## How hard is this puzzle ?

Everything about Sudoku that doesn't fit in one of the other sections

### How hard is this puzzle ?

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.
oxykent

Posts: 2
Joined: 11 June 2006

### Solution

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
keith
2017 Supporter

Posts: 215
Joined: 03 April 2006

### Another Solution

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
Carcul

Posts: 724
Joined: 04 November 2005

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).
ravel

Posts: 998
Joined: 21 February 2006

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.
oxykent

Posts: 2
Joined: 11 June 2006

wheres your grid maker? i wanna amke one
bootstrap

Posts: 5
Joined: 18 June 2006

### How hard is this puzzle ?

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

Cec
Cec

Posts: 1039
Joined: 16 June 2005

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".
tso

Posts: 798
Joined: 22 June 2005