April 19, an outsider

Discuss the <a href="http://www.sudocue.net/daily.php">Daily Sudoku Nightmare</a> here
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Ruud
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April 19, an outsider

Post by Ruud »

Just to let you know,

todays Daily Nightmare is not from my own collection. It's a scrambled version of one presented by somebody on a forum far far away...

It lacks symmetry, but makes up by letting you choose to solve it the very hard way, or perform an ingenious technique that I will explain tomorrow (unless the Nightmare gang already discovers it)

I'm confident you can do it. 8-)

Enjoy, Ruud.
“If the human brain were so simple that we could understand it, we would be so simple that we couldn't.” - Emerson M Pugh
David Bryant
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Look at column 1

Post by David Bryant »

Hi, Ruud!

I'm not sure if this is the "easy way" or not, but I noticed a naked triplet in column 1, which made the rest of the puzzle relatively straightforward. Some coloring on the "5"s and "7"s finished it off. dcb
keith
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Defeated?

Post by keith »

I get to a stage where all the possibilities are pairs, except for four squares which each have three possibilities. If I can eliminate <7> from three of these squares, the fourth solves the puzzle with a BUG.

Except, I cannot find a reasonable way to resolve the <7>'s.

Code: Select all


+-------------+-------------+-------------+
| 89  19  3   | 18  57  4   | 2   6   57  | 
| 157 6   4   | 3   17  2   | 9   57  8   | 
| 2   78  57  | 9   578 6   | 1   4   3   | 
+-------------+-------------+-------------+
| 17  3   9   | 4   2   8   | 57  157 6   | 
| 68  5   16  | 7   9   13  | 38  2   4   | 
| 4   78  2   | 6   13  5   | 38  17  9   | 
+-------------+-------------+-------------+
| 369 19  16  | 5   38  7   | 4   89  2   | 
| 39  2   57  | 18  4   13  | 6   89  57  | 
| 57  4   8   | 2   6   9   | 57  3   1   | 
+-------------+-------------+-------------+

Keith
Ruud
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Post by Ruud »

Hi guys,

I knew I could count on you 2 to give it a try.

Here is my solution:

Starting position:

Code: Select all

. . 3|. . .|. 6 .
. 6 4|. . .|9 . 8
2 . .|. . .|1 . .
-----+-----+-----
. 3 9|4 2 8|. . 6
. . .|. 9 .|. . .
4 . 2|. . 5|. . 9
-----+-----+-----
. . .|5 . 7|4 . 2
. . .|. . .|. . .
. . 8|2 . .|. 3 1
After basics,
a naked pair in column 7... more basics...
a naked pair in box 9,
the naked triple in column 1,
a hidden pair in row 8,
a naked pair in column 3... more basics...
brings us here:

Code: Select all

.------------------.------------------.------------------.
| 89    1789  3    | 189   14578 14   | 2     6     57   |
| 157   6     4    | 13    1357  2    | 9     57    8    |
| 2     789   57   | 89    578   6    | 1     4     3    |
&#58;------------------+------------------+------------------&#58;
| 17    3     9    | 4     2     8    | 57    157   6    |
| 68    5     16   | 7     9     13   | 38    2     4    |
| 4     178   2    | 6     13    5    | 38    17    9    |
&#58;------------------+------------------+------------------&#58;
| 369   19    16   | 5     38    7    | 4     89    2    |
| 39    2     57   | 138   1348  134  | 6     89    57   |
| 57    4     8    | 2     6     9    | 57    3     1    |
'------------------'------------------'------------------'
At this moment, you can find a swordfish for digit 5 in rows 1,3,8... which takes you on a path with more subsets, another swordfish, some coloring, an XYZ-wing culminating in a N-star constellation.

...but wait...there is an interesting development:

Code: Select all

.------------------.------------------.------------------.
| 89    1789  3    | 189   14578 14   | 2     6     57   |
| 157   6     4    | 13    1357  2    | 9     57    8    |
| 2     789   57   | 89    578   6    | 1     4     3    |
&#58;------------------+------------------+------------------&#58;
| 17    3     9    | 4     2     8    | 57    157   6    |
| 68   *5     16   |*7     9     13   | 38    2     4    |
| 4    *178   2    | 6     13   *5    | 38    17    9    |
&#58;------------------+------------------+------------------&#58;
| 369   19    16   |*5     38   *7    | 4     89    2    |
| 39    2     57   | 138   1348  134  | 6     89    57   |
| 57    4     8    | 2     6     9    | 57    3     1    |
'------------------'------------------'------------------'
Look at the cells I marked with a star. Normally, you do not care about cells that are solved, but take another look.

What if R6C2 contains a 7? Then there would be an isolated group of digits 5 and 7 in box 458, rows 567 and columns 246. This isolates the remaining candidates for 5 and 7 with no given value. As a result, there are 2 ways to place the remaining candidates 5 and 7. There would be at least 2 solutions to the puzzle.

Not when we assume a unique solution. So we can eliminate R6C2 digit 7 as a candidate, which allows us to solve the remainder of the puzzle with singles only.

This is a reversed uniqueness situation, a.k.a. reversed BUG. I like it because it is so easy to see, it uses completed cells, and it is so easy to build into the next version of my solver :D

In this puzzle, it significantly shortens the solving path.

David, have you been solving the same puzzle?

Ruud.
David Bryant
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Oops! I goofed.

Post by David Bryant »

Ruud wrote:David, have you been solving the same puzzle?
Yes, I was working the same puzzle. But I made a lucky(?) mistake, so my "solution" wasn't really valid.

At the point you illustrated I started chasing the chain of "5"s and "7"s, and I must have miscolored a link somewhere, because I thought I had proved that r4c8 = 1. Looking at it again I see that coloring doesn't allow that deduction.

The thing is, r4c8 = 1 is enough to solve the puzzle, so I didn't notice my logic error until I went back and re-examined the steps I had taken. My bad. dcb :?

PS I like your explanation, Ruud. It's really just a variation on the "non-unique rectangle", but this one's a "non-unique hexagon." Neat!
Myth Jellies
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Post by Myth Jellies »

I commented on the other site, so I didn't want to wreck your surprise. Nice explanation by the way. Remember that your starred cells forming your non-unique deadly pattern (aka unavoidable set) have to at least contain all of the initially given clues for those digits. I think you can have other solved clues outside.
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