The New Sudoku Players' Forum

[Pupp]

Is there a name for this technique?
EDIT: Update puzzle to correct mistakes. (was missing 2 digits.) -That's what happens when I have to manually input a puzzle from my cell phone to my desktop. It's puzzle number 5033 on Sudoku 10,000 (Hard 1): starting position.

Code: Select all

 *-----------------------------------------------------------------------------*
 | 358     2       4589    | 7       6       45      | 1       389     3589    |
 | 358     4589    4589    | 12458   45      1245    | 23569   23689   7       |
 | 1       6       578     | 258     9       3       | 25      4       58      |
 *-------------------------+-------------------------+-------------------------|
 | 9       1457    3       | 1456    2       14567   | 8       67      56      |
 | 256     57      2567    | 569     8       567     | 4       1       3569    |
 | 568     14578   145678  | 3       457     14567   | 5679    679     2       |
 *-------------------------+-------------------------+-------------------------|
 | 7       159     12569   | 2456    345     8       | 2369    2369    13469   |
 | 268     3       12689   | 246     47      2467    | 2679    5       14689   |
 | 4       58      2568    | 256     1       9       | 2367    23678   368     |
 *-----------------------------------------------------------------------------*

If you look at the number 1, it looks like there are two finned X-wings super imposed on each other at a 90 deg. angle.
r2c4, r26, r4c2, r4c4, r4c6, r6c6

I was stuck and just sorta looking for something, and was a bit tired of research, so I kinda puzzled out that there might be something important about the pivot cell. I did this with other puzzles, but I wanted to make sure it was not a fluke. If you look at the cells, r4c6 is a pivot point of both finned X-wings.

So I deleted that number and it worked. It was a number that could be deleted. It happened on a different puzzle much later, and in that case it, the puzzle just was really easy to solve then. But this time I just check the analyze button and it said it was good to delete.

I wanted to mention this is actually the start of the puzzle. It's on Sudoku 10,000 Hard 1 level. FYI there are easier cells to deal with first, as far as solving the puzzle.

I'm thinking technically, cell r2c4 (in this example), is spurious, but I suspect the that particular formation will always look like two super imposed finned X wings.

[denis_berthier]

.
You're right about the existence of two similar patterns at right angles; but one of them is not a finned x-wing(*) and none of them can eliminate anything in this PM by itself.

It is also true that, in this particular grid, r4c6 is ≠ 1.
Indeed, it can be shown (using only Naked and Hidden Pairs involving other parts of the grid) that setting r4c6 = 1 implies a contradiction. This means using the T&E(S2, n1r4c6) procedure.

But I can't see any general reason, based only on the common existence of the two orthogonal patterns (independent of other parts of the grid) why one could eliminate n1r4c6.

(*) in a finned x-wing in rows (resp. in columns), the fin must be in the same block and same row (resp. column) as some non-fin candidate.

[Pupp]

I'll keep seeing if this pattern always is true.

It comes up on about 20% of the puzzles, at this level... rough estimate.

[Pupp]

.
You're right about the existence of two similar patterns at right angles; but one of them is not a finned x-wing(*) and none of them can eliminate anything in this PM by itself.

It is also true that, in this particular grid, r4c6 is ≠ 1.
Indeed, it can be shown (using only Naked and Hidden Pairs involving other parts of the grid) that setting r4c6 = 1 implies a contradiction. This means using the T&E(S2, n1r4c6) procedure.

But I can't see any general reason, based only on the common existence of the two orthogonal patterns (independent of other parts of the grid) why one could eliminate n1r4c6.

(*) in a finned x-wing in rows (resp. in columns), the fin must be in the same block and same row (resp. column) as some non-fin candidate.

What's the T&E procedure?

Also, I just leaned how to do fins, so I haven't mastered them yet, but I couldn't think of any other way to describe the pattern.

[yzfwsf]

The puzzle has 53 solutions.Curious how to solve logically .

[denis_berthier]

What's the T&E procedure?

Given a set of rules T (with the confluence property), in any resolution state, if C is a candidate, T&E(T, C) is the following procedure: suppose C is true and apply the rules in T as long as they can make some change. If this leads to a contradiction, then C is false.

[Pupp]

The puzzle has 53 solutions.Curious how to solve logically .

Let me double check to make sure I set it up correctly.

OK, I missed a couple digits.

Code: Select all

 *-----------------------------------------------------------------------------*
 | 358     2       4589    | 7       6       45      | 1       389     3589    |
 | 358     4589    4589    | 12458   45      1245    | 23569   23689   7       |
 | 1       6       578     | 258     9       3       | 25      4       58      |
 *-------------------------+-------------------------+-------------------------|
 | 9       1457    3       | 1456    2       14567   | 8       67      56      |
 | 256     57      2567    | 569     8       567     | 4       1       3569    |
 | 568     14578   145678  | 3       457     14567   | 5679    679     2       |
 *-------------------------+-------------------------+-------------------------|
 | 7       159     12569   | 2456    345     8       | 2369    2369    13469   |
 | 268     3       12689   | 246     47      2467    | 2679    5       14689   |
 | 4       58      2568    | 256     1       9       | 2367    23678   368     |
 *-----------------------------------------------------------------------------*


[Pupp]

How the heck do you use Hodoku?

I hit the "solve up to" button, it has no problem, but when I try to find steps, it says no solution... even if it's blatantly obvious there is a single hidden candidate in a box. Also the "solve up to" button just solves the entire puzzle with no steps.

[Pupp]

What's the T&E procedure?

Given a set of rules T (with the confluence property), in any resolution state, if C is a candidate, T&E(T, C) is the following procedure: suppose C is true and apply the rules in T as long as they can make some change. If this leads to a contradiction, then C is false.

I have no idea what your talking about. Is this a generalized procedure in logic puzzles, or some sort of sudoku technique?

If you could link a webite with an explanation, I'd appreciate that.

[Hajime]

T&E stands for trail and error. You try a candidate in a cell and if this leads to a invalid puzzle (no solution or many solutions) the "guess" was wrong and you can eliminate that candidate for that cell. Normally for computer solvers, not for pencil&paper solvers.
The guessing is far beyond methods like skyscrapers or kites, what are actually x-chains of length four. That are considered not guessing.

[Leren]

Code: Select all

.2.76.1..........716..93.4.9.3.2.8......8.41....3....27....8....3.....5.4...19...

The puzzle now solves with basics. They way I use Hodoku most of the time is :

1. Paste the puzzle from the clipboard into the main screen. If it is valid Hodoku will solve it.

2. In the top menu choose View / Solution path. In the right hand pane are all the steps. You can move through them one at a time, or if you want to look at a particular step, double click on it.

Leren

[Pupp]

T&E stands for trail and error. You try a candidate in a cell and if this leads to a invalid puzzle (no solution or many solutions) the "guess" was wrong and you can eliminate that candidate for that cell. Normally for computer solvers, not for pencil&paper solvers.
The guessing is far beyond methods like skyscrapers or kites, what are actually x-chains of length four. That are considered not guessing.

Thanks.

[Mathimagics]

[T&E is] Normally for computer solvers, not for pencil&paper solvers.

Objection, your honour!

I use T&E all the time! And so do many participants in Sudoku competitions, I am led to believe ...

Are we not human?

Or perhaps we are just not normal?

[Hajime]

Objection, your honour!

Granted

[denis_berthier]

T&E stands for trail and error. You try a candidate in a cell and if this leads to a invalid puzzle (no solution or many solutions) the "guess" was wrong and you can eliminate that candidate for that cell.

The problem with such old definitions is, "leads to" means nothing if you don't say what it means. Indeed, for any candidate C that is not in the solution, C logically leads to a contradiction. That's why, very long ago, I introduced a precise definition, where T&E depends on the rules one is allowed to use.

Normally for computer solvers, not for pencil&paper solvers.

I totally agree with Mathimagics two points:
- most human solvers use T&E and almost nothing else;
- it is widely acknowledged that world championships rely mostly on T&E.