The New Sudoku Players' Forum

[wychwood]

Hi folks, me again, here in my ignorance!

OK, here is a puzle that I did quite well with until I got to the position shown below:

Code: Select all

 *--------------------------------------------------*
 | 2    5    7    | 36   1    36   | 4    8    9    |
 | 9    1    6    | 8    4    27   | 3    27   5    |
 | 8    3    4    | 27   5    9    | 1    6    27   |
 |----------------+----------------+----------------|
 | 7    9    5    | 134  2    13   | 8    14   6    |
 | 1    8    3    | 467  9    67   | 2    5    47   |
 | 4    6    2    | 157  8    157  | 9    17   3    |
 |----------------+----------------+----------------|
 | 56   7    1    | 29   3    8    | 56   249  24   |
 | 35   2    8    | 59   6    4    | 7    39   1    |
 | 356  4    9    | 125  7    125  | 56   23   8    |
 *--------------------------------------------------*

Now the hint I got was to eliminate a number from r5c6 using 'colours'. Now I have a basic understanding of colours and doing it led me to an elimination in that cell that led to a complete solution.
BUT - my problem with colours is that, as far as I understand it, it has to start with a "suppose that bivalue cell is value X, what happens to other bivalue cells with that number in it, starting with one(s) that can see it?"

Now, that smacks of trial and error again to me and, as you know by now, I am not fond of that approach if possible.

So, is there an alterntaive way of solving this puzzle, or an alternative way of eliminating the digit in r5c6, that is more logical in its approach?

I am beginning to get there with some of these 'advanced techniques', but its taking time!! Please bear with me.

Neil

[Steve R]

Code: Select all

*---------------------------------------*
| 2    5 7 | 36  1  36   | 4   8    9   |
| 9    1 6 | 8   4  27A  | 3   27a  5   |
| 8    3 4 | 27  5  9    | 1   6    27A |
|----------+-------------+--------------|
| 7    9 5 | 134 2  13   | 8   14   6   |
| 1    8 3 | 467 9  67   | 2   5    47a |
| 4    6 2 | 157 8  157  | 9   17   3   |
|----------+-------------+--------------|
| 56   7 1 | 29  3  8    | 56  249  24  |
| 35   2 8 | 59  6  4    | 7   39   1   |
| 356  4 9 | 125 7  125  | 56  23   8   |
*---------------------------------------*


Colouring is a matter of building up chains of conjugates for a particular entry, here 7. The cells marked A and a in the grid are conjugates so precisely one of A and a stands for “contains 7.”

As r5c6 is an associate of both A and a, it cannot contain 7.

Steve

[Sped]

Code: Select all

 
 *--------------------------------------------------*
 | 2    5    7    | 36   1    36   | 4    8    9    |
 | 9    1    6    | 8    4    27A  | 3    27a  5    |
 | 8    3    4    | 27   5    9    | 1    6    27A  |
 |----------------+----------------+----------------|
 | 7    9    5    | 134  2    13   | 8    14   6    |
 | 1    8    3    | 467  9   6(7)  | 2    5    47a  |
 | 4    6    2    | 157  8    157  | 9    17   3    |
 |----------------+----------------+----------------|
 | 56   7    1    | 29   3    8    | 56   249  24   |
 | 35   2    8    | 59   6    4    | 7    39   1    |
 | 356  4    9    | 125  7    125  | 56   23   8    |
 *--------------------------------------------------*


Colors does not rely on bivalue cells. It relies on conjugate pairs of cells. By conjugate it is meant that one cell must be true for a candidate, and the other false, or vice versa.

Look at the 7s in row 2. There are two of them, r2c6 and r2c8. One of them must be true for 7 and the other false. They form a conjugate pair. Mark r2c6 "A" and r2c8 "a".

Look at box 3. There are exactly two 7s, r2c8 and r3c9. One must be true for 7 and the other false. r2c8 is already marked "a", so mark r3c9 "A". Either all the "A" cells are true for 7 or all the "a" cells are true for 7.

Look at column 9. There's a conjugate pair of 7s in r9c3 and r9c5. r9c3 is already an "A" so mark R9c5 an "a". Either all the "A" cells are 7 or all the "a" cells are 7.

Now, look at r5c6. It shares a column with the "A" in r2c6, so if "A" is true for 7 r5c6 cannot be a 7. It also shares a row with "a", so if "a" is true for 7 r5c6 cannot be a 7.

Since either "a" or "A" must be a 7, and r5c6 sees both, it cannot possibly be a 7.

So exclude the 7 from r5c6.

Simple Sudoku uses blue for "A" and green for "a" in this case.

I don't see how this could be considered trial and error. It's easy to see that either all the greens or all the blues are 7, so any cells that see both blue and green cannot possibly be 7.

Simple.

If you don't like coloring, a simple xy chain produces the same exclusion:


7-(r2c6)-2-(r2c8)-7-(r3c9)-2-(r7c9)-4-(r5c9)-7

Pick any of the bivalue cells in the chain and set it to one of its possibilities, notice what that implies for r2c6 and r5c9. Then set it to its other possible value and follow the implications. You'll see that either r2c6 or r5c9 has to be a 7. So r5c6, which sees both, cannot be a 7.

Code: Select all


 *--------------------------------------------------*
 | 2    5    7    | 36   1    36   | 4    8    9    |
 | 9    1    6    | 8    4    27*  | 3    27^  5    |
 | 8    3    4    | 27   5    9    | 1    6    27^  |
 |----------------+----------------+----------------|
 | 7    9    5    | 134  2    13   | 8    14   6    |
 | 1    8    3    | 467  9   6(7)  | 2    5    47*  |
 | 4    6    2    | 157  8    157  | 9    17   3    |
 |----------------+----------------+----------------|
 | 56   7    1    | 29   3    8    | 56   249  24^  |
 | 35   2    8    | 59   6    4    | 7    39   1    |
 | 356  4    9    | 125  7    125  | 56   23   8    |
 *--------------------------------------------------*


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.

Another solution would be to observe that if r9c1<>3 the puzzle would have multiple solutions, since there would be a deadly pattern : 56 in r7c17 r9c17. Since we assume there is but one solution, r9c1=3 and it's all singles from there.

Code: Select all

 
 *--------------------------------------------------*
 | 2    5    7    | 36   1    36   | 4    8    9    |
 | 9    1    6    | 8    4    27   | 3    27   5    |
 | 8    3    4    | 27   5    9    | 1    6    27   |
 |----------------+----------------+----------------|
 | 7    9    5    | 134  2    13   | 8    14   6    |
 | 1    8    3    | 467  9    67   | 2    5    47   |
 | 4    6    2    | 157  8    157  | 9    17   3    |
 |----------------+----------------+----------------|
 | 56*  7    1    | 29   3    8    | 56*  249  24   |
 | 35   2    8    | 59   6    4    | 7    39   1    |
 | 356* 4    9    | 125  7    125  | 56*  23   8    |
 *--------------------------------------------------*


The four cells above form a unique rectangle. If r9c1 <>3, then the grid would look like this:

Code: Select all

 
 *--------------------------------------------------*
 |                |                |                |
 |                |                |                |
 |                |                |                |
 |----------------+----------------+----------------|
 |                |                |                |
 |                |                |                |
 |                |                |                |
 |----------------+----------------+----------------|
 | 56             |                | 56             |
 |                |                |                |
 | 56             |                | 56             |
 *--------------------------------------------------*


This is a dealdly pattern because there would be two solutions. Swap the 5s and 6s in the rectangle and everything would still work out.

[wychwood]

Thanks guys, that really helps.

Not only am I a beginner with some of these techniques, I am only just geting to grips with some of the lingo that has been developed - even the basic terms like 'house' are something I do not use easily yet, so things like bivariate and conjugate are even more rare in my vocabulary.

But I will get there, eventually!!

Thanks again
Wychwood

[wapati]

There is a skyscraper on 7s that pretty much solves the puzzle, as well,
after you spot the hidden triple in c4,r145.

Code: Select all

------
| 36 
| 8   
| 27 
+-----
| 34-1
| 46-7
| 157
+-----
| 29 
| 59 
| 125
------

Code: Select all

.------------.------------.------------.
| 2   5   7  | 36  1   36 | 4   8   9  |
| 9   1   6  | 8   4   27*| 3   27* 5  |
| 8   3   4  | 27  5   9  | 1   6   2-7|
:------------+------------+------------:
| 7   9   5  | 34  2   13 | 8   14  6  |
| 1   8   3  | 46  9   67*| 2   5   47*|
| 4   6   2  | 157 8   157| 9   1-7 3  |
:------------+------------+------------:
| 56  7   1  | 29  3   8  | 56  249 24 |
| 35  2   8  | 59  6   4  | 7   39  1  |
| 356 4   9  | 125 7   125| 56  23  8  |
'------------'------------'------------'

[wapati]

or an alternative way of eliminating the digit in r5c6, that is more logical in its approach?

Neil

A finned-x-wing removes the same candidate, it is more logical?

Code: Select all

.------------.------------.------------.
| 2   5   7  | 36  1   36 | 4   8   9  |
| 9   1   6  | 8   4   27 | 3   27  5  |
| 8   3   4  |*27  5   9  | 1   6  *27 |
:------------+------------+------------:
| 7   9   5  | 34  2   13 | 8   14  6  |
| 1   8   3  |*467 9   6-7| 2   5  *47 |
| 4   6   2  |*157 8   157| 9   17  3  |
:------------+------------+------------:
| 56  7   1  | 29  3   8  | 56  249 24 |
| 35  2   8  | 59  6   4  | 7   39  1  |
| 356 4   9  | 125 7   125| 56  23  8  |
'------------'------------'------------'

[ravel]

The easiest way to solve it is with the unique rectangle (type 1) in the marked cells (r79c14), saying, that r9c1 cannot be 5 or 6.

Code: Select all

*---------------------------------------*
| 2    5 7 | 36  1  36   | 4   8    9   |
| 9    1 6 | 8   4  27   | 3   27   5   |
| 8    3 4 | 27  5  9    | 1   6    27  |
|----------+-------------+--------------|
| 7    9 5 | 134 2  13   | 8   14   6   |
| 1    8 3 | 467 9  67   | 2   5    47  |
| 4    6 2 | 157 8  157  | 9   17   3   |
|----------+-------------+--------------|
|#56   7 1 | 29  3  8    |#56  249  24  |
| 35   2 8 | 59  6  4    | 7   39   1   |
|#356  4 9 | 125 7  125  |#56  23   8   |
*---------------------------------------*


Just note, that the corners of such a rectangle must be in two boxes. Then enjoy the fact that a grid with

Code: Select all

 12 . . | 12 . .
 12 . . | 12 . .
 .  . . | .  . .

is not possible, when the puzzle has a unique solution.

[Added:]
Neil,
to save (the first of) us these "start program/copy/paste/save as/open"-operations, please do following:
Login, go to your first post above, press the "Edit" button, mark your grid with the mouse, press the "Code" button and then press the "Preview" button.

[wychwood]

Hi all

Thanks ravel, I agree, that is perhpas the simplest solution and one I overlooked.

Thanks also for the tip about code etc - not sure I know what's going on there but I can see that it makes the format of the puzzle a little more legible and the shape of the puzzle more symmetrical.

There are obviously a load of rules and tips that I need to read if I am to continue using this forum on a regular basis

[udosuk]

ravel and Neil,

You guys should probably notice that the "simplest solution" offered by ravel has been shown earlier by Sped 4 posts ago, so he should really get some credit for it...


And Neil, here is a brief faq about the BBCode we use in this forum... I suggest you spend a few minutes reading it if you want to post more regularly here... BTW it's available in the posting screen (near the Options) if you're observant enough...

Also, you should probably take a look at this page to learn a few basic features about Simple Sudoku (I presume it's what you're using now)... It also includes brief explanations of Colors, Multi-colors & XY-Wings...

Also, please check the Options from your Simple Sudoku menu bar, and try to disable the "Show All Candidates while Filtering" feature (Ctrl-H)... That way, next time you use the hints for a Colors/Multi-colors move, you can easily see which digit is involved...

I personally think all techniques involving only one digit or one house (i.e. row/column/block) should not be considered trial & error... Those includes Colors & Multi-colors, which involve only one digit...

In fact, most of these colouring moves can be expressed as finned/mutant version of turbot fish or larger-sized fish such as swordfish, jellyfish, squirmbags... But fishing/marinology is a very advanced subject within the BSc (Sudoku) degree and you need to spend quite a lot of time to excel at spotting/catching them...

[ravel]

ravel and Neil,

You guys should probably notice that the "simplest solution" offered by ravel has been shown earlier by Sped 4 posts ago, so he should really get some credit for it...

Sorry, i overlooked that.

[wychwood]

Thanks agin guys.

udosuk, you are of course totally correct about the earlier response from sped, and thanks for the links about the BBcode and about Simple Sudoku

re Simple Sudoku. To be honest, I tend to only use it for two reasons:
1 occasionally when I get bored at my work I have a go at a problem or two;
2. to use it to post the forum by inputting the problem I am struggling with.

I still prefer the good old paper versions, quite honestly, and doing the 'boring repetitive' stuff of adding candidates by hand, This way, I find that you can sometimes be selective about which candidates you include, so as not to clutter up the grid too much. It also means you cut down on soem of the exclusion work later on.

Thanks for all your help and encouragement, folks.