Help please! Is this extreme puzzle unsolvable?

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Help please! Is this extreme puzzle unsolvable?

Postby MarkRobert » Wed Mar 08, 2017 12:49 pm

Hi, I would be really grateful for some help with this puzzle which has me stumped. It is from the magazine PuzzleLife Sudoku Extreme.

I know from scanning the answers that the resolved cells are correct.

Using single digit colouring on the 1s I have tried eliminating 1 as a candidate from Row 2, Column 3; Row 5, Column 1; and Row 5, Column 4, as it appears to be a Colour Trap where these three cells can see opposite cells for a 1 in those rows or columns.

However, this appears to leave me with a puzzle which is unsolvable without resorting to trial by error.

Is there another solution?

Thanks

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Re: Help please! Is this extreme puzzle unsolvable?

Postby JasonLion » Thu Mar 09, 2017 3:45 am

An X-Wing and a BUG+1 will reduce the puzzle to being solvable with just singles.
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Re: Help please! Is this extreme puzzle unsolvable?

Postby Leren » Thu Mar 09, 2017 6:30 am

745289613...5374282384619753.264..97.74.....295..728.45.78..3.14....3....637.42.9

An alternative to Jason's solution will avoid the BUG +1 situation, which some may find a bit obscure.

Code: Select all
*-----------------------------------------------------*
| 7    4    5     | 2    8    9     | 6    1    3     |
| 16   19   169   | 5    3    7     | 4    2    8     |
| 2    3    8     | 4    6    1     | 9    7    5     |
|-----------------+-----------------+-----------------|
| 3   a18   2     | 6    4    58    | 15   9    7     |
| 168  7    4     | 139  19   58    | 15   36   2     |
| 9    5   *6-1   | 13   7    2     | 8    36   4     |
|-----------------+-----------------+-----------------|
| 5   c29   7     | 8    29   6     | 3    4    1     |
| 4   b28  d19    | 19   25   3     | 7    58   6     |
| 18   6    3     | 7    15   4     | 2    58   9     |
*-----------------------------------------------------*

There is an XY chain in the cells marked a-b-c-d which proves that at least one of cells a or d must be 1, so Row 6 Column 3 must not be 1, so it solves to 6 and the rest of the puzzle solves in singles.

If you are unfamiliar with XY chains let me know and I'll explain further.

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Re: Help please! Is this extreme puzzle unsolvable?

Postby MarkRobert » Thu Mar 09, 2017 8:21 pm

Thanks Leren, I haven't quite got to grips with XY chains yet. An explanation on how to identify and apply them would be great. :D
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Re: Help please! Is this extreme puzzle unsolvable?

Postby Leren » Fri Mar 10, 2017 3:01 am

OK, I'll explain how this particular XY chain works in words and refer you to some teaching sites that have good general explanations and nicely worked examples.

An XY chain consists of a string of bi-value cells, where one candidate is common to adjacent cells in the chain and the adjacent cells can see each other.

The idea is to start and end on the same candidate, and you can then eliminate that candidate from cells that can see the first and last cells in the chain.

So, with this one, start by assuming that cell a is not 1, then it must be 8. So cell b can't be 8, so it must be 2. So cell c can't be 2 so it must be 9. So cell d can't be 9, so it must be 1.

So, summarizing this, if cell a is not 1, cell d is 1. You then reverse the argument and start with cell d and assume that it is not 1 and following the cells in order d-c-b-a you will conclude that cell a is 1.

What all this proves is that at least one of cell a and cell d must be 1. Since the target elimination cell, which I've marked with a * in the diagram can see both cells a and d it can't be 1.

This particular XY chain is of length 4 but they can be of just about any length. The shortest useful XY chain is of length 3 and is called an XY Wing, which you may have heard about.

The teaching site XY chain examples can be found here and here and just for good measure you can also read about XY Wings on the same sites here and here.

Leren

PS An alternative solution is to first apply the X Wing, as Jason suggested, as shown in the following diagram : The X Wing is in 1's in rows 68 / c34 in the cells marked * and eliminates the 1's in r2c3 and r5c4 as shown.

Code: Select all
*-----------------------------------------------------*
| 7    4    5     | 2    8    9     | 6    1    3     |
| 16   19   69-1  | 5    3    7     | 4    2    8     |
| 2    3    8     | 4    6    1     | 9    7    5     |
|-----------------+-----------------+-----------------|
| 3    18   2     | 6    4    58    | 15   9    7     |
| 168  7    4     | 39-1 19   58    | 15   36   2     |
| 9    5   *16    |*13   7    2     | 8    36   4     |
|-----------------+-----------------+-----------------|
| 5    29   7     | 8    29   6     | 3    4    1     |
| 4   28   *19    |*19   25   3     | 7    58   6     |
| 18   6    3     | 7    15   4     | 2    58   9     |
*-----------------------------------------------------*

This brings you to here, where a length 3 XY chain ie an XY Wing in cells a, b and c, solves r9c1 and the whole puzzle. I suspect that this was what the magazine had in mind as the preferred solution.

Code: Select all
*-----------------------------------------------------*
| 7    4    5     | 2    8    9     | 6    1    3     |
|a16   19  b69    | 5    3    7     | 4    2    8     |
| 2    3    8     | 4    6    1     | 9    7    5     |
|-----------------+-----------------+-----------------|
| 3    18   2     | 6    4    58    | 15   9    7     |
| 168  7    4     | 39   19   58    | 15   36   2     |
| 9    5    16    | 13   7    2     | 8    36   4     |
|-----------------+-----------------+-----------------|
| 5    29   7     | 8    29   6     | 3    4    1     |
| 4    28  c19    | 19   25   3     | 7    58   6     |
|*8-1  6    3     | 7    15   4     | 2    58   9     |
*-----------------------------------------------------*

An alternative move at this point, suggested by Jason, is to apply a BUG+1 move, which forces r5c1 to be 1. If you really wan't know why this is True, read about the BUG principle here .

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Re: Help please! Is this extreme puzzle unsolvable?

Postby MarkRobert » Fri Mar 10, 2017 1:21 pm

D'oh. I can't believe I did not spot the X-Wing. Thanks Jason and Leren for the XY explanation. Definitely something I need to learn.
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