The New Sudoku Players' Forum

[Pupp]

Here's an interesting swordfish puzzle. [According to Sudoku Explainer it has a swordfish in it.]

I did this, logically, without ever finding, or even looking for the swordfish. I spotted this particular pattern, so I just kept looking for more and eventually I cracked the puzzle.
I was so impressed by the puzzle construction, I put it through SE just out of curiosity of the puzzle's difficulty, which was only 3.8, but very satisfying to solve.

I used Anduko 3 on my phone, and this was the first puzzle I tried.

Code: Select all

  +----------------------+----------------------+----------------------+
        | 4      389    13689  | 2      7      139    | 36     5      368    |
        | 1368   2      5      | 1368   1368   13     | 9      37     4      |
        | 3689   389    7      | 3689   35689  4      | 36     2      1      |
        +----------------------+----------------------+----------------------+
        | 359    1      239    | 379    349    6      | 3457   8      237    |
        | 35689  3789   23689  | 13789  13489  12379  | 134567 1347   2367   |
        | 368    4      2368   | 5      138    1237   | 1367   9      2367   |
        +----------------------+----------------------+----------------------+
        | 7      5      1389   | 4      1369   139    | 2      13     39     |
        | 2      39     4      | 1379   1359   13579  | 8      6      379    |
        | 139    6      139    | 1379   2      8      | 1347   1347   5      |
        +----------------------+----------------------+----------------------+

The pattern is a 3 corner pattern: 3 sets of pairs. Each pair has a common number, and an uncommon number. You solve the corner cell, by picking the uncommon number.

Code: Select all

 
[1,2]...............[1,3]
[1,4]

 The answer is "2" in the corner cell.

Is there a name for that technique?

[Leren]

Yes, it's a very powerful technique that can often make difficult puzzles easy to solve. It called ... A Lucky Guess ! ALG for short. Leren

[Pupp]

I'll call it the LCD

or

Least Common Denominator technique.

It's 1 am, so I'll post proofs starting tommow.
It works with more than 2 pencil marks, as long only a single digit is a least commom denominator.

[coloin]

Please make clear which cell in the puzzle posted is the ALG/LCD .....?

[Leren]

Here is a simple example with a BUG + 1 Solution

Code: Select all

*--------------------------------*
| 27  9  25   | 6 1 3 | 57 8  4  |
| 68  48 46   | 2 5 7 | 1  3  9  |
| 3  *57 1    | 8 4 9 | 2  56 67 |
|-------------+-------+----------|
| 9   6  8    | 5 7 1 | 4  2  3  |
| 4   3  7    | 9 2 6 | 8  1  5  |
| 1   25 25   | 3 8 4 | 79 69 67 |
|-------------+-------+----------|
|*67 *47 4-36 | 1 9 2 | 35 45 8  |
| 28  28 9    | 4 3 5 | 6  7  1  |
| 5   1  34   | 7 6 8 | 39 49 2  |
*--------------------------------*

According to what I understand Pupp is saying, if instead of the BUG, you consider the 3 cells marked * you should make r7c2 = 4, the non common digit in r3c2 & r7c12. And the solution ?

Code: Select all

*------------------------*
| 7  9 2 | 6 1 3 | 5 8 4 |
| 8  4 6 | 2 5 7 | 1 3 9 |
| 3 *5 1 | 8 4 9 | 2 6 7 |
|--------+-------+-------|
| 9  6 8 | 5 7 1 | 4 2 3 |
| 4  3 7 | 9 2 6 | 8 1 5 |
| 1  2 5 | 3 8 4 | 7 9 6 |
|--------+-------+-------|
|*6 *7 4 | 1 9 2 | 3 5 8 |
| 2  8 9 | 4 3 5 | 6 7 1 |
| 5  1 3 | 7 6 8 | 9 4 2 |
*------------------------*

r7c2 = 7, the common digit of the three * cells. If r7c2 was set to 4, I would call this technique IUG (An Unlucky Guess). Leren

[Pupp]

Right now, I'm trying to figure out why it works so often. I have an idea of one potential rule. If it works, it would be an easy rule.

The rule concerns excluding potential candidate groups of 3 cells. It would vastly narrow down when a solver could even consider using the technique.

I did a bunch of sudoku problems, so I'm seeing a pattern, but I need to do more puzzles to see if this potential rule will exclude groups of 3 cells correctly every time.

[Pupp]

Please make clear which cell in the puzzle posted is the ALG/LCD .....?

Right now, I"m trying to figure out if there is anyway to get this thing into an actual technique. It might be days, or weeks. I'm not a sudoku'holic. I have days where I'm glad to play several games, and stretches of days I'm not in the mood to play at all.

I did spot a highly likely exclusion pattern. I don't see anything else that even comes close to an exclusion pattern. I did post about this some months ago, but I have a better grasp of what I'm seeing on the board now. Before, it didn't occur to me to look for an exclusion pattern.

It would be pointless to show you the group of cells I posted earlier, when I posted the puzzle. It did work, but that's meaningless if I can't figure out a way to know for a certain fact that filling in the corner cell will be the correct answer every time.

[Leren]

Code: Select all

+----------------------+----------------------+----------------------+
| 4      389    13689  | 2      7      139    | 36     5      368    |
| 1368   2      5      | 1368   1368   13     | 9     *37     4      |
| 3689   389    7      | 3689   35689  4      | 36     2      1      |
+----------------------+----------------------+----------------------+
| 359    1      239    | 379    349    6      | 3457   8      237    |
| 35689  3789   23689  | 13789  13489  12379  | 134567 1347   2367   |
| 368    4      2368   | 5      138    1237   | 1367   9      2367   |
+----------------------+----------------------+----------------------+
| 7      5      1389   | 4      1369   139    | 2     *13    *39     |
| 2      39     4      | 1379   1359   13579  | 8      6      379    |
| 139    6      139    | 1379   2      8      | 1347   1347   5      |
+----------------------+----------------------+----------------------+

One possibility for the 3 cells in your puzzle are marked *. Picking the non-common digit 1 in r7c8 will solve the puzzle correctly, and the avoid the Swordfish so it would be an example of ALG on this occasion.

So I'd say your technique will work about 50% of the time.

Leren

[mith]

I suspect it works more than 50% of the time - though obviously not 100% of the time, given the counterexamples that have already been found.

Attached is the puzzle after basics (before the Swordfish), with all occurrences of the pattern (give or take me being blind). Of the cells in question, 6 of the 7 will give the correct answer (7 of the 8 choices of three cells, since one cell appears twice).

In this particular puzzle, one of the cells happens to be part of a Skyscraper; things like this are likely to be present sometimes, where one end or the other of the "corner" pattern must be the common digit (this isn't one of those cases, though - the two "ends" of the Skyscraper are both 39.

Just from the limited information of the "pattern", you would expect it to happen more than 50% of the time, as SpAce pointed out in the previous thread - if our cells are AB - AC - AD, then there are these valid solutions just considering those three cells (obviously the real situation is more complicated):

ACA
ACD
BCA
BCD
BAD

4/5 of these would give the correct result from the "pattern". So it's probably not *just* a lucky guess - more like an educated guess (which is still some degree of trial and error).

All that said, none of this proves that there is or isn't some form of this pattern that is always correct (by further limiting what counts), but there isn't currently any compelling reason to think there is. (Pupp, if you think there is, then by all means, try to prove it. I just don't see what you're hoping to accomplish asking a second time what a pattern is called when you haven't shown it is always valid.)

[Leren]

My guess as to why the pattern might work more than 50% of the time is that it might be related to the so-called Aligned Pair Exclusion or Aligned Triple Exclusion.

Why I say so-called is that when you work out how it works, the Pair or Triple don't actually have to be aligned, in fact they don't even have to see each other. If this is the answer then unfortunately you will have to consider other cells, to make it work 100% of the time, so as it stands it would be incomplete. The best writeup I've found on this topic is on Andrew Stuart's site here.

Leren

[Pupp]

Leren, I'm not ignoring your posts.
......

I'm just trying to process patterns at the moment.
.......

Can anybody link that page that shows how SE rates difficulty by technique?

PS. I got a reference level Paradigm sub-woofer for a song practically, and after hooking it up to my soundbar, suddenly my entire library looks different. I watched Cinderella and it felt like the pumpkin was bouncing in my living room as the carriage turned back into a pumpkin. Then I watched Star Wars: Rogue one....


Hmmm.... should I play Sudoku or watch movies???....

[Pupp]

Been really busy lately. The novelty of the new subwoofer wore off.

I found that link about Sudoku Explorer rating list.

http://forum.enjoysudoku.com/revision-of-se-ratings-and-resolution-rules-t36376.html

I'll use that as a list of what I need to learn and what order to learn them in.

It will also let me hone into technuques that I need to look up diamond or pearl puzzles, so I can focus on learning the technique and not hoping to spot the technique in a random puzzle.