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n00bs & daily nightmare sudokus (Sept. 15th)

 
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Tomi
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PostPosted: Fri Sep 15, 2006 11:05 am    Post subject: n00bs & daily nightmare sudokus (Sept. 15th) Reply with quote

Hi guys,

The daily nightmare site says: "Puzzles found on this page are extremely difficult and require the full arsenal of techniques available".

So, the thing is, I really don't know any of the advanced techiques and in fact, I visited this site today for the first time and tried to read the advanced section. Woosh, didn't understand a thing. However, I decided to print out this day's (Sept. 15th) daily nightmare. First it looked almost impossible, but then after 45 minutes, the numbers just kept on coming. I finished this day's nightmare sudoku in under hour. I was really surprised, 'cause I thought there would be no way I could solve that bad boy. And I didn't guess ANY of the numbers, I just figured them out.

I've been filling out sudokus for about 6 months as of now. So was todays daily nightmare exceptionally easy or what? How is it possible for a n00b like me to solve this thing at all, not to mention under an hour? Do you all use those advanced fish/x-wing/dirty hippo/durka-durka techniques?
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Ruud
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PostPosted: Fri Sep 15, 2006 12:13 pm    Post subject: Reply with quote

Hi Tomi,

Many players often use advanced solving techniques without knowing their names. To classify and explain them to other people, we have to give them a name, some form of notation and a "formal" definition of the technique.

If you can post a walkthrough how you solved this Nightmare, others may be able to tell you which techniques you have used. Even better, it would be fantastic if you have found a new method. We are eager to learn new tricks.

cheers,
Ruud
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David Bryant
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PostPosted: Fri Sep 15, 2006 12:15 pm    Post subject: Try some of these Reply with quote

Hello, Tomi.

Try this one, and this one. After you've whizzed through those two, you might try this one. dcb Smile
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Tomi
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PostPosted: Fri Sep 15, 2006 6:00 pm    Post subject: Reply with quote

Ruud wrote:
Hi Tomi,

Many players often use advanced solving techniques without knowing their names.

Yeah, I actually thought about this, but then again, those techniques and methods sounded so complex, I thought that maybe I was using use some of the techniques without knowing it or their names. I wouldn't remember the whole solving process step-by-step even if I wanted, so I'm not gonna even try, heh. When I'm done with scanning the most obvious pair, I start putting missing numbers over the columns and next to rows. Then I just look if there's numbers that cross out every missing number except for that one and put it in its right place. Then there are cases when I notice that a certain "pair" is bound to be in two certain places, but I'm not able to tell wich way. Those are the only numbers I mark on the sudoku. Well hey, I scanned my solution so you can take a look at my markings.

Spoiler warning: http://koti.mbnet.fi/lanmas/Scanned%20at%2015.9.2006%2020-54.jpg

Thanks guys!
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David Bryant
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PostPosted: Fri Sep 15, 2006 10:31 pm    Post subject: Maybe we can reconstruct it ... Reply with quote

Hello again, Tomi!

I looked at your picture, but couldn't really make much sense out of it. So I thought I'd take a slightly different tack. I started the puzzle from the beginning and applied all the "elementary" techniques that you described. After a bit I get to this point.
Code:
 *--------------------------------------------------------------------*
 | 19     2      5      | 6      34     34     | 8      79     179    |
 | 39     4      7      | 8      5      1      | 23     6      29     |
 | 13     8      6      | 2      9      7      | 4      35     15     |
 |----------------------+----------------------+----------------------|
 | 6      5      8      | 4      127    9      | 1237   237    27     |
 | 2      3      19     | 5      17     8      | 167    479    4679   |
 | 7      19     4      | 3      12     6      | 125    2589   2589   |
 |----------------------+----------------------+----------------------|
 | 8      6      2      | 7      34     345    | 9      1      45     |
 | 4      19     3      | 19     68     25     | 2567   2578   25678  |
 | 5      7      19     | 19     68     24     | 26     248    3      |
 *--------------------------------------------------------------------*

What would be the next number you'd put in right here, and why? dcb
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Tomi
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PostPosted: Sat Sep 16, 2006 9:52 am    Post subject: Re: Maybe we can reconstruct it ... Reply with quote

David Bryant wrote:
Hello again, Tomi!

I looked at your picture, but couldn't really make much sense out of it. So I thought I'd take a slightly different tack. I started the puzzle from the beginning and applied all the "elementary" techniques that you described. After a bit I get to this point.
Code:
 *--------------------------------------------------------------------*
 | 19     2      5      | 6      34     34     | 8      79     179    |
 | 39     4      7      | 8      5      1      | 23     6      29     |
 | 13     8      6      | 2      9      7      | 4      35     15     |
 |----------------------+----------------------+----------------------|
 | 6      5      8      | 4      127    9      | 1237   237    27     |
 | 2      3      19     | 5      17     8      | 167    479    4679   |
 | 7      19     4      | 3      12     6      | 125    2589   2589   |
 |----------------------+----------------------+----------------------|
 | 8      6      2      | 7      34     345    | 9      1      45     |
 | 4      19     3      | 19     68     25     | 2567   2578   25678  |
 | 5      7      19     | 19     68     24     | 26     248    3      |
 *--------------------------------------------------------------------*

What would be the next number you'd put in right here, and why? dcb

Ok, so the next thing I did from here was that I tested how the board would "react" if I put 1 on the 6th row's 2nd column, 'cause I noticed that would give me number 2 on the 5th column on the 6th AND leave 5, 8 and 9 for the last 3 numbers of the 6th row. Then on the 7th column there's already 8 and 9, so that gave me 5 on the 7th column of 6th row. Then it all began to wrap up, as I knew I had a "house" on the 7th box.
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unkx80
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PostPosted: Sat Sep 16, 2006 4:49 pm    Post subject: Re: Maybe we can reconstruct it ... Reply with quote

Tomi wrote:
Ok, so the next thing I did from here was that I tested how the board would "react" if I put 1 on the 6th row's 2nd column


Sounds like trial-and-error to me... I think guessing and trial-and-error are frowned by the sudoku community.
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Ruud
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PostPosted: Sat Sep 16, 2006 5:38 pm    Post subject: Reply with quote

unkx80 wrote:
Sounds like trial-and-error to me

It sounds even more like guessing. I've checked what the implications are when you place a 1 in r6c2.

This is the resulting grid:

Code:
.------------------.------------------.------------------.
| 19    2     5    | 6     34    34   | 8     79    179  |
| 39    4     7    | 8     5     1    | 23    6     29   |
| 13    8     6    | 2     9     7    | 4     35    15   |
:------------------+------------------+------------------:
| 6     5     8    | 4     17    9    | 1237  237   27   |
| 2     3     9    | 5     17    8    | 167   47    467  |
| 7     1     4    | 3     2     6    | 5     89    89   |
:------------------+------------------+------------------:
| 8     6     2    | 7     34    345  | 9     1     45   |
| 4     9     3    | 1     68    25   | 267   2578  25678|
| 5     7     1    | 9     68    24   | 26    248   3    |
'------------------'------------------'------------------'

There is nothing in the grid that justifies the move.

When we plug in the alternative candidate, it takes a long series of cascading singles to find this conflict:

Code:
.---------.---------.---------.
| 19 2  5 | 6  4  3 | 8  79*1 |
| 9  4  7 | 8  5  1 | 3  6  2 |
| 3  8  6 | 2  9  7 | 4  5 *1 |
:---------+---------+---------:
| 6  5  8 | 4  2  9 | 1  3  7 |
| 2  3  1 | 5  7  8 | 6  4  9 |
| 7  9  4 | 3  1  6 | 5  2  8 |
:---------+---------+---------:
| 8  6  2 | 7  3  5 | 9  1  4 |
| 4  1  3 | 9  8  2 |*7 *7  6 |
| 5  7  9 | 1  6  4 | 2  8  3 |
'---------'---------'---------'


When you do not check the alternative, you are guessing, which is even more frowned upon by the Sudoku community.

Now the following move is called XY-Wing. I will explain it without using the jargon:

Code:
.------------------.------------------.------------------.
| 19    2     5    | 6     34    34   | 8    #79   -179  |
| 39    4     7    | 8     5     1    | 23    6    *29   |
| 13    8     6    | 2     9     7    | 4     35    15   |
:------------------+------------------+------------------:
| 6     5     8    | 4     127   9    | 1237 -237  #27   |
| 2     3     19   | 5     17    8    | 167  -479   4679 |
| 7     19    4    | 3     12    6    | 125   2589  2589 |
:------------------+------------------+------------------:
| 8     6     2    | 7     34    345  | 9     1     45   |
| 4     19    3    | 19    68    25   | 2567  2578  25678|
| 5     7     19   | 19    68    24   | 26    248   3    |
'------------------'------------------'------------------'


the cell in row 2, column 9 has digits 2 and 9 left. I marked it *
when this * cell contains 2, the cell in row 4, column 9 must be 7 (#)
when this * cell contains 9, the cell in row 1, column 8 must be 7 (#)
Either of the 2 cells marked # must be 7 in the solution.
The 3 cells marked with - cannot contain a 7, because they would be disabled by both # cells. As a direct result, we can place digit 7 in row 1, column 8.

Ruud
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Tomi
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PostPosted: Sat Sep 16, 2006 7:45 pm    Post subject: Reply with quote

Ruud wrote:


When you do not check the alternative, you are guessing, which is even more frowned upon by the Sudoku community.

Okey-dokey. Thou shalt smite me and I shalt not guess numbers anymore. Wink
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David Bryant
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PostPosted: Sat Sep 16, 2006 10:19 pm    Post subject: Guess if you want to Reply with quote

Tomi wrote:
... I shalt not guess numbers anymore.

Hi again, Tomi!

There's nothing "wrong" with guessing numbers. Any time you have reduced the number of possibilities in a single cell to two you can of course make a guess, with a 50% chance of being right. On a very tough puzzle, that may in fact be the quickest way to find the solution.

The problem is that it's impossible to create a "very tough" sudoku puzzle that's entirely immune to lucky guesses. Every puzzle contains several "magic squares" that, when completed correctly, reduce the rest of the puzzle to a simple series of eliminations. So if you want to just guess at the right number, go ahead. Most of the time you'll be wrong, or you won't hit on a "magic square", but every once in a while you'll get lucky and solve a "very tough" puzzle in just a few minutes.

Ruud has illustrated one way to make progress past this point in the puzzle without guessing. Here's another way.
Code:
 *--------------------------------------------------------------------*
 | 19     2      5      | 6      34*    34*    | 8      79     179    |
 | 39     4      7      | 8      5      1      | 23     6      29     |
 | 13     8      6      | 2      9      7      | 4      35     15     |
 |----------------------+----------------------+----------------------|
 | 6      5      8      | 4      127    9      | 1237   237    27     |
 | 2      3      19     | 5      17     8      | 167    479    4679   |
 | 7      19     4      | 3      12     6      | 125    2589   2589   |
 |----------------------+----------------------+----------------------|
 | 8      6      2      | 7      34*    345*   | 9      1      45     |
 | 4      19     3      | 19     68     25     | 2567   2578   25678  |
 | 5      7      19     | 19     68     24     | 26     248    3      |
 *--------------------------------------------------------------------*

Notice the four cells (r17c56) marked with an asterisk above. If r7c6 contains either a "3" or a "4" then the solution to this puzzle is not unique -- it would be possible to interchange "3" and "4" around the corners of the rectangle to obtain another solution.

Since one of the rules of Sudoku is that the solution must be unique, and since Ruud always checks his puzzles carefully to be certain this is so before he publishes them, you can rely on the uniqueness of the solution and deduce that r7c6 = 5 in this position. Oh -- people call this a "Type 1 Unique Rectangle". dcb
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Tomi
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PostPosted: Sat Sep 23, 2006 5:43 pm    Post subject: Reply with quote

Thanks guys. I've studied some of the techniques. I just completed today's (23rd) Daily Nightmare without ANY guessing. I don't know which of the advanced techniques I used, but this time I made a whole bunch of small numbers in the columns whenever I got stuck. Helped me a lot. It took 50 minutes to complete it.
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