The New Sudoku Players' Forum

[m_b_metcalf]

Code: Select all

 . . 1 . . . 2 . .
 . 3 . 4 . 5 . 6 .
 6 . . . . . . . 3
 . 5 . 6 . 4 . 7 .
 . . . . . . . . .
 . 8 . 7 . 3 . 5 .
 4 . . . . . . . 9
 . 9 . 8 . 7 . 3 .
 . . 3 . . . 6 . .

..1...2...3.4.5.6.6.......3.5.6.4.7...........8.7.3.5.4.......9.9.8.7.3...3...6..

[shye]

i wanted to try and solve this the intended way. since it wasn't completely logical i'll instead just talk about my thought process on trying to find the backdoor

first step i did was to obtain the solution grid, which i would use to compare the opening position to. i didnt use computer assistance for any of this solve, so it was through a mixture of logic and guessing that i got this solution
it gave me this to look at:

Code: Select all

 Opening                                   Solution
+-----------+-----------+-----------+     +----------+----------+----------+
|*5  #47  1 |#39 *36 *6 | 2   .  *5 |     | B7  4  1 |  3 B8  6 |  2  9  5 |
| .   3   . | 4   .   5 | .   6   . |     |  9  3  8 |  4  2  5 |  7  6  1 |
| 6   .  *5 | .   .   . |*5   .   3 |     |  6  2  5 |  9  7  1 | A8  4  3 |
+-----------+-----------+-----------+     +----------+----------+----------+
|*3   5  #29| 6   .   4 |*3   7   . |     | B2  5  9 |  6  1  4 |  3  7  8 |
|*3  *6   . |*5  *5   . |*3   .  *6 |     |  3 D7  4 |  2  5  8 | A9  1  6 |
| .   8  *6 | 7   .   3 | .   5  *6 |     |  1  8  6 |  7  9  3 |  4  5 E2 |
+-----------+-----------+-----------+     +----------+----------+----------+
| 4  *6  *8 |*3  *3  *6 |*7   .   9 |     |  4  6 A7 | A1  3  2 | B5  8  9 |
| .   9  *6 | 8  *46  7 | .   3   . |     |  5  9 C2 |  8 A6  7 |  1  3  4 |
|*8   .   3 | .  *4   . | 6   .  *7 |     |  8  1  3 |  5  4  9 |  6  2  7 |
+-----------+-----------+-----------+     +----------+----------+----------+

since backdoors must give stte, i figured tracking all of the 2 candidate truths in the puzzle would be the best approach
i notated on the left all the bilocals (*) and bivalues (#) i could find
i then looked at the solution to find all instances of placements that would directly affect these marks to give at least two singles (not including itself)
i notated on the right the placements that gave the most damage. letters correspond with how many direct singles they give (A=2, B=3, C=4...)

now it was time to test these, starting with the most powerful

2r6c9(E) - i was a bit upset to see this wasn't as useful as it seemed, but it made sense given most of the singles it gave on my map were the same candidate (6)
7r5c2(D) - this one was much more interesting, it did similar things to what 2r6c9 did but getting 4r1c2 was a lot more useful. it didn't solve it though, but it brings it down to a fun difficulty and could be solved with basics, uniqueness, and wings
2r8c3(C) - pretty underwhelming, it ran dry immediately after the guaranteed singles
7r1c1(B) - entering B territory, but not completely losing hope because this one gives 4r1c2 which was useful earlier. while this didn't give as much immediate progress, this one is interesting because it solves with just an m-wing after
8r1c5(B) - rather useless
2r4c1(B) - wasn't expecting this to be the one after having no luck with 8r1c5, but it worked!

after all of this i started to analyse the puzzle with software, and ran through the remaining notation to see if anything else worked or came close to working
of the others, 7r7c3(A) was surprising because it did a lot of damage and even solves with an AHS w-wing (or 4 truth AIC, if thats too fancy)


i couldnt find any others. not sure if this was insightful for you but i had fun with this anyway
=> 2r4c1 stte

[m_b_metcalf]

i couldnt find any others. not sure if this was insightful for you but i had fun with this anyway
=> 2r4c1 stte

Dear shye,

Many thanks for this analysis!

Mike