Invalid Puzzles

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Invalid Puzzles

Postby Solgor » Tue Jun 03, 2014 3:19 am

I have been an avid Sudoku fan for about five years, but in all that time I have not been sure what constitutes an invalid puzzle. I have been reading a lot on the subject but I am still not sure. I hope someone here can straighten me out.

Here is an illustration I got from the Hodoku site. The simple sample below shows a rectangle with three givens and one not given.

2 Given 4 Given

4 Given 2 NOT Given

According to Hodoku the 2 on bottom must be removed to avoid an invalid puzzle. However, a great many times the puzzle does not permit you to eliminate the 2, in other words the 2 on the bottom become the candidate for that cell. Does that prove that the puzzle is invalid?

Your help would be appreciated.
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Postby Pat » Tue Jun 03, 2014 6:51 am

Solgor wrote:I have been an avid Sudoku fan for about five years, but in all that time I have not been sure what constitutes an invalid puzzle. I have been reading a lot on the subject but I am still not sure. I hope someone here can straighten me out.

Here is an illustration I got from the Hodoku site. The simple sample below shows a rectangle with three givens and one not given.

2 Given 4 Given

4 Given 2 NOT Given

According to Hodoku the 2 on bottom must be removed to avoid an invalid puzzle. However, a great many times the puzzle does not permit you to eliminate the 2, in other words the 2 on the bottom become the candidate for that cell. Does that prove that the puzzle is invalid?


HoDoKu knows the definition of the word given,
and would never say what you accuse it of saying
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Re: Invalid Puzzles

Postby eleven » Tue Jun 03, 2014 11:11 am

Solgor,

what Pat means is, what you call "givens" in fact must be solved cells.

If you want to see an "invalid", multi-solution puzzle, just take a solution grid and remove the 2 numbers, which form such a rectangle, e.g.
Code: Select all
 +-------+-------+-------+
 | 4 6 9 | 7 . 2 | 5 . 1 |
 | 7 1 2 | 5 . 4 | 6 . 9 |
 | 8 3 5 | 6 9 1 | 2 4 7 |
 +-------+-------+-------+
 | 1 4 7 | 2 5 8 | 9 6 3 |
 | 3 2 6 | 4 7 9 | 1 5 8 |
 | 9 5 8 | 3 1 6 | 4 7 2 |
 +-------+-------+-------+
 | 6 7 3 | 1 2 5 | 8 9 4 |
 | 5 8 1 | 9 4 3 | 7 2 6 |
 | 2 9 4 | 8 6 7 | 3 1 5 |
 +-------+-------+-------+
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Re: Invalid Puzzles

Postby daj95376 » Tue Jun 03, 2014 3:13 pm

Solgor wrote:I have been an avid Sudoku fan for about five years, but in all that time I have not been sure what constitutes an invalid puzzle. I have been reading a lot on the subject but I am still not sure. I hope someone here can straighten me out.

Here is an illustration I got from the Hodoku site. The simple sample below shows a rectangle with three givens and one not given.

2 Given 4 Given

4 Given 2 NOT Given

According to Hodoku the 2 on bottom must be removed to avoid an invalid puzzle. However, a great many times the puzzle does not permit you to eliminate the 2, in other words the 2 on the bottom become the candidate for that cell. Does that prove that the puzzle is invalid?

Your help would be appreciated.


Okay, after reading your message (several times) and the responses to it, I have (half) an idea what you're asking.

The grid below should represent an example of your scenario. Only the four cells in question are shown.

Code: Select all
 +-----------------------------------+
 |  . *2  .  |  .  .  .  |  . *4  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  . *4  .  |  .  .  .  |  .  2X .  |  ->  X is one or more candidates other than "2"
 +-----------------------------------+

If any of the cells marked (*) is a clue/given in the original puzzle, then cell "2X" can be "2". This is why you can't eliminate "2" sometimes.

If all of the cells marked (*) are solved cells, then cell "2X" can not be "2".

_
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Re: Invalid Puzzles

Postby coloin » Tue Jun 03, 2014 3:18 pm

A valid puzzle has exactly one solution
An invalid puzzle may have zero solutions - or 2-or-more solutions -as shown by eleven

A valid puzzle consists of givens [ the clues given to you at the beginning by the setter] [this is the accepted meaning of the term]
A valid puzzle has potentially 9 options [pencil marks] for each cell without a given clue. [This would be termed an inserted clue or a solved cell]
Only one of these is compatible with the solution - the other 8 will give a constraint [trivial or complex] and result in an invalid puzzle with zero solutions.

In easy puzzles - it is easy to insert the correct clues
In hard puzzles - it may be difficult to show that an option to add a clue gives an invalid puzzle solution / constraint.
in super-hard puzzles - it may even be difficult to see the eventual constraint by adding two clues [where one or both is incorrect]

Assuming that a puzzle is valid can be used to solve a puzzle - and the use of this technigue is up to the individual.
daj95376 shows this technique to exclude the 2 - with the proviso that the other 4,4,2 clues are not given clues in the original puzzle.

C
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Re: Invalid Puzzles

Postby Solgor » Tue Jun 03, 2014 4:04 pm

I appreciate your replies fellas but a lot of the jargon used is way over my head. I knew it would be hard to explain my question in words so I guess I failed to get my point across. However I think daj got to the point when he said that:

+-----------------------------------+
| . *2 . | . . . | . *4 . |
| . . . | . . . | . . . |
| . *4 . | . . . | . 2X . | -> X is one or more candidates other than "2"
+-----------------------------------+

If any of the cells marked (*) is a clue/given in the original puzzle, then cell "2X" can be "2". This is why you can't eliminate "2" sometimes.

If all of the cells marked (*) are solved cells, then cell "2X" can not be "2".

In my example ALL of the Cells starred are solved cells but when I want to eliminate the 2 marked X it is the wrong move as my Simple Sudoku grid flashes an error message which means that the 2X must be used as the solved cell. I come back to my original question, does the fact that I am forced to use the 2X as the solved cell mean that the puzzle is invalid?
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Re: Invalid Puzzles

Postby JasonLion » Tue Jun 03, 2014 4:43 pm

If I am following your description correctly, it means something is going wrong. However that could be in the original puzzle or it could be something else you did in the solving process.

It would be a big help if you could post a specific puzzle that you are having this issue with.
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Re: Invalid Puzzles

Postby eleven » Tue Jun 03, 2014 8:58 pm

Solgor wrote:In my example ALL of the Cells starred are solved cells but when I want to eliminate the 2 marked X it is the wrong move as my Simple Sudoku grid flashes an error message which means that the 2X must be used as the solved cell.

Did you really get the difference between given and solved ?
Since you are not interested in theory: in Simple Sudoku the givens have a lightly darker background than the solved cells.
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Re: Invalid Puzzles

Postby Solgor » Tue Jun 03, 2014 9:31 pm

You hit the nail on the head, I think a puzzle like this is invalid, something is wrong with the puzzle. This action appears before I even start the solving process. I always use Simple Sudoku and I test a puzzle for validity before I start. Here is a puzzle you can check:


005020100040090027900000600000005271800000000200063508000000000006078002109000006

Note that R1C1 not solved R1C5 solved 2

R6C1 solved 2 R6C5 solved 6

R1C1 has three candidates including a 6. When I try to remove the 6 to avoid a puzzle with more than one solution Simple Sudoku flashes a red warning that I have made an invalid elimination. This of course means that I have to use the 6 as a solved cell thus causing a puzzle with more than one solution.

I don't know how better to explain this question, I hope that you can help.
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Re: Invalid Puzzles

Postby champagne » Wed Jun 04, 2014 2:11 am

Solgor wrote:
I don't know how better to explain this question, I hope that you can help.


As said jasonlion, an example is usually the best way to understand where is(/are) the problem(s).

a) The uniqueness rule works only in a rectangle made of 2 rows, 2 columns, 2 boxes.
Here you have 4 boxes.

b) 3 of the 4 cells are given, not solved. One given would be enough (in a valid rectangle) to avoid the possibility to exchange the 2 digits

That puzzle is valid,

Last point, but here I have no answer, in the solution r1c1=7. I don't understand why the solver tells you that your elimination is not correct. Possibly the solver did not find at that point a rule to apply explaining why you could clear 6r1c1.

my solver clears it at that point using a XY loop (working in Sudoku Explainer mode)

Code: Select all
367 678  5     |34678 2    467   |1     3489   349 
36  4    138   |5     9    16    |38    2      7   
9   1278 12378 |13478 1348 147   |6     3458   345 
---------------------------------------------------
346 69   34    |489   48   5     |2     7      1   
8   5    147   |12479 14   12479 |349   6      349 
2   179  147   |1479  6    3     |5     49     8   
---------------------------------------------------
457 278  2478  |1346  1345 12469 |34789 134589 3459
45  3    6     |149   7    8     |49    1459   2   
1   278  9     |234   345  24    |3478  3458   6   


EDIT: a situation in the solving process where a UR is partially solved is relatively academic. It is a position that my solver does not study.
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