The New Sudoku Players' Forum

[munchy]

I have a sudoku book. This is a diabolical puzzle. I am familiar with all of the basic strategies (though not sure what they are called.) Could somebody, without telling me specifically what to do, give me a hint as to where to look next and something that will tell me how to find the next number? It seems to me like the next step is to guess!

Thanks,
Munchy

[emm]

Hi Munchy - no need to guess

Xwing of 4s

XYwings

BUG

If you're unsure of these terms download this excellent free programme - Sudoku Susser - and search the manual

[munchy]

You're right, this is a neat little programme. I checked the manual. So far I have only addressed the x-wing. Let me know if I got it right or if I am way off base. You said "x-wing of 4s." After reading the definition of x-wing, I highlighted the ones I suspected of being an x-wing in orange. And this means I can get rid of the 4s in the green boxes?

If I am right, I will address the other two terms.

Thanks!!!!

Munchy

[emm]

Bang on, Munchy!

There are other great programmes for techniques but I think Susser is the most comprehensive.

It was generous of me to say it's free - you can make a donation. It's worth it.

[Carcul]

Code: Select all

 *----------------------------------------------------------*
 | 347    23     247 | 8      5      24  | 1      6      9  |
 | 9      5      1   | 6      3      7   | 8      4      2  |
 | 46     26     8   | 1      24     9   | 7      3      5  |
 |-------------------+-------------------+------------------|
 | 367    9      27  | 5      2678   238 | 4      1      78 |
 | 8      1      247 | 9      247    234 | 23     5      6  |
 | 3467   236    5   | 37     24678  1   | 23     9      78 |
 |-------------------+-------------------+------------------|
 | 5      4      6   | 37     78     38  | 9      2      1  |
 | 1      7      3   | 2      9      6   | 5      8      4  |
 | 2      8      9   | 4      1      5   | 6      7      3  |
 *----------------------------------------------------------*

In order to avoid a Two Incompatible Loops (TIL) situation, we must have r3c5=4 which solve the puzzle. The reader is invited to find those two TILs as an exercise.

Carcul

[munchy]

Thanks Emm! Of course I will donate. I am an excellent donor. So for the next step I removed the 4s in question. From what I could gather from the Susser's definition of the XY Wing, Here's what I have come up with (refer to image.) The lightest yellow (2 7) would represent an XY pair. It is row buddies with the orange (2 3) which becomes the XZ pair, and it is block buddies with the gold (3 7) which is the YZ pair. That means that any buddies that the orange and gold boxes have in common cannot contain a 3. I have highlighted those buddies in blue. One is the 9, which can be nothing but the 9. The other buddy is the other of the 2 3 twins. Since that cannot be 3, it now becomes the 2, making the 2 3 in the orange box the 3.

Is that right? I'm off to figure out what a BUG is! Thanks again Emm! An Carcul, I will check out what you're trying to tell me after I've finished doing the other stuff. Thanks so much for all of your input thus far!

-Munchy

[TKiel]

They are also both buddies to r5c6, which can have the 3 excluded.

Tracy

[munchy]

OK, yeah, it would have been helpful to realize that as well... but I probably missed it because I realized that when R5C7 became 3, then R5C6 automatically could not be 3.

I'll get better at this.

I'm a little confused re: the BUG, but I want to keep plugging at itg before I give up and start asking questions.

Thanks,
Munchy

[Crazy Girl]

Munchy,
There is a great collection of basic to advanced solving techniques with links to the different topics found at the link below, included in this list is a (Bivalue Universal Grave) BUG link which you should find helpful.

Collection of solving techniques

[Sped]

After the X Wing and XY Wing and other simpler steps we end up here:

Code: Select all

 
 *--------------------------------------------------*
 | 37*  23   47   | 8    5    24   | 1    6    9    |
 | 9    5    1    | 6    3    7    | 8    4    2    |
 | 46   26   8    | 1    24   9    | 7    3    5    |
 |----------------+----------------+----------------|
 | 36^  9    2    | 5    68   38   | 4    1    7    |
 | 8    1    47   | 9    27   24   | 3    5    6    |
 | 4(7) 36^  5    | 37*  467  1    | 2    9    8    |
 |----------------+----------------+----------------|
 | 5    4    6    | 37   78   38   | 9    2    1    |
 | 1    7    3    | 2    9    6    | 5    8    4    |
 | 2    8    9    | 4    1    5    | 6    7    3    |
 *--------------------------------------------------*


It's easy to slove it with a short XY chain. There are probably numerous chains that would solve it, Here's one:

7-(r6c4)-3-(r6c2)-6-(r4c1)-3-(r1c1)-7 which eliminates the 7 in r6c1, reducing the puzzle to singles.

Above, the ends of the chain are marked with *, the other cells in the chain are marked with ^, and the candidate that gets excluded has () around it. r6c1 loses its 7 because it sees both the start of the chain in r6c4 and the end of the chain in r1c1.

In nice loop notation:

[r6c1]-7-[r6c4]-3-[r6c2]-6-[r4c1]-3-[r1c1]-7-[r6c1], => r6c1<>7


A more interesting way to solve it, though, is to recognize that it's a classic BUG+1. BUG is described here:

http://forum.enjoysudoku.com/viewtopic.php?t=2352

From that article: A Bivalue Universal Grave (BUG) is any grid in which all the unsolved cells have two candidates, and if a candidate exists in a row, column, or box, it shows up exactly twice.

A BUG grid cannot have a unique solution. It may have no solutions, or more than one solution, but never one solution.

This grid is called a BUG+1 because only one cell is keeping it from being a BUG,

Code: Select all

 *--------------------------------------------------*
 | 37   23   47   | 8    5    24   | 1    6    9    |
 | 9    5    1    | 6    3    7    | 8    4    2    |
 | 46   26   8    | 1    24   9    | 7    3    5    |
 |----------------+----------------+----------------|
 | 36   9    2    | 5    68   38   | 4    1    7    |
 | 8    1    47   | 9    27   24   | 3    5    6    |
 | 47   36   5    | 37   467  1    | 2    9    8    |
 |----------------+----------------+----------------|
 | 5    4    6    | 37   78   38   | 9    2    1    |
 | 1    7    3    | 2    9    6    | 5    8    4    |
 | 2    8    9    | 4    1    5    | 6    7    3    |
 *--------------------------------------------------*


r6c5 is the only unsolved cell that is not bivalue. All the other unsolved cells have exactly two candidates. Furthermore, with the exception of r6c5, any candidates that appear in a group do so twice.

Lok at column 1. It has two 3s, two 7s, and two 4s. Box 1 has two 3s, two 7s, two 2s, two 4s, and two 6s.

This grid is almost a BUG, and remember, a BUG grid is invalid. We can use this to solve the puzzle.

What would it take to make this grid a BUG? Well, we'd have to do something to r6c5, which is the only non-bivalue cell. If we remove one candidate from r6c5 we can make this a BUG, which, of course, would be invalid. But removing which candidate makes this a BUG?

Remove the 4? No. There are two 4s in row 6 and column 5, and box 5. Remove the 4 and those groups would have only a single 4, so there would be no BUG.

Remove the 6? No. There are two 6s in row 6 and column 5, and box 5. Remove the 6 and those groups would have only a single 6, so there would be no BUG.

Remove the 7? Yes! There are 3 7s in row 6, 3 7s in box 5, and one 7 in column 5. If we remove the 7 from r6c5 we will have a BUG, which, as we know, would be invalid.

Here's what the grid would look like if we remove the 7 from r6c5:

Code: Select all


INVALID!!  This grid is a BUG
 *--------------------------------------------------*
 | 37   23   47   | 8    5    24   | 1    6    9    |
 | 9    5    1    | 6    3    7    | 8    4    2    |
 | 46   26   8    | 1    24   9    | 7    3    5    |
 |----------------+----------------+----------------|
 | 36   9    2    | 5    68   38   | 4    1    7    |
 | 8    1    47   | 9    27   24   | 3    5    6    |
 | 47   36   5    | 37   46   1    | 2    9    8    |
 |----------------+----------------+----------------|
 | 5    4    6    | 37   78   38   | 9    2    1    |
 | 1    7    3    | 2    9    6    | 5    8    4    |
 | 2    8    9    | 4    1    5    | 6    7    3    |
 *--------------------------------------------------*


Look at it. All the unsolved cells are bivalue i.e. they have exactly two candidates. Every candidate that appears in a row, column or box does so exactly twice. This is a BUG, which, of course, is invalid.

We get an invalid grid if we remove the 7 from r6c5. Therefore, r6c5 must be a 7.

So set r6c5 to 7 and it's all singles after that.

Whenever you have a grid that is all bivalue except for one cell, it is worthwhile to look and see if it's almost a BUG. They often are, and it's a fun and easy way to finish a puzzle.