## Backdoors and puzzle difficulty level

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

### Backdoors and puzzle difficulty level

Hi all,
I have found, but you certainly have, that the harder a puzzle is, the less backdoors it has after it has been reduced by the basic techniques TB = { simple, closed set, alignment}. I'm talking about S-backdoor which allows to solve the puzzle with only singles after reduction by the TB.
For example, the extreme puzzle N°3 of Yzfwfs has no S-backdoor. The tarek puzzle of April 17, 2020 has 21.
Is there an established correspondence between the level of difficulty of a puzzle and the number of S-backdoors it has? Has this topic been covered?
Sincerely
Robert
Mauriès Robert

Posts: 486
Joined: 07 November 2019
Location: France

### Re: Backdoors and puzzle difficulty level

Hi Robert,

The Backdoor has to be defined by the technique set (in the case you mentioned, you have defined the techniques set as "TB")
The Backdoor Size is the minimum number of "ON" guesses that would reduce the puzzle to solvable using "TB" rules.
The Backdoor number is the number of different backdoor combinations available.

From all of the discussions that I have been involved in, the Backdoor number only establishes if your puzzle is harder than "TB" or not.

tarek

tarek

Posts: 3748
Joined: 05 January 2006

### Re: Backdoors and puzzle difficulty level

From all of the discussions that I have been involved in, the Backdoor number only establishes if your puzzle is harder than "TB" or not.

tarek
agreed

limitation of applied techniques{TB} only solves until x depth
then the question is how many single guesses or combined guesses does it take to reach a point where it can be solved by the techniques enabled{TB}.

to my knowledge with TB established as Singles only:
the hardest puzzles to date needed a back door size 3. {3 singles placed together at the same time to solve grid to all singles}

limited correlation between difficulty and back door size:
the only information you could gain from it is the likely hood of a guess solving to completion base on the settings of TB
Some do, some teach, the rest look it up.

StrmCkr

Posts: 1206
Joined: 05 September 2006

### Re: Backdoors and puzzle difficulty level

StrmCkr wrote:to my knowledge with TB established as Singles only:
the hardest puzzles to date needed a back door size 3. {3 singles placed together at the same time to solve grid to all singles}

limited correlation between difficulty and back door size:
the only information you could gain from it is the likely hood of a guess solving to completion base on the settings of TB

puzzles of backdoor size 4 exist, but they're not very hard (i.e. you need to place at minimum 4 numbers in the puzzle at the same time to reduce it to singles only)
dobrichev wrote:
Code: Select all
`..............1.23.45.2..6............17....852..9.3.1....4.......2.9.5.976.5..3. ED=6.6/1.2/1.2`

this is singles backdoor size 4 and it solves with a bunch of turbot fishes and an xy-wing

in general there isn't much correlation at all between difficulty and backdoor size. this beauty is backdoor size 3 and solves with pairs and a naked triplet. the easter monster is also backdoor size 3
999_Springs

Posts: 542
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

### Re: Backdoors and puzzle difficulty level

is backdoor size 3 and solves with pairs and a naked triplet. the Easter monster is also backdoor size 3

ah that is what it was subsets + singles for those. thanks for confirming that.

didn't know some one found {mind you i didn't read too much into that topic} size 4 singles that is interesting. what size is it with subsets ?
Some do, some teach, the rest look it up.

StrmCkr

Posts: 1206
Joined: 05 September 2006