November 11, 2016

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Re: November 11, 2016

Postby Leren » Sat Nov 12, 2016 8:29 pm

What all this boils down to is : Is it possible to create a valid Sudoku solution having a pattern like this in a band or stack

Code: Select all
1..|.2.|...
...|.1.|.2.
2..|...|.1.

If it is, then it would obviously be possible to create a similar solution with all cells the same except for the 1's and 2's being swapped.

When reducing the solution to a puzzle by removing cell contents, at least one of the six cells must remain a clue, otherwise the puzzle would have 2 solutions.

If it is not possible, then Sudtyro2's move would be correct, but I've never seen anything that supports this and I suspect that it is possible to create such a solution.

Sounds like a good challenge for the expert puzzle creators, such as those who engage in the patterns game, to resolve this issue.

The 4 cell case

Code: Select all
1..|.2.
2..|.1.

is absolutely possible, with a good example by Andrew Stuart here. This is the basis for the (not very well known on this site) Avoidable Recangle move.

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Re: November 11, 2016

Postby eleven » Sun Nov 13, 2016 11:44 am

Leren wrote:I had a look at RW's post and he says :
Code: Select all
1..|...|...
...|...|...
2..|1..|...
-----------
...|...|...
...|...|...
...|...|...
-----------
...|...|...
...|...|...
...|...|...

Assume these are the only given, or logically solved, instances of numbers 1 and 2 on the grid. If we placed number 2 in r1c4, then we would have two number pairs that can be defined by two rows (1 and 3) two columns (1 and 4) and 2 boxes (1 and 2). That means that in each other unit left on the grid there has to be exactly two spaces reserved for numbers 1 and 2, which in the end will lead to a bug => we can safely remove candidate 2 from r1c4.

My underlining of the word given. This statement, taken literally, Is wrong.

Seems, that you misunderstood it. RW says, the only given, or logically solved, instances of numbers 1 and 2 on the grid. And he means the whole grid. This is, why it is called reverse bug. Not the digits you are looking at, would lead to a non unique solution, but the other 12's.
However in the puzzle given in this thread you see 4 and 6 givens outside the 6 cells, so you can't use it.
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Re: November 11, 2016

Postby SteveG48 » Sun Nov 13, 2016 2:12 pm

Ah, more clarification. Thanks. So now that we understand what RW was saying, was he correct?
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Re: November 11, 2016

Postby eleven » Sun Nov 13, 2016 5:53 pm

Of course he was correct. Just read what he said here. If r1c4=2 and all other digits are resolved, what will remain for the 12's in the other 7 boxes/rows/columns ? A BUG.

[Added:] If that still is not clear: Wherever you have a 1 in the remaining puzzle, you must have a 2, cause none is given and the resolved 12 cells can't help you. When the other digits are resolved, in each unit (box, row, column) exactly 2 cells will remain with exactly 2 candidates (here 12). This is the definition of a BUG.
btw it turned out that reverse bugs, which make real progress in a puzzle, are very very rare.
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Re: November 11, 2016

Postby Leren » Sun Nov 13, 2016 7:39 pm

Seems to me this has degenerated into an argument about whether or not the term Given means Clue or not. According to Sudopedia it does. If you look here It says, inter alia:

Given : A digit placed in a cell by the puzzle setter. It cannot be changed by the player. and Clue : An alias used for given.

Here is Andrew Stuart's example puzzle :

Code: Select all
5..4.3..1
.........
.4..2..39
..5..2...
9.6...4.3
..87..6..
81..7..4.
.........
6..3.1..7

Here is the unique solution :

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

Notice the digits 1 and 2 in r23c35. Looks like a DP, right ? Why was this pattern possible in the unique solution ? Simple - r3c5 = 2 is a Given (Clue) according to the terminology used in Sudopedia.

Suppose at some stage in the puzzle you had concluded that r2c5 and r3c3 were both 1. Could you remove 2 from r2c3 ? No, because r3c5 is a Given (Clue) according to the terminology used in Sudopedia..

Suppose you placed 2 in r2c3 to complete the apprent DP in 12. Would this cause a BUG in 12 in the rest of the puzzle ? Obviously not. Why not ? Because r3c5 is a Given (Clue) according to the terminology used in Sudopedia..

Do I sound like I am repeating myself ?

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Re: November 11, 2016

Postby SteveG48 » Sun Nov 13, 2016 8:26 pm

eleven wrote:Of course he was correct. Just read what he said here. If r1c4=2 and all other digits are resolved, what will remain for the 12's in the other 7 boxes/rows/columns ? A BUG.

[Added:] If that still is not clear: Wherever you have a 1 in the remaining puzzle, you must have a 2, cause none is given and the resolved 12 cells can't help you. When the other digits are resolved, in each unit (box, row, column) exactly 2 cells will remain with exactly 2 candidates (here 12). This is the definition of a BUG.
btw it turned out that reverse bugs, which make real progress in a puzzle, are very very rare.


OK, then that being agreed, it would seem to me that we can safely remove the caveat "or logically solved" from RW's criterion, and say that the reverse BUG applies if there are no given instances of the numbers on the grid and outside the reverse BUG pattern. After all, if a number has been logically solved, then it can be "unsolved" as well.
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Re: November 11, 2016

Postby eleven » Sun Nov 13, 2016 8:56 pm

Leren wrote:Suppose you placed 2 in r2c3 to complete the apprent DP in 12. Would this cause a BUG in 12 in the rest of the puzzle ? Obviously not. Why not ? Because r3c5 is a Given (Clue) ...

It does not, because in the rest of the puzzle a 2 or 3 (in this case both) are givens (resp. resolved cells, when the 1's in r2c5,r3c3 are resolved). If this would not be the case, the puzzle could not be unique with 2 in r2c3.
See the samples in the original reverse bug threads here and here.
You could also have a reverse MUG with the same argument, but i dont know a real live example for that.
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