The New Sudoku Players' Forum

[qiuyanzhe]

In the page Mathematics of Sudoku it is claimed that adding numbers may make a puzzle more difficult, along with an example puzzle involving UR and the extra given breaking it. In my opinion, if uniqueness solving techniques are forbidden, then adding numbers should never make a puzle harder.

But I noticed that in the latest difficulty rating that I know, Finned X-Wings are rated as 3.4, while Skyscrapers are rated as 6.6. This allows us to make a puzzle harder by adding the number at * that converts the Finned X-Wing into a Skyscraper.

Code: Select all

x=original X-Wing, f=original fin, *=extra number
. x . | . x . | . . .
------+-------+------
f * . | . x . | . . .

Here is an example, with Finned X-Wing on 1 in columns 37:
(There is a Skyscraper on 4 in rows 27 that does not work much.)

Code: Select all

. . . | . . . | 8 . 3
3 . . | 5 7 . | . . 2
. . 6 | . . 9 | 7 . .
------+-------+------
. . . | 4 . . | 5 . 9
. . 5 | . 8 . | 4 . .
1 4 . | . . . | . . 8
------+-------+------
. 9 7 | . . 1 | . . 5
. . . | . . . | . . .
5 . 2 | . . 4 | 3 . .


With extra 4@r2c3, the Finned X-Wing becomes a Skyscraper,thus difficulty raises from 3.4 to 6.6:

Code: Select all

. . . | . . . | 8 . 3
3 . 4 | 5 7 . | . . 2
. . 6 | . . 9 | 7 . .
------+-------+------
. . . | 4 . . | 5 . 9
. . 5 | . 8 . | 4 . .
1 4 . | . . . | . . 8
------+-------+------
. 9 7 | . . 1 | . . 5
. . . | . . . | . . .
5 . 2 | . . 4 | 3 . .


I don't think such things should be allowed, so I suggest increasing the rating of Finned X-Wing or decrease that of Skyscraper(I prefer the latter).

[Pat]

in the latest difficulty rating that I know,
Finned X-Wings are rated as 3.4,
while Skyscrapers are rated as 6.6

where do you see these ratings ?

[qiuyanzhe]

where do you see these ratings ?

Sudoku 10000+ Android app

[m_b_metcalf]

I don't think such things should be allowed, so I suggest increasing the rating of Finned X-Wing or decrease that of Skyscraper(I prefer the latter).

Code: Select all

000000803300570002006009700000400509005080400140000008097001005000000000502004300 ED=7.3/7.3/2.6

000000803304570002006009700000400509005080400140000008097001005000000000502004300 ED=6.6/6.6/2.6

[qiuyanzhe]

I am sorry for making this mistake. I just heard from someone that in some programs Finned X-wings are rated lower than Skyscrapers. The cause may be applying the rules about fin on standard X-wing.

[champagne]

In the page Mathematics of Sudoku it is claimed that adding numbers may make a puzzle more difficult...

Let me try another answer

First of all, rating has no clear definition.

If we refer to Sudoku Explainer's rating, the tool used in the game, the rating is split in three terms
Hardest step
Hardest step before first assignment
difficulty of the first step.

If you add all clues assigned before the hardest step, you have a good chance to end with the first step being the hardest. this is trivial.

Another topic is the use of uniqueness solving techniques (say Unique rectangles to stay simple).

It is well known that uniqueness techniques limit the call to harder solving techniques.
When you have several interleaving unique rectangles, applying only one of them can destroy the second one and force the use of harder techniques. The only way to prevent this is to apply all of them in once, what does not do Sudoku Explainer. Solving (through assignment) one of the Unique Rectangle can then increase the rating, but this is not so common.

[eleven]

Nice example !

For me personally the non-grouped skyscraper (which is a finned sashimi x-wing) is easier to spot than the finned x-wing (here a grouped skyscraper).
But people, who are used to search for x-wings plus a bit more, might see it different.