Some Stratospherically Strenuous Sudoku

Question

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.

Answer 1

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.

Answer 2

I solved these Sudoku with a computer program. Its outputs ("reasonings") for each of the given boards can be found here.

My solutions are the same as Luciferangel's, so I won't repeat them here in the post (you can find them at the bottom of the files linked above).

My program performs a recursive backtracking search, which works as follows:

• The algorithm (deterministically) chooses a cell and makes a guess as to its value (e.g. guessing that cell A3 is a 3).

• Then it tries to solve the puzzle taking that guess as an assumption.

• If no solution is found (i.e. backtracking), it tries a different guess (e.g. guessing that cell A3 is a 6).

• When all possible values for that cell have been exhausted, the algorithm outputs 'no solution' (e.g. cell B2 cannot be filled)

I made a couple optimizations to better simulate how a human might approach the puzzle.

• For every cell, the program takes the intersection of the missing numbers in its corresponding row, column, and box. If this intersection has only one number, it immediately fills in that cell (e.g. cell A7 can only be a 8). If the intersection has no numbers in it, it outputs 'no solution' (e.g. cell H9 cannot be filled).

• For every row, column, and box, the program looks at the intersections computed above to see how many cells each missing number could go in to. If only one box could be filled with a given number, it immediately fills in that cell (e.g. cell B1 is the only cell in the top-left box that can be a 6). If no boxes can be filled with a given number, it outputs 'no solution' (e.g. no 1s can be placed in row G).

Each of the puzzles takes on the order of a thousand steps to solve (as opposed to my previous solution which took on the order of a hundred thousand steps per board).

Answer 3

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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