What's my next move ? ? ?

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What's my next move ? ? ?

Postby quentin24 » Mon Mar 13, 2006 9:08 pm

This puzzle has had me scratching my head for over a month now. I keep looking at it, but can't seem to solve it.

It's a five star (out of six) from my local paper (Mpls Star Tribune). I'm posting the orginal followed by the point at where I got stuck. Seems like I have to guess, but isn't there a lgical solution? What's my next move?

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

7    3    6  | 1     4    9   | 8   5   2
1    5    9  | 268   68   268 | 7   34  34
24   24   8  | 7     3    5   | 9   6   1
-------------+----------------+--------------
5    6    24 | 248   9    1   | 234 7   348
8    9    24 | 24    7    3   | 5   1   6
3    1    7  | 5     68   2468| 24  48  9
-------------+----------------+--------------
9    7    5  | 3     1    48  | 6   2   48
246  248  1  | 9     5    468 | 34  348 7
46   48   3  | 468   2    7   | 1   9   5
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Postby tarek » Mon Mar 13, 2006 9:34 pm

some advanced techniques,

I would try to target the candidate 4 in r4c9 through colouring or using a finned x-wing.

an xy wing is still needed if the finned x-wing is used..........

tarek
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Postby CathyW » Mon Mar 13, 2006 11:14 pm

Or uniqueness does it. r4c4 must be 8 otherwise the puzzle would have two solutions with the 2s and 4s in r4c34, r5c34 being able to be swapped around.
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Postby quentin24 » Tue Mar 14, 2006 12:11 am

You could solve it either way with the 2 & 4's being swapped? Seems silly that a puzzle can have two solutions. That's the kind of thing that makes me want to walk away from Sudoku.
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Postby TKiel » Tue Mar 14, 2006 3:34 am

Quentin24,

CathyW basically said if r4c4 wasn't 8, then the puzzle would have two solutions. Because most (good) puzzles do only have one solution, any placement that makes the puzzle have more that a single solution can be excluded as invalid.

Tracy
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Postby QBasicMac » Sun Mar 26, 2006 7:54 pm

TKiel wrote:the puzzle would have two solutions

r4c34 and r5c34 are this:
24 248
24 24

The theory is that r5c4=8 since otherwise we would have
24 24
24 24
Which obviously leads to two solutions.

I say, SO?? Maybe the puzzle is bogus.

Use T*E and eliminate the 8. That leads quickly to

Code: Select all
+-------------+--------------+---------------+
| 7    3   6  | 1    4   9   | 8    5    2   |
| 1    5   9  | 268  68  268 | 7    {3}  {3} |
| 24   24  8  | 7    3   5   | 9    6    1   |
+-------------+--------------+---------------+
| 5    6   24 | 24   9   1   | {2}  7    8   |
| 8    9   24 | 24   7   3   | 5    1    6   |
| 3    1   7  | 5    68  268 | {2}  4    9   |
+-------------+--------------+---------------+
| 9    7   5  | 3    1   {8} | 6    2    4   |
| 246  24  1  | 9    5   46  | 3    8    7   |
| 46   48  3  | 468  2   7   | 1    9    5   |
+-------------+--------------+---------------+

which is bogus due to two 2's in column 7.

Good. Now we have established 8 and know for sure we made no bad assumptions.

The
24 248
24 24
pattern is good to look for because it gives a good T&E path to check.

Mac
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