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These three sudoku are particularly irksome, can you logically deduce the solutions to all (or any!) ...and provide your reasoning?

They are all proper sudoku - each has a unique solution.

They can, of course, be solved by brute force (I can get their solution in milliseconds too).

  1. "$13$ cigars, $8$ doughnuts, and $2$ false exits for Columbo."

       1  2  3   4  5  6   7  8  9
    +---------+---------+---------+
    A| 1  ·  · | ·  9  · | ·  ·  5 |A
    B| ·  ·  4 | ·  ·  · | 1  ·  · |B
    C| ·  7  · | ·  ·  1 | ·  6  · |C
    +---------+---------+---------+
    D| ·  ·  9 | ·  3  · | 2  ·  · |D
    E| ·  ·  · | ·  ·  8 | ·  ·  3 |E
    F| 3  ·  · | 9  ·  5 | ·  ·  · |F
    +---------+---------+---------+
    G| 2  ·  · | ·  8  · | ·  ·  9 |G
    H| ·  ·  1 | ·  ·  · | 7  ·  · |H
    J| ·  6  · | ·  ·  · | ·  4  · |J
    +---------+---------+---------+
    1  2  3   4  5  6   7  8  9

  2. "$59$ little grey cells for Poirot."

           1  2  3   4  5  6   7  8  9
    +---------+---------+---------+
    A| ·  ·  9 | ·  ·  3 | 4  ·  · |A
    B| ·  2  · | ·  ·  · | ·  ·  8 |B
    C| 1  ·  · | ·  ·  · | ·  5  · |C
    +---------+---------+---------+
    D| ·  8  · | ·  ·  · | ·  ·  1 |D
    E| 5  ·  · | ·  ·  · | ·  2  · |E
    F| ·  ·  6 | ·  ·  7 | 9  ·  · |F
    +---------+---------+---------+
    G| ·  ·  · | ·  3  5 | ·  ·  · |G
    H| ·  ·  3 | 6  7  · | ·  ·  · |H
    J| ·  ·  · | 9  4  · | 7  ·  · |J
    +---------+---------+---------+
    1  2  3   4  5  6   7  8  9

  3. "$22$ premises for Sherlock."

       1  2  3   4  5  6   7  8  9
    +---------+---------+---------+
    A| 3  ·  · | ·  ·  6 | ·  4  · |A
    B| ·  ·  · | ·  2  · | 1  ·  · |B
    C| ·  5  · | ·  ·  · | ·  ·  8 |C
    +---------+---------+---------+
    D| ·  8  · | 9  ·  3 | ·  7  · |D
    E| ·  ·  · | ·  ·  · | 8  ·  5 |E
    F| 7  ·  · | ·  ·  · | ·  9  · |F
    +---------+---------+---------+
    G| 9  ·  · | 6  ·  4 | ·  ·  · |G
    H| ·  2  · | ·  1  · | ·  ·  · |H
    J| ·  ·  6 | 7  ·  · | ·  ·  · |J
    +---------+---------+---------+
    1  2  3   4  5  6   7  8  9


These sudoku are not my own creations, they are permutations of other's work. I will credit their creators to the best of my ability when the puzzling is done. here...

These were permuted from some entries in the "Hardest Sudokus" database, which was available via the New Sudoku Player's Forum (no https version) as compiled by the user champagne. I cannot find the posts for the first two, so below are
My title - "DB author text" - forum user name (DB date) original in column-major order:

  1. Columbo - "elev" - eleven* (?) ........94....92......7..45..1.3.....7.6..9..8....7..2.3.7..8....6.1....9....5.2.
  2. Poirot - "dob" - dobrichev* (12 Dec 2003) .......12......345..3..46....2..1.3..7..6....8..9.......5..2..4.6..8....9..7.....
  3. Sherlock - "OW" - Obi-Wahn (Aug 2015) 5.6...7...1.3.....8...5.9.....1...2.....8.6.7.....2.4.7...9...6.3...42....5......

* I think

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  • $\begingroup$ I find it interesting that all of the words from sudoku 1's sentence start with a letter that can be used for a coordinate. $\endgroup$
    – Deusovi
    Jul 19, 2016 at 7:07
  • $\begingroup$ @Deusovi Heh, 13CIGARS8DOUGHNUT5AND2FALS3EXIT5FO2COLUMBO. $\endgroup$ Jul 19, 2016 at 7:52
  • $\begingroup$ Is that comment a hint, or just something unintentional but mildly interesting? $\endgroup$
    – Deusovi
    Jul 19, 2016 at 7:53
  • 2
    $\begingroup$ @ColdFrog the toughest are far less likely to be produced while maintaining Nikon's symmetric clues ideal, nice though it is. $\endgroup$ Jul 19, 2016 at 20:35
  • 1
    $\begingroup$ @justhalf thanks for the nudge - I have done my best, but should have done so earlier. $\endgroup$ Sep 30, 2021 at 22:10

2 Answers 2

6
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Question 1

This one was quite hard.

   1  2  3   4  5  6   7  8  9
 +---------+---------+---------+
A| 1  2  6 | 4  9  7 | 8  3  5 |A
B| 9  5  4 | 8  6  3 | 1  2  7 |B
C| 8  7  3 | 5  2  1 | 9  6  4 |C
 +---------+---------+---------+
D| 7  4  9 | 1  3  6 | 2  5  8 |D
E| 6  1  5 | 2  7  8 | 4  9  3 |E
F| 3  8  2 | 9  4  5 | 6  7  1 |F
 +---------+---------+---------+
G| 2  3  7 | 6  8  4 | 5  1  9 |G
H| 4  9  1 | 3  5  2 | 7  8  6 |H
J| 5  6  8 | 7  1  9 | 3  4  2 |J
 +---------+---------+---------+
   1  2  3   4  5  6   7  8  9

Question 2

Easier than the first

   1  2  3   4  5  6   7  8  9
 +---------+---------+---------+
A| 8  6  9 | 5  1  3 | 4  7  2 |A
B| 4  2  5 | 7  6  9 | 1  3  8 |B
C| 1  3  7 | 4  2  8 | 6  5  9 |C
 +---------+---------+---------+
D| 7  8  2 | 3  9  4 | 5  6  1 |D
E| 5  9  4 | 1  8  6 | 3  2  7 |E
F| 3  1  6 | 2  5  7 | 9  8  4 |F
 +---------+---------+---------+
G| 9  7  1 | 8  3  5 | 2  4  6 |G
H| 2  4  3 | 6  7  1 | 8  9  5 |H
J| 6  5  8 | 9  4  2 | 7  1  3 |J
 +---------+---------+---------+
   1  2  3   4  5  6   7  8  9

Question 3

This one took a while too

   1  2  3   4  5  6   7  8  9
 +---------+---------+---------+
A| 3  1  2 | 8  9  6 | 5  4  7 |A
B| 8  7  9 | 4  2  5 | 1  3  6 |B
C| 6  5  4 | 1  3  7 | 9  2  8 |C
 +---------+---------+---------+
D| 2  8  5 | 9  6  3 | 4  7  1 |D
E| 4  9  3 | 2  7  1 | 8  6  5 |E
F| 7  6  1 | 5  4  8 | 2  9  3 |F
 +---------+---------+---------+
G| 9  3  8 | 6  5  4 | 7  1  2 |G
H| 5  2  7 | 3  1  9 | 6  8  4 |H
J| 1  4  6 | 7  8  2 | 3  5  9 |J
 +---------+---------+---------+
   1  2  3   4  5  6   7  8  9

All in all, it took me about a week in my free time to do all of these. I am on my holidays so I spent hours each day, racking my brain through these. Definitely some of the harder ones that I have seen.

My Reasoning

I used the cross-hatching method as shown in this Link. And if that didn't work out, I would start over again.

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  • $\begingroup$ Welcome to Puzzling Stack Exchange. Note that the question says “and provide your reasoning”. $\endgroup$ Aug 27, 2016 at 3:58
  • $\begingroup$ @PeregrineRook Noted and edited $\endgroup$ Aug 27, 2016 at 4:13
  • $\begingroup$ Cross-hatching on its own would yield just one number across the three, a single 2 in 3. "22 premises for Sherlock." and then nothing more, so you did something beyond that; did you not take notes on other logical deductions you made? $\endgroup$ Aug 27, 2016 at 4:41
  • 1
    $\begingroup$ @JonathanAllan Ahhh i see what you mean. I am not sure how to explain to you logically but yeah. i did it just with a pencil eraser and a lot of time. hahah. good questions tho $\endgroup$ Aug 27, 2016 at 9:56
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    $\begingroup$ FYI my home brewed solver solves all of them in milliseconds :p It also gives no logical reasoning. $\endgroup$ Aug 27, 2016 at 9:59
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I don't think you are going to get a better logical explanation of a solve for these. I ran them through Sudoku Explainer and they all got a score of SE 11.8 or SE 11.9 which is well in the range of not reasonably human solvable. I also ran them through multiple other human style solvers and they all choked. It's possible there is some obscure method that none of the solvers I used have implemented yet but it is more likely there is no straightforward human friendly logical solution to them. Following is the output of Sudoku Explainer for each board. If you want more step by step info I suggest you get Sudoku Explainer:

13 cigars, 8 doughnuts, and 2 false exits for Columbo.
Analysis results
Difficulty rating: 11.8
This Sudoku can be solved using the following logical methods: 
55 x Hidden Single 
1 x Direct Hidden Pair 
1 x Naked Single 
3 x Pointing 
2 x Claiming 
5 x Naked Pair 
1 x Hidden Pair 
1 x BUG type 1 
5 x Turbot Fish 
1 x Forcing X-Chain 
2 x Bidirectional Cycle 
5 x Forcing Chain 
1 x Nishio Forcing Chains 
1 x Cell Forcing Chains 
4 x Region Forcing Chains 
6 x Dynamic Cell Forcing Chains 
15 x Dynamic Region Forcing Chains 
8 x Dynamic Contradiction Forcing Chains 
7 x Dynamic Contradiction Forcing Chains (+) 
1 x Dynamic Double Forcing Chains (+) 
9 x Dynamic Contradiction Forcing Chains (+ Forcing Chains) 
6 x Dynamic Contradiction Forcing Chains (+ Multiple Forcing Chains) 
1 x Dynamic Contradiction Forcing Chains (+ Dynamic Forcing Chains) 

59 little grey cells for Poirot.
Analysis results
Difficulty rating: 11.8
This Sudoku can be solved using the following logical methods: 
59 x Hidden Single 
8 x Pointing 
9 x Claiming 
6 x Naked Pair 
3 x Hidden Pair 
4 x Naked Triplet 
1 x Swordfish 
1 x XYZ-Wing 
3 x Bidirectional Y-Cycle 
2 x Turbot Fish 
1 x Forcing X-Chain 
10 x Forcing Chain 
1 x Bidirectional Cycle 
4 x Nishio Forcing Chains 
1 x Cell Forcing Chains 
3 x Region Forcing Chains 
1 x Dynamic Cell Forcing Chains 
16 x Dynamic Contradiction Forcing Chains 
1 x Dynamic Region Forcing Chains 
5 x Dynamic Contradiction Forcing Chains (+) 
2 x Dynamic Region Forcing Chains (+) 
3 x Dynamic Contradiction Forcing Chains (+ Forcing Chains) 
2 x Dynamic Contradiction Forcing Chains (+ Multiple Forcing Chains) 
3 x Dynamic Cell Forcing Chains (+ Dynamic Forcing Chains) 
1 x Dynamic Contradiction Forcing Chains (+ Dynamic Forcing Chains) 
3 x Dynamic Region Forcing Chains (+ Dynamic Forcing Chains) 

22 premises for Sherlock:
Analysis results
Difficulty rating: 11.9
This Sudoku can be solved using the following logical methods: 
55 x Hidden Single 
2 x Direct Hidden Pair 
6 x Pointing 
1 x Claiming 
2 x Naked Pair 
1 x Unique Rectangle type 1 
1 x Turbot Fish 
1 x Bidirectional Cycle 
4 x Forcing Chain 
2 x Cell Forcing Chains 
4 x Region Forcing Chains 
7 x Dynamic Region Forcing Chains 
5 x Dynamic Contradiction Forcing Chains 
1 x Dynamic Region Forcing Chains (+) 
1 x Dynamic Contradiction Forcing Chains (+) 
1 x Dynamic Region Forcing Chains (+ Forcing Chains) 
6 x Dynamic Contradiction Forcing Chains (+ Forcing Chains) 
6 x Dynamic Contradiction Forcing Chains (+ Multiple Forcing Chains) 
6 x Dynamic Contradiction Forcing Chains (+ Dynamic Forcing Chains) 
1 x Dynamic Cell Forcing Chains (+ Dynamic Forcing Chains) 
2 x Dynamic Region Forcing Chains (+ Dynamic Forcing Chains) 
```
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