The New Sudoku Players' Forum

[Pupp]

1. look for 3 cells in an "L" pattern. Like 3 corners of a box.

2. There needs to be 3 different pairs of pencil mark numbers.

3. There needs to a single number that is in all 3 cells. Also known as a common denominator.

4. The 2nd number in the 3 cells have to be all different.

eg: example: pm is pencil mark , "2" is the common denominator.

cell "a" = pm 2,7
cell "b" = pm 2,8 and is the corner cell
cell "c" = pm 2,4

the "8" in the corner cell is the correct number to put in cell "b".

And it might scale up to triple pencil mark numbers where there are 2 common denominators.

[SpAce]

Hidden Text: Show

1. look for 3 cells in an "L" pattern.

2. There needs to be 3 different pairs of pencil mark numbers.

3. There needs to a single number that is in all 3 cells. Also known as a common denominator.

4. The 2nd number in the 3 cells have to be different.

eg: example: pm is pencil mark , "2" is the common denominator.

cell "a" = pm 2,7
cell "b" = pm 2,8 and is the corner cell
cell "c" = pm 2,4

the "8" in the corner cell is the correct number to put in cell "b".

Ok. I think I see such a pattern (27)r3c7, (29)r4c7, (24)r4c3:

Code: Select all

.-----------.---------------.-------------.
| 1  9  6   | 2     4   7   | 3    5    8 |
| 8  2  7   | 3     5   1   | 4    6    9 |
| 3  4  5   | 68    9   68  | 27*  27   1 |
:-----------+---------------+-------------:
| 7  8  24* | 1     6   49  | 29*  3    5 |
| 5  6  1   | 89    2   3   | 89   4    7 |
| 9  3  24  | 578   78  458 | 1    28   6 |
:-----------+---------------+-------------:
| 6  7  89  | 589   3   2   | 58   1    4 |
| 4  5  3   | 6789  1   689 | 678  789  2 |
| 2  1  89  | 4     78  56  | 56   789  3 |
'-----------'---------------'-------------'

Does that mean I can safely place 9 in r4c7?

[Pupp]

I've been using that technique for weeks. It's long past the guessing stage for me.

Okay. Let's assume so. Can you give the exact specifications of the pattern so the rest of us could learn to use it? What I see in this case is this:

We have three bivalue cells with one common digit (2) and three other digits (4,8,7) -- one for each cell. One of the three cells (let's call that a pivot cell) sees the other two (via row and column). All three cells are in different boxes. According to you, that pattern somehow proves that the non-common digit (8) can be placed in the pivot cell.

Does that describe your pattern in general, or is there something I'm missing? Is there anything that can be different (like two cells in the same box)?

In other words, you should be able to give me enough information to be able to recognize the same pattern in any puzzle (that has it) and safely execute the placement. Can you do that?

I"ll have to get back on that after I do some more puzzles. I need to do some sleuthing on why it works so often, and also figure out what's different about the other 3 cells that was pointed out. Right now, I noticed that in the 3 cells that was pointed out, that 2 of the cells are next to each other. I'm wondering if that is important. I don't recall using the technique with cells that were next to each other. There are some other things I'm curious about too. Maybe the technique is valid if I can refine what to look for.

I'd have to do a bunch of puzzles to figure it out. I can't just look at a single puzzle.

[mith]

Try looking at the single puzzle SpAce just posted. (Which is the same puzzle, just with a few extra digits filled in.)

[SpAce]

I"ll have to get back on that after I do some more puzzles. I need to do some sleuthing on why it works so often

It might actually have a relatively high probability of working, because the non-common digit in the pivot cell has four possible combinations (with the other two cells) and the common digit only one.

Thus, you could indeed be making educated guesses, but guesses nonetheless. Often is not good enough in sudoku. Unless a pattern works always and the reason can be explained with logic, it's guessing. (I just proved that it doesn't work always.)

(Btw, could someone with relevant software actually test if that probability hypothesis is true? Or can someone with better math skills tell the answer directly? It would be kind of interesting.)

Hidden Text: Show

, and also figure out what's different about the other 3 cells that was pointed out. Right now, I noticed that in the 3 cells that was pointed out, that 2 of the cells are next to each other. I'm wondering if that is important. I don't recall using the technique with cells that were next to each other. There are some other things I'm curious about too. Maybe the technique is valid if I can refine what to look for.

I'd have to do a bunch of puzzles to figure it out. I can't just look at a single puzzle.

I could save you some time. There's no logic within those three cells that could make that placement with any kind of certainty. I'm sorry. You'd spend your time more wisely by learning actually working techniques.

Sorry to disappoint you, but I can't encourage you to look for miracles that don't exist.

[mith]

If all the information we have is the alternatives in those three cells, then yes, four possibilities for the non-common digit to one for the common digit.

Hard to say if that holds up as a probability though; obviously any puzzle with that configuration would have more information available, and ending up in that configuration may bias you one way or the other.

[SpAce]

Hard to say if that holds up as a probability though; obviously any puzzle with that configuration would have more information available, and ending up in that configuration may bias you one way or the other.

Exactly. That's why I think the only way to get the right ballpark would be by testing a large enough sample with software. My manual testing of a huge sample of four cases hit the correct number 50% of the time.

[Pupp]

Hard to say if that holds up as a probability though; obviously any puzzle with that configuration would have more information available, and ending up in that configuration may bias you one way or the other.

Exactly. That's why I think the only way to get the right ballpark would be by testing a large enough sample with software. My manual testing of a huge sample of four cases hit the correct number 50% of the time.

Yep. I'll definitely be on the lookout for that technique, and try to get a better understanding. I need to do a lot more puzzles to get a better frame of reference.

I never really looked for board positions that have more than 1 available set of candidate cells. Curious if it always works if there is only a single set 3 cells, and then if there is a way to figure out if a particular set of 3 cells will work if there are multiple sets of 3 cells to pick from, if it can work at all.

[mith]

Curious if it always works if there is only a single set 3 cells

No need to be curious: it doesn't always work, as SpAce already demonstrated. It's a guess. It may be better than a 50-50 guess, but it is still a guess.

[Pupp]

Curious if it always works if there is only a single set 3 cells

No need to be curious: it doesn't always work, as SpAce already demonstrated. It's a guess. It may be better than a 50-50 guess, but it is still a guess.

I don't think any gestapo is going to bust my door down and demand I stop trying to figure out a new Sudoku technique.

I can pursue my curiosity at my own leisure. Not like it's a consuming process, since all I need to do is look at puzzle positions as I come by them. I'm certainly not going to go out of my way to find a specific set of puzzles for my hypothesis. Sudoku is just a relaxing hobby for me. At least it is now.I'm sure I'll get frustrated again when I get another round of harder puzzles. (The next major section of puzzles is "Fiendish", which is below the "Nightmare" section in Sudoku 10000 Plus.)

[mith]

I'm not suggesting you shouldn't be curious in general. Try to figure out all the new techniques you can!

But you posted about a technique on a sudoku forum, and were quickly provided an example of where it fails. You are of course welcome to ignore that, and continue using the pattern when you spot it. Eventually you will try to use it and it will fail and you will need to backtrack. ~shrug~ All I'm saying is you aren't going to prove that it always works, because it doesn't always work. (And hey, there is nothing inherently wrong with educated guessing, if you find it satisfying. Speed solvers use educated guesses sometimes, and backtrack when they don't work.)

[edit]Apologies though, I did misread what I quoted in my previous post. I think I can safely say it is not always true even when there is only one such pattern available, but SpAce's offering is not a direct counterexample of that.[/edit]

[Pupp]

I dunno. I switched from Hard 1 to Hard 5, going from under 10 mintes to about 40.minutes to solve. I'll keep looking into my hypothosis, but at best, it will be several weeks before I can figure out if it works in any particular curcumstance. After doing some harder puzzles, it does seem to fall apart. But perhaps it might be ok if it was the only 3 cell combo on the board. But the Hard 5 puzzles frequently have both multiple instances of 3 cell sets of numbers, or the conundrum of 4 or 5 cells where the 3 cell pattern overlaps. Something I didn't anticipate.

In any event, as long as I'm having fun, it's all good. But again I suspect if the pattern is viable at all, it has to be the only possible 3 cell combo on the board, making it usable, at best, in easier puzzles, but probably still a "hack" move that speed players might use that are looking for a way to speed guess a solution.

[urhegyi]

first.png (14.62 KiB) Viewed 560 times

I polished my first self-created sudoku to solve with the same strategy but with less givens, only 24 at the beginning.

Code: Select all

...2.7..8...3....9.45.9.....8.....3.....2..4793....1..67......4..3.1....21.4.....

[Cenoman]

I polished my first self-created sudoku to solve with the same strategy but with less givens, only 24 at the beginning.

The puzzle is now minimal (i.e. no given can be dropped without creating a multi-solution puzzle)
Anyhow, the pencil marks after running basics are the same as the previous one.

BTW, if you intend to post your puzzles again, please could you give them also as a text chain (as tarek or mith or others do) ? .png picture are not pastable...