have posted above has two solutions.
___________________________________________________________

There were no asterisks so I came to the conclusion that the BUG was on 6 in r4c58, r6c58 and on 9 in r6c89 and r8c89.

Am I correct?

Again, thanks for your help.

Mike
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keith



Joined: 19 Sep 2005
Posts: 3340
Location: near Detroit, Michigan, USA

PostPosted: Thu Feb 01, 2018 3:57 pm    Post subject: Reply with quote

Mike,
Code:
+-------------+-------------+-------------+
| 5   7   3   | 1   2   4   | 9   8   6   |
| 4   9   1   | 5   8   6   | 7   2   3   |
| 6   8   2   | 3   9   7   | 15  4   15  |
+-------------+-------------+-------------+
| 13  4   9   | 7   16  35  | 8   56  2   |
| 2   6   5   | 9   4   8   | 3   1   7   |
| 8   13  7   | 2   16  35  | 4  *569 59  |
+-------------+-------------+-------------+
| 13  2   6   | 8   7   9   | 15  35  4   |
| 7   13  8   | 4   5   2   | 6   39  19  |
| 9   5   4   | 6   3   1   | 2   7   8   |
+-------------+-------------+-------------+

The rule is, you cannot have each unsolved candidate appear twice in each row, column, or box. In a BUG+1, every unsolved cell has two candidates, except one.

The recipe: pick a house (box, row, or column) containing the cell with more than two candidates. In the margin, write down the candidates, with the two-digit cells first:

R6: 13 16 35 59 569
B6: 56 59 569
C8: 56 35 39 569

Now, starting from the left, black out the first two occurrences of each candidate. So, R6 becomes, for 1:
R6: X3 X6 35 59 569
For 3:
R6: XX X6 X5 59 569
For 6:
R6: XX XX X5 59 5X9
For 5:
R6: XX XX XX X9 5X9
For 9:
R6: XX XX XX XX 5XX

So, R6C8 must be 5. I leave it to you to do the same for the box and column.

You will very quickly learn how to do this just by looking at the puzzle.

WARNING: There are puzzles where all but one cell has two candidates, but the pattern is not a BUG.

Extra Credit: There are puzzles that are BUG+2 or BUG+3. They can be quite fun to figure out.

Keith
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mtharp



Joined: 19 Jun 2006
Posts: 30

PostPosted: Thu Feb 01, 2018 4:42 pm    Post subject: Reply with quote

Keith, thanks.

I will work on the extra credit.

Mike
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immpy



Joined: 06 May 2017
Posts: 199

PostPosted: Thu Feb 01, 2018 6:52 pm    Post subject: Reply with quote

The WARNING has me intrigued...puzzles where all but one cell has two candidates, yet the pattern is NOT a BUG. I didn't think this could be possible. I would be interested in understanding this phenomenon.

cheers all...immp
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keith



Joined: 19 Sep 2005
Posts: 3340
Location: near Detroit, Michigan, USA

PostPosted: Fri Feb 02, 2018 1:25 am    Post subject: Reply with quote

immpy wrote:
The WARNING has me intrigued...puzzles where all but one cell has two candidates, yet the pattern is NOT a BUG. I didn't think this could be possible. I would be interested in understanding this phenomenon.

cheers all...immp


All I can say is I have seen examples. I am not in the habit of collecting exemplars of different puzzle types.

I think I can easily find a partial example.

Keith
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