The New Sudoku Players' Forum

[bridgenut]

Hi everyone! Merry Christmas and Happy Chanukah!
I am new to this site, but I am addicted to duplicate bridge and sudokus. I have done sudokus for years, originally as "Number Places" in Dell Puzzle Magazines.
Those were relatively easy. I am delighted to see sudokus getting harder. I have bought the hand-held game and the board game and save the ones from the newspapers. I thought I was good at sudokus, but I find some of them are really tough, and I get stuck. I use all the techniques listed on this website, and I still get stuck on some of the puzzles.
Could someone please define the word "uniqueness" in relation to solving sudokus? Also, this site introduced me to "candidate lists" for the harder puzzles. Apparently, the solver makes another grid and fills in possibilities for the unknown and unsolved cells.
Lastly, has anyone seen the sudoku in the latest Readers' Digest? I am stuck on that one, gradually filling in cells as I figure them out. Does anyone have any tips for that puzzle?
Thanks all!
Pats4949

[MCC]

Hi Bridgenut
Merry Christmas and a Happy Chanukah to you.

Check out this link for uniqueness.

Also, if post your puzzle and your candidate list I'm sure someone will be able to provide some help to get you on your way.

[bridgenut]

Thanks. How does one post a sudoku? I am technically challenged; how do I post a sudoku grid partially filled in as others have on this site? Thanks, Pats4949

[QBasicMac]

Could someone please define the word "uniqueness" in relation to solving sudokus?

DanO posted Menneske no. 5460770 on Oct 18, 2005 as a good example of the use of "uniqueness":

Code: Select all

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


After solving all easy stuff, we end up here:

Code: Select all

The second way of showing grids is the "candidate list" or "pencilmarks" you enquired about. The point is to keep in each unsolved cell the list of possible digits as deduced so far.

The grid you see would normally be very difficult to solve. However, if you believe the uniquesness method is reliable, you look for patterns like the 4's marked with a plus above.

The argument is this: If the final solution has a 4 placed in r8c2 then the marked cells will be thus:
4 9
9 4

But if that is the case, then whoever made up the puzzle goofed because there is more than one solution. You show me a SuDoku solution with that pattern and I will show you another solution with this pattern:
9 4
4 9

So, the argument goes, since the source of the puzzle is known to be a reliable one-solution-only source, then r8c2 cannot be 9 and it cannot be 4. So we can place a 1 there!

"Uniqueness" refers to the fact that you believe the puzzle has only one solution.

That's about it. Personally, I don't like it. I always assume that all puzzles from any source can have multiple solutions. So I would have to try 1 and 4. That is no different than simple trial and error except the pattern is an excellent clue to what cell to start guessing in.

Mac

Edit: This post is incorrect. See later correction by TSO. Ignore further posts by me in this thread at least.

[bridgenut]

THANKS MCC AND QBasicMac. Thanks for explaining uniqueness so well.
I still have two dumb questions. I am a veteran at solving easy and medium sudokus, but the hard ones are taking longer than they should.
First question is, could someone please explain the code used to pinpoint a cell such as r8c2?
The second is, how does one post a sudoku grid, whether only with original numbers, with some missing ones filled in or completed here as so many of you have? In answering this, please keep in mind I am severely technically challenged-lol!
Also, any more tips for solving them more quickly and efficiently?
THANKS; SO GLAD I FOUND THIS SITE.
Pats4949 (Baltimore, MD, USA)

[tso]

DanO posted Menneske no. 5460770 on Oct 18, 2005 as a good example of the use of "uniqueness":

Code: Select all

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


After solving all easy stuff, we end up here:

Code: Select all

+---------------+-------------------+---------------+
| 39   139  2   | 4     8      57   | 57   6   139  |
| 4    6    139 | 2     13579  1357 | 57   8   139  |
| 7    8    5   | 19    139    6    | 29   4   1239 |
+---------------+-------------------+---------------+
| 1    5    34  | 8     347    237  | 6    9   24   |
| 8    39   349 | 16    1346   123  | 124  7   5    |
| 2    7    6   | 15    145    9    | 14   3   8    |
+---------------+-------------------+---------------+
| 359  2    139 | 1569  1569   4    | 8    15  7    |
| 59  +149  7   | 3     159    8    |+49   2   6    |
| 6   +49   8   | 7     2      15   | 3    15 +49   |
+---------------+-------------------+---------------+


The grid you see would normally be very difficult to solve. However, if you believe the uniquesness method is reliable, you look for patterns like the 4's marked with a plus above.

The argument is this: If the final solution has a 4 placed in r8c2 then the marked cells will be thus:
4 9
9 4

But if that is the case, then whoever made up the puzzle goofed because there is more than one solution. You show me a SuDoku solution with that pattern and I will show you another solution with this pattern:
9 4
4 9

So, the argument goes, since the source of the puzzle is known to be a reliable one-solution-only source, then r8c2 cannot be 9 and it cannot be 4. So we can place a 1 there!

"Uniqueness" refers to the fact that you believe the puzzle has only one solution.

That's about it. Personally, I don't like it. I always assume that all puzzles from any source can have multiple solutions. So I would have to try 1 and 4. That is no different than simple trial and error except the pattern is an excellent clue to what cell to start guessing in.

Mac

1) Though this puzzle does have a uniqueness rectangle, the four cells you have marked DO NOT FORM ONE, and in fact, the answer you suggest is incorrect! Row 8, column 2 is actually 4, not 1!

2) The uniqueness rectangle is r12c67, marked with plus signs below. The candidates 5 and 7 can be eliminated from r2c6.

Code: Select all

+---------------+-------------------+---------------+
| 39   139  2   | 4     8     +57   |+57   6   139  |
| 4    6    139 | 2     13579 +1357 |+57   8   139  |
| 7    8    5   | 19    139    6    | 29   4   1239 |
+---------------+-------------------+---------------+
| 1    5    34  | 8     347    237  | 6    9   24   |
| 8    39   349 | 16    1346   123  | 124  7   5    |
| 2    7    6   | 15    145    9    | 14   3   8    |
+---------------+-------------------+---------------+
| 359  2    139 | 1569  1569   4    | 8    15  7    |
| 59   149  7   | 3     159    8    | 49   2   6    |
| 6    49   8   | 7     2      15   | 3    15  49   |
+---------------+-------------------+---------------+


3) The four cells must be in TWO rows, TWO columns and TWO boxes. That's why they are referred to as uniqueness RECTANGLES rather than quadralaterals. The four you have marked are in THREE columns. No deductions or inference can be made. Since the two cells in box 9 are in different columns, their contents cannot be swapped without changing the contents of those two columns.

4) As far as personally not liking it -- I don't like the fact that the earth is round -- that doesn't make it flat. This tactic is no more or less dependent on the underlying validity of the puzzle as any other. If the puzzle you are working on is flawed -- it might have 100 solutions -- or it might hve none! In a puzzle with no solutions, if you can still call it a puzzle, any tactic can be crash. You could have something like:

Code: Select all

[123.]|[12..][12..]
------+------------
[23..]|[....][....]
[23..]|[....][....]


One naked pair "proves" that the cell in the upper left is 3, while the other "proves" that it is 1. Your reasoning tells me that I should blame the tactic rather than the fact that the puzzle is flawed.

Now, it's perfectly fine to have a puzzle in which it is stipulated that there are multiple solutions, and yes, when solving one of these, you cannot apply uniqueness rectangles or BUG. A puzzle *could* be presented as having exactly two solutions -- this is perfectly valid and it would require adjustments in your solving methods. But if you are solving a puzzle that is stipulated to have one solutions but actually has dozens or hundreds -- what exactly is the point? To merely fill in the cells so that there are no contradictions? You admit that you sometimes guess -- if you do, you will eventually fill in the cells completely and never realize that the puzzle had multiple solutions. If you don't, you will eventually reach a standstill where no other deduction is possible -- and be pissed that you wasted your time on a crappy puzzle. You would be no more or less disappointed if you tried to use a uniqueness rectangle.

The sources for puzzles with unique solutions are very ubiquitous. Puzzles created by Pappocom software, Simple Sudoku, Sadman, Solo, retrieved by Susser and dozens and dozens of others always have a unique solution.

[tso]

THANKS MCC AND QBasicMac. Thanks for explaining uniqueness so well.
I still have two dumb questions. I am a veteran at solving easy and medium sudokus, but the hard ones are taking longer than they should.
First question is, could someone please explain the code used to pinpoint a cell such as r8c2?
The second is, how does one post a sudoku grid, whether only with original numbers, with some missing ones filled in or completed here as so many of you have? In answering this, please keep in mind I am severely technically challenged-lol!
Also, any more tips for solving them more quickly and efficiently?
THANKS; SO GLAD I FOUND THIS SITE.
Pats4949 (Baltimore, MD, USA)

"r8c2" means "row 8, column 2"

Read this for the basic terms used here.

If you ever want to see exactly how a post was formatted, click on the QUOTE button on the upper right of the post.


First, make sure "DISABLE BBCode in this post" is UNCHECKED. The box is just below the window in which you type your post.

To post a grid manually so that it appears most readable, type these six charactors leaving out the spaces: [ c o d e ]

Then enter your puzzle, using periods for empty cells, for example:

3....2.87
...93.4.6
..9...5..
.7.54....
9...1...5
....96.7.
..5...6..
8.2.53...
76.4....3

Then type [ / c o d e ] at the end -- again, leave out the spaces. The results are:

Code: Select all

3....2.87
...93.4.6
..9...5..
.7.54....
9...1...5
....96.7.
..5...6..
8.2.53...
76.4....3


If you like, you can add spaces between cells and/or gridlines like this:

Code: Select all

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


You can also simple select the diagram and then click the CODE button -- it's just above the posting window. Experiment and press PREVIEW to see your results without posting.


Paul's Pages is one of many websites that will export nice diagrams for you.


The free Simple Sudoku is one of many software aps that will create diagrams of the grid and of the pencil marks.

Code: Select all

 *-----------*
 |3..|..2|.87|
 |...|93.|4.6|
 |..9|...|5..|
 |---+---+---|
 |.7.|54.|...|
 |9..|.1.|..5|
 |...|.96|.7.|
 |---+---+---|
 |..5|...|6..|
 |8.2|.53|...|
 |76.|4..|..3|
 *-----------*

 
 *-----------------------------------------------------------------------------*
 | 3       145     146     | 16      6       2       | 19      8       7       |
 | 125     1258    178     | 9       3       1578    | 4       12      6       |
 | 1246    1248    9       | 1678    678     1478    | 5       123     12      |
 |-------------------------+-------------------------+-------------------------|
 | 126     7       1368    | 5       4       8       | 12389   12369   1289    |
 | 9       2348    3468    | 2378    1       78      | 238     2346    5       |
 | 1245    123458  1348    | 238     9       6       | 1238    7       1248    |
 |-------------------------+-------------------------+-------------------------|
 | 14      1349    5       | 1278    278     1789    | 6       1249    12489   |
 | 8       149     2       | 167     5       3       | 179     149     149     |
 | 7       6       1       | 4       28      189     | 1289    1259    3       |
 *-----------------------------------------------------------------------------*

His site has one of the most popular tutorials. Another popular one is on SadMan Sudoku.

The free Sudoku Susser will also make diagrams. The sample puzzles that come with it explain in detail how lots of tactics work, including the uniqueness rectangles and loops. Robert's tutorial is extensive. It isn't on the site, but comes with the download. (It's free.) His software gives the most verbose descriptions of why certain tactics work.

Most important, being "severely technically challenged" is a description of WHERE you are, not WHAT you are.

[QBasicMac]

1) Explain the code used to pinpoint a cell such as r8c2?
2) how does one post a sudoku grid

1) No code. You just have to stare and stare. Some people have a natural talent and can spot things easily, some even without pencilmarks. Others, like me, have to stare a long time and sometimes even then can never see it and have to give up and ask for help or use some cheater program.

2) To post a grid, you have to prepare it using NOTEPAD, etc. then put {code} at the front and {/code} at then end. The forum automatically treats such a block by conserving spacing so stuff looks nice. Otherwise, like all internet posting, multiple spaces are converted to single spaces and leading spaces are lost.

But use square brackets instead of curly brackets. I used curley otherwise you would not see what I am trying to show.

{code}
a b c
{/code}

I am now posting the same exact stuff as above, but with square brackets:

Code: Select all

             a           b             c


See the difference?

Mac

[QBasicMac]

1) Explain the code used to pinpoint a cell such as r8c2?

LOL - As TSO noted,I simply goofed and identified the wrong pattern. Hope you are not too confused now.

Luckily, my placement of 1 was incorrect. If I had, by blind luck, selected the right number, it would be more confusing. Luckily, too, that TSO also has nothing better to do on Christmas day than monitory forums.

Bottom line, pay better attention to the grid and you will solve puzzles a LOT better than me. (Read TSO's explanation)

Mac

Edit:

Even more funny: after too much eggnog, I concluded that by "pinpoint r8c2" you meant come to the conclusion that the values in that cell need inspection. I think TSO read your meaning better: You meant "having seen a reference to r8c2, how do I find what cell of the puzzle you are talking about?".

I'm logging off until MUCH later.

[QBasicMac]

Hi, tso,

So it is true that there is no problem that other 5's and 7's exist?
I made some placements and see that indeed it isn't (in this case)

So one needs to find a rectangle
57 57
57x 57

and not worry about other 5's and 7's in the boxes?

(More confused than I thought)

Mac

Code: Select all

+-------------------+---------------|
| 4     8     +57   |+57   6   139  |
| 2     13579 +1357 |+57   8   139  |
| 19    139    6    | 29   4   1239 |
+-------------------+---------------+

+-------------------+---------------|
| 4     8      7    | 5    6   139  |
| 2     5      13   | 7    8   139  |
| 19    139    6    | 29   4   1239 |
+-------------------+---------------+


[bridgenut]

Wow! Thanks all! I have another great site to go to besides bridgebaseonline when I want to play-the bridge site is interactive; sudokus is a soliataire game.
A cell is identified how? You all use a letter number combination to reference a particular cell. The top left cell, for example, would be what? R I guess is right, L left. I can't quite pinpoint cells and wish to know how to read the references to particular cells.
Also, are there interactive sudokus here where you play with others and take turns or compete? So far I have only done sudokus solitairily. However, the board game can be played interactively.
Merry Christmas and Happy Chanukah and happy holidays to all,
Pats4949
Baltimore, Maryland, USA

[ihope127]

"r" stands for "row", and "c" stands for "column".

(By the way, a person can post tags "normally" by sticking "dummy tags" inside of them: for example, [code] can be posted as [co[b][/b]de].)

[bridgenut]

lol d'uh thanks was thinking r was right dum de dum dum

[tso]

(By the way, a person can post tags "normally" by sticking "dummy tags" inside of them: for example, [code] can be posted as [co[b][/b]de].)

Didn't realize that -- that's useful to know.

Hi, tso,

So it is true that there is no problem that other 5's and 7's exist?
I made some placements and see that indeed it isn't (in this case)

So one needs to find a rectangle
57 57
57x 57

and not worry about other 5's and 7's in the boxes?

Correct. In your partial diagram, because the rectangle exists in 2 columns, 2 rows and 2 boxes, not one of the other 77 cells can influence just ONE of the four cells. I made a similar mistake at first, thinking that it was enough for the four cells to form a rectangle -- but if the four cells are in four different boxes, it does not work.

I take a look at the PDF tutorial that comes with Sudoku Susser. Another good reason to accept the unique rectangles tactic is that are so many interesting things that can be done with them and the many variations. (BUG is the extreme version of Uniqueness tests.) For example, this is a Mad Overlord calls this a Type 3 Unique Rectangle:

Code: Select all

[....][....][349.]
[....][....][....]
[1234][1234][..34]
------------------
[12..][12..][....]
[....][....][....]
[....][....][....]

Since at least one of r3c12 must be EITHER 3 or 4 -- it forms a sort of "quantum cell" that contains the possibilities [34]. This forms a naked pair with r3c3 -- allowing you to place a 9 in r1c3! But if we insist on proving that the puzzle has a unique solution, we have to ignore this clever and satisfying deduction. And more importantly, Uniqueness Rectangles are much easier to spot than most other advanced tactics -- they all start with a naked pair and you can tell within a few seconds if a rectangle exists.

[Lardarse]

In your partial diagram, because the rectangle exists in 2 columns, 2 rows and 2 boxes, not one of the other 77 cells can influence just ONE of the four cells.

Aaaaaaaaaaaaaaah... That's how you explain it...

I assume that the rule can't be used in a puzzle where the diagonals count if 1 of the 4 cells is on the diagonal.