## Standardizing the Uniqueness descriptions...

Advanced methods and approaches for solving Sudoku puzzles
That's great Ruud, thanks I recall reading a posting a while back that said that types 1 and 3 were the most common and the others were quite rare. I think I've got the code right, I don't have much of a means to test it yet...
gaby

Posts: 15
Joined: 25 October 2005

I've really appreciated learning about uniqueness, even if I don't implement it at the Sudoku Assistant, http://www.stolaf.edu/people/hansonr/sudoku.

I've added the uniqueness rule to my description of the 12 intersection rules of the basic methods of solving Sudoku.

http://www.stolaf.edu/people/hansonr/sudoku/12rules.htm

I think the extension there to nxn Sudoku might interest some.

Comments appreciated.
Bob Hanson

Posts: 75
Joined: 04 December 2005

Sorted now. Found a bug in my type 2 code, which I've now fixed. Type 4 works fine as well. Now it handles types 1-4, in A and B versions. Now it's time to update the dictionary...
gaby

Posts: 15
Joined: 25 October 2005

Types 1 and 4 are actually the most common forms, with 2 slightly less common and 3 a tad uncommon.
Lummox JR

Posts: 125
Joined: 22 September 2005

### Deadly Loop, Triple and Quad

I'd like to add a little to The Ultimate Guide to Unique Rectangles.

Start with the Mepham Group, 4/4/08.

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

The basic strategies get me this:

.------------------.------------------.-----------------.
| 2 7 8 | 3 4 9 | 1 6 5 |
| 1349 13 346 | 5 28 68 | 48 7 29 |
| 49 5 46 | 267 278 1 | 48 3 29 |
:-----------------+-----------------+-----------------:
| 5 2 7 | 8 1 4 | 6 9 3 |
| 34 *348 9 | 67 5 67 | 2 *48 1 |
| 6 *48 1 | 9 3 2 | 7 5 *48 |
:-----------------+-----------------+-----------------:
| 37 9 23 | 4 278 78 | 5 5 6 |
| 17 6 24 | 17 9 5 | 3 *248 *48 |
| 8 14 5 | 12 6 3 | 9 24 7 |
'------------------'------------------'------------------'

Look at squares (5,2),(6,2),(5,8),(6,9),(8,8),(8,9). They all have a 4 and 8. Without the 2 and 3 they would form an deadly ambiguous group that turns a corner. I think you call this a loop. Either the 3 in (5,2) or the 2 in (8,8) must be part of our solution. Now look at the 8s. There are only two in each box so they must be in (6,2),(5,8),(8,9) or (5,2),(6,9),(8,8) but they can't be in (5,2),(6,9),(8,8) because these contain both the 2 and 3 which we need at least one of. The 8s must be in (6,2),(5,8),(8,9). Knowing this doesn't help me solve the sudoku but at least I'm closer.

Leave out the 1, 3 and 7 in (2,1),(3,1),(2,5),(3,5),(2,7),(3,7),(2,9),(3,9) and a deadly quad is exposed. I don't know what to do with it but at least it's an example. A deadly triple would be similar. I'm not sure if this is the same type of deadly quad the MadOverlord is referring to or not since it wouldn't be limited to a Type 3. Can it still be called a Unique "Rectangle" if it's in the shape of an L?

There is another type of deadly ambiguous triple from the Mepham Group, 4/25/08.

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

The basic strategies get me this:

.------------- --.---------------.-----------------.
| 6 9 5 | 4 1 3 | 8 7 2 |
| 3 7 4 | 8 2 9 |*15 *56 *16 |
| 2 1 8 | 7 6 5 | 4 9 3 |
:---------------+----------------+---------------:
| 179 2 179| 3 4 6 | 79 8 5 |
| 8 5 3 | 2 9 7 | 6 1 4 |
| 79 4 6 | 1 5 8 | 2 3 79 |
:---------------+----------------+---------------:
| 4 6 79 | 5 8 1 | 3 2 79 |
| 17 8 2 | 9 3 4 |*157 *56 *16 |
| 5 3 19 | 6 7 2 | 19 4 8 |
'----------------'---------------'------------------'

Look at (2,7),(2,8),(2,9) and (8,7),(8,8),(8,9). Leave out the 7 and you have a pair of deadly triples (as opposed to three pairs). (8,7) must be the 7 and the solution falls into place.

Sorry I haven't figured out how to use the [Code] or how to make things line up better. Does anyone have a link on how to use this stuff?
John Meyer

Posts: 3
Joined: 11 June 2008

### Re: Deadly Loop, Triple and Quad

John Meyer wrote:Start with the Mepham Group, 4/4/08.

Code: Select all
`2 . .|. 4 .|. . 5 . . .|5 . .|. 7 . . 5 .|. . 1|. 3 . -----+-----+----- . . 7|8 . .|6 . . . . 9|. 5 .|2 . . . . 1|. . 2|7 . . -----+-----+----- . 9 .|4 . .|. 1 . . 6 .|. . 5|. . . 8 . .|. 6 .|. . 7`

The basic strategies get me this:

Code: Select all
` +--------------------------------------------------------------+ |  2     7     8     |  3     4     9     |  1     6     5     | |  1349  13    346   |  5     28    68    |  48    7     29    | |  49    5     46    |  267   278   1     |  48    3     29    | |--------------------+--------------------+--------------------| |  5     2     7     |  8     1     4     |  6     9     3     | |  34    348   9     |  67    5     67    |  2     48    1     | |  6     48    1     |  9     3     2     |  7     5     48    | |--------------------+--------------------+--------------------| |  37    9     23    |  4     278   78    |  5     5     6     | |  17    6     24    |  17    9     5     |  3     248   48    | |  8     14    5     |  12    6     3     |  9     24    7     | +--------------------------------------------------------------+`

The original puzzle has multiple solutions.

The PM does as well. The PM also has two 5s in [box 9] and one of them is a 1 in the original puzzle.

You might want to fall back and regroup since your second puzzle has similar problems!
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

### Re: Deadly Loop, Triple and Quad

John Meyer wrote:Sorry I haven't figured out how to use the [Code] or how to make things line up better. Does anyone have a link on how to use this stuff?

Here's a start.

Also, you could try copying your puzzle first to a program like Simple Sudoku. From there, click copy and the puzzle will be properly formatted when you paste it between the Code tags:
[code]paste[/code]

Luke
2015 Supporter

Posts: 435
Joined: 06 August 2006
Location: Southern Northern California

### Re: Deadly Loop, Triple and Quad

Luke451, your demonstration reminds me of a knife salesman showing his customers how sharp his knife was by repeatingly using it to cut his fingers but it didn't even inflict a wound.

John Meyer wrote:Sorry I haven't figured out how to use the [Code] or how to make things line up better. Does anyone have a link on how to use this stuff?

Luke451 wrote:Here's a start.

Also, you could try copying your puzzle first to a program like Simple Sudoku. From there, click copy and the puzzle will be properly formatted when you paste it between the Code tags:
[code]paste[/code]

... then you'll get this effect:
Code: Select all
`paste`

udosuk

Posts: 2698
Joined: 17 July 2005

### Re: Deadly Loop, Triple and Quad

udosuk wrote:Luke451, your demonstration reminds me of a knife salesman showing his customers how sharp his knife was by repeatingly using it to cut his fingers but it didn't even inflict a wound.

Obviously, if you've just copied a grid and then "paste" it between the code tags you'll get the puzzle and not the word "paste."

Luke
2015 Supporter

Posts: 435
Joined: 06 August 2006
Location: Southern Northern California

### Re: Deadly Loop, Triple and Quad

Luke451 wrote:
udosuk wrote:Luke451, your demonstration reminds me of a knife salesman showing his customers how sharp his knife was by repeatingly using it to cut his fingers but it didn't even inflict a wound.

Obviously, if you've just copied a grid and then "paste" it between the code tags you'll get the puzzle and not the word "paste."

Obviously, you didn't get my meaning of that statement. I'll give you a full day to think about it again.
udosuk

Posts: 2698
Joined: 17 July 2005

Obviously, this 30 months old thread should have been left sleeping on page 311 of the forums... The descriptions and terminology is very outdated.

John Meyer, to learn more about uniqueness technique, you can look through the "uniqueness tests" links in this post. The patterns you describe have already been discussed in the BUG-lite-thread.

RW
RW
2010 Supporter

Posts: 1000
Joined: 16 March 2006

### Re: Deadly Loop, Triple and Quad

I wrote:Obviously, you didn't get my meaning of that statement. I'll give you a full day to think about it again.

Okay, a full day is up (almost). This was supposed to be a riddle for both Luke451 and John Meyer (as well as others) to figure out. But unfortunately none of them paid much attention.

The problem is, Luke451 was trying to demonstrate to John Meyer on how to use the [code] tags. He even went to all the troubles of including the string "[code]paste[/code]" in his post. But he didn't bother to check why it didn't appear in the following manner:
Code: Select all
`paste`

My "knife salesman" analogy was directed to this fact. A teacher tried to teach a student a trick by performing it once himself. But it didn't work to any effect and the teacher walked away thinking the job was done. I just found it very funny.
udosuk

Posts: 2698
Joined: 17 July 2005

Udo, my friend,

Oh, I have been paying attn. I had to beat up on my buddies on the golf course b4 I cld get back to this pressing matter .

You have a valid point, but on one condition. The condition would be that the estimable Mr. John Meyer would not be able to figure out that he should paste the grid between the code tags rather than type the word "paste." I gave the gentleman enough credit to know that. If John has never heard of cut and paste, then, boy, ya got me. The joke's on me, or should I say riddle? The only one that can answer that is Mr. Meyer himself. So, John buddy, help me out here. You know what cut and paste is, right?

Ah, probably it's just that I don't get Aussie humor...

Luke
2015 Supporter

Posts: 435
Joined: 06 August 2006
Location: Southern Northern California

Luke, my dear friend,

Mmm... You still didn't get the point at all. I guess you haven't been paying enough attention.

Your usage of the word "paste" to replace a grid is perfectly okay for me. I also trust John Meyer knows what "cut and paste" is. That's not the issue at all.

My point is, you typed the following line:

[code]paste[/code]

It could have been anything else in the middle, e.g.:

[code]Hello Luke451[/code]

[code]123456789[/code]

Or even a whole solution grid in the middle:

[code]
+-------------+--------------+---------------+
| 2 9 157 | 147 134 6 | 45 37 8 |
| 34 8 17 | 5 134 147 | 2 69 69 |
| 34 57 6 | 8 2 9 | 1 37 45 |
+-------------+--------------+---------------+
| 59 15 2 | 19 6 3 | 8 4 7 |
| 7 16 8 | 1249 5 14 | 69 129 3 |
| 69 3 4 | 129 7 8 | 569 1269 1569 |
+-------------+--------------+---------------+
| 568 2 9 | 3 148 145 | 7 16 146 |
| 68 467 3 | 147 148 2 | 469 5 1469 |
| 1 457 57 | 6 9 457 | 3 8 2 |
+-------------+--------------+---------------+
[/code]

The bloody point is, why the heck the lines above weren't displayed as the following instead:
Code: Select all
`paste`

Code: Select all
`Hello Luke451`

Code: Select all
`123456789`

Code: Select all
`+-------------+--------------+---------------+|  2   9  157 |  147 134  6  |  45  37    8  ||  34  8   17 |   5  134 147 |  2   69   69  ||  34  57  6  |   8   2   9  |  1   37   45  |+-------------+--------------+---------------+|  59  15  2  |  19   6   3  |  8    4    7  ||  7   16  8  | 1249  5   14 |  69  129   3  ||  69  3   4  |  129  7   8  | 569 1269 1569 |+-------------+--------------+---------------+| 568  2   9  |   3  148 145 |  7   16   146 ||  68 467  3  |  147 148  2  | 469   5  1469 ||  1  457  57 |   6   9  457 |  3    8    2  |+-------------+--------------+---------------+`

It's the fact that you didn't investigate how and why that happened which amused me.
udosuk

Posts: 2698
Joined: 17 July 2005

Hoo-kay. The light is starting to come on. I guess I'm too new at this stuff to try answers questions. The blind leading the blind.

Really, I was just trying to help the guy out. The method I described has worked for me, so I didn't see the holes in my procedure. Maybe you could help me out. The only way I can make [code]this[/code] happen is to "Disable BBCode in this post."

Oh, and I'm glad my floundering has at least been a source of amusement for ya. I'd hate waste everyone's time for nothing!

Luke
2015 Supporter

Posts: 435
Joined: 06 August 2006
Location: Southern Northern California

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