How hard is this puzzle ?

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How hard is this puzzle ?

Postby oxykent » Sun Jun 11, 2006 2:23 pm

Hello, I wrote a little program that generates Sudoku grids, here is the hardest grid I could create :
Code: Select all
 . . . | . 6 . | . . .
 2 6 . | . 4 9 | 1 . .
 1 5 . | . . . | 4 . .
-------+-------+-------
 4 . . | 2 . 6 | . 8 .
 5 2 . | . . 4 | 9 . .
 . . 6 | 5 . . | 2 4 .
-------+-------+-------
 . . 2 | 9 5 . | 6 . 4
 . 4 1 | . . . | 7 2 .
 . 7 5 | . . . | . 9 .


I'd like to know how you guys would rate this grid, I could not solve it myself but I'm no expert at all.
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Solution

Postby keith » Sun Jun 11, 2006 2:47 pm

I think people will rate this from medium to hard, depending on the solution sequence they find. Using singles only, you get to here:

Code: Select all
+-------------+-------------+-------------+
| 378 9   4   | 1   6   5   | 38  37  2   |
| 2   6   378 | 378 4   9   | 1   5   378 |
| 1   5   378 | 378 378 2   | 4   6   9   |
+-------------+-------------+-------------+
| 4   13  9   | 2   37  6   | 5   8   137 |
| 5   2   378 | 378 1   4   | 9   37  6   |
| 378 138 6   | 5   9   38  | 2   4   137 |
+-------------+-------------+-------------+
| 38  38  2   | 9   5   7   | 6   1   4   |
| 9   4   1   | 6   38  38  | 7   2   5   |
| 6   7   5   | 4   2   1   | 38  9   38  |
+-------------+-------------+-------------+

There is an XYZ-wing whose reduction is not very helpful. There is also a Unique Rectangle, whose reduction is not very useful.

To solve the puzzle, note the strong links on <7> in R1 and R6. This means one or both of R1C8 and R6C9 must be <7>, so R5C8 must be <3>.

This pattern is sometimes called a fork. It is multi-coloring on the value <7>. (The strong link in C1 is not needed to make this elimination.)

Keith
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Another Solution

Postby Carcul » Mon Jun 12, 2006 8:06 am

Code: Select all
+-------------+-------------+-------------+
| 378 9   4   | 1   6   5   | 38  37  2   |
| 2   6   378 | 378 4   9   | 1   5   378 |
| 1   5   378 | 378 378 2   | 4   6   9   |
+-------------+-------------+-------------+
| 4   13  9   | 2   37  6   | 5   8   137 |
| 5   2   378 | 378 1   4   | 9   37  6   |
| 378 138 6   | 5   9   38  | 2   4   137 |
+-------------+-------------+-------------+
| 38  38  2   | 9   5   7   | 6   1   4   |
| 9   4   1   | 6   38  38  | 7   2   5   |
| 6   7   5   | 4   2   1   | 38  9   38  |
+-------------+-------------+-------------+

{ATILA(3,7): r1c1|r1c8|r5c8|r5c3|r2c3 or r3c3},

which implies that both r2c3/r3c3 cannot be "8" and that solves the puzzle.
I would rate this puzzle as "Easy".

Carcul
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Postby ravel » Mon Jun 12, 2006 10:05 am

Sudoku ratings are very relative.
A puzzle needing simple coloring (or 2 strong links) is easy for Carcul and some others here, while i guess, most here would rate it medium, most newspapers and many sudoku sites would rate it very hard. It is also too hard for the SUPERIOR puzzles, which i think, are rated v/hard by the Pappocom software.
So take the rating you like:)

PS: See this recent post by Ruud about rating systems. You can find his program on his site (but i dont have it because it needs the .NET framework stuff for the installation).
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Postby oxykent » Mon Jun 12, 2006 3:42 pm

Thanks for the inputs !

As far as I can see, this grid is very hard if you only know the basic solving techniques, but it gets much easier if you know some of the advanced techniques.

This is close to what I wanted to achieve here, a grid suitable for learning more advanced techniques.
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Postby bootstrap » Mon Jun 19, 2006 5:29 am

wheres your grid maker? i wanna amke one
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How hard is this puzzle ?

Postby Cec » Mon Jun 19, 2006 1:16 pm

bootstrap wrote:wheres your grid maker? i wanna amke one

Click HERE

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Postby tso » Tue Jun 20, 2006 1:55 pm

Who is faster, the winner of the marathon or the 100 meter dash? The difficulty of a puzzle, beyond being subjective, cannot satisfactorily squished onto a linear scale.

This puzzle requires only one deduction other than singles to solve. At the start of the puzzle, there are many singles available, so that part will be subjectively easy for most people. There will be fewer and few available at a time -- eventually only one, then none. At this point, in my opinion, the simplest thing do do is simple (not muliple) coloring on 7's. After that, the singles come faster and faster.

After the singles run out:
Code: Select all
+-------+-------+-------+
| . 9 4 | 1 6 5 | . . 2 |
| 2 6 . | . 4 9 | 1 5 . |
| 1 5 . | . . 2 | 4 6 9 |
+-------+-------+-------+
| 4 . 9 | 2 . 6 | 5 8 . |
| 5 2 . | . 1 4 | 9 . 6 |
| . . 6 | 5 9 . | 2 4 . |
+-------+-------+-------+
| . . 2 | 9 5 7 | 6 1 4 |
| 9 4 1 | 6 . . | 7 2 5 |
| 6 7 5 | 4 2 1 | . 9 . |
+-------+-------+-------+


Applying simple coloring to the 7s:
Code: Select all
*--------------------------------------------------*
|-378  9    4    | 1    6    5    | 38  +37   2    |
| 2    6    378  | 378  4    9    | 1    5   -378  |
| 1    5    378  | 378  378  2    | 4    6    9    |
|----------------+----------------+----------------|
| 4    13   9    | 2    37   6    | 5    8    137  |
| 5    2    378  | 378  1    4    | 9   -37   6    |
|+378  138  6    | 5    9    38   | 2    4   -137  |
|----------------+----------------+----------------|
| 38   38   2    | 9    5    7    | 6    1    4    |
| 9    4    1    | 6    38   38   | 7    2    5    |
| 6    7    5    | 4    2    1    | 38   9    38   |
*--------------------------------------------------*


Code: Select all
*--------------------------------------------------*
|-7    .    .    | .    .    .    | .   +7    .    |
| .    .    7    | 7    .    .    | .    .   -7    |
| .    .    7    | 7    7    .    | .    .    .    |
|----------------+----------------+----------------|
| .    .    .    | .    7    .    | .    .    7    |
| .    .    7    | 7    .    .    | .   -7    .    |
|+7    . .  .    | .    .    .    | .    .   -7    |
|----------------+----------------+----------------|
| .    .    .    | .    .    .    | .    .    .    |
| .    .    .    | .    .    .    | .    .    .    |
| .    .    .    | .    .    .    | .    .    .    |
*--------------------------------------------------*


Those marked with a '-' can be excluded.

Personally, I woudn't have been able to solve this without using pencilmarks, so I wouldn't call it "easy". But I didn't need to use pencil marks until coloring the 7s, and by then, no cell needed more than three marks, so I woudn't call it "hard".
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