The New Sudoku Players' Forum

[champagne]

I did not work before on the back doors, but I had to do it recently and faced a problem.
My question is

What is the difference between a 2 cells backdoor and T&E(3)??

Trying to produce non degenerated tridagon in a solution grid, I got so many grids that rating appeared as a bottleneck in the process.

I decided using the brute force DLL to select sudokus with a back door of 2 cells.(I had no available code to do it before).
I tested “loki” among others and was surprised to see it is solved with a backdoor of 2 cells.

I assumed that this was coming from the set of rules used in the brute force and started the coding of a brute force limited to the singles.
Surprise for me, “loki” remains solved “singles to the end” if 2 given are added.

Having a fresh code, I checked carefully the path under control of skfr, my rating code, but I could not see any error.

Code: Select all

57....9..........8.1.........168..4......28.9..2.9416.....2.....6.9.82.4...41.6.. loki
576843921493261578218759436951687342647132859832594167184326795365978214729415683 solution grid


If we add the given 1r1c9 and 7 r9c1

Code: Select all

57....9.1........8.1.........168..4......28.9..2.9416.....2.....6.9.82.47..41.6..


Then the puzzle can be solved just by

Last cell in unit
singles in cells
last cell for a digit in unit

what I think is the definition for “singles to the end”

What else is in T&E(3) to explain that loki has been classified T&E(3).

[yzfwsf]

999_Springs wrote:

Code: Select all

123  12   123 |456  45   456 |789  78   789
456  45   456 |789  78   789 |123  12   123
789  78   789 |123  12   123 |456  45   456
--------------+--------------+-------------
12   23   13  |45   56   46  |78   89   79
45   56   46  |78   89   79  |12   23   13
78   89   79  |12   23   13  |45   56   46
--------------+--------------+-------------
13   123  12  |46   456  45  |79   789  78
46   456  45  |79   789  78  |13   123  12
79   789  78  |13   123  12  |46   456  45


The size of the backdoor of this sukaku is 9, but in T&E (1).Based on this, it is speculated that there may not be a fixed correlation between T&E and Backdoor size.

[champagne]

Thanks ysfwsf. It does not tell me what is T&E, but I learned that it is very far from the back door

[yzfwsf]

T&E is for individual candidate, not for the entire puzzle. Backdoor is aimed at the entire puzzle, which means that one step can lead to STTE, while T&E requires many steps to lead to STTE. Some puzzles may also require only one single T&E elimination to lead to STTE.I speculate that only the T&E part is related to the backdoor.

[Maxito_Bahiense]

Not an expert on T&E (apologies in advance for conceptual errors) but my understanding is the following:

• An n-size (singles) backdoor is a set of n candidates such that if assumed true (written in) collapses the grid to stte. Similarly, we could define the backdoor for basics such as singles and locked candidates.
• A puzzle is in T&E (singles) if assuming one candidate true, a contradiction can be found solving the grid with singles, and hence finding that the original candidate can be eliminated. A puzzle is in T&E n (singles) if n candidates must be assumed true until we find a contradiction by singles.

Hence, according to your findings, you can solve Loki by writing in two correct candidates, and you can write in 2 incorrect digits still not finding a contradiction just using singles.

[champagne]

Thanks to both for this information
This also tells me that a filler of the millions puzzles seen daily having a non degenerative tridagon based on the the back doors is not he right idea to save rating time and select puzzles of interest. I have seen puzzles in mith's file of 4000k puzzles with a one clue backdoor and a very high rating.