## A question about difficulty rating

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

### A question about difficulty rating

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 . 33 . . | 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 . 33 . 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).
qiuyanzhe

Posts: 76
Joined: 21 August 2017
Location: China

### re: Skyscraper and Finned X-Wing

qiuyanzhe wrote:
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 ?

Pat

Posts: 3710
Joined: 18 July 2005

### Re: A question about difficulty rating

Pat wrote:where do you see these ratings ?

Sudoku 10000+ Android app
qiuyanzhe

Posts: 76
Joined: 21 August 2017
Location: China

### Re: A question about difficulty rating

qiuyanzhe wrote: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=7.3/7.3/2.6000000803304570002006009700000400509005080400140000008097001005000000000502004300 ED=6.6/6.6/2.6`

m_b_metcalf
2017 Supporter

Posts: 9822
Joined: 15 May 2006
Location: Berlin

### Re: A question about difficulty rating

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.
qiuyanzhe

Posts: 76
Joined: 21 August 2017
Location: China

### Re: A question about difficulty rating

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

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.
champagne
2017 Supporter

Posts: 6861
Joined: 02 August 2007
Location: France Brittany

### Re: A question about difficulty rating

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.
eleven

Posts: 2013
Joined: 10 February 2008