## What's my next move ? ? ?

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### What's my next move ? ? ?

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 `
quentin24

Posts: 2
Joined: 13 March 2006

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

tarek

Posts: 2760
Joined: 05 January 2006

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.
CathyW

Posts: 316
Joined: 20 June 2005

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.
quentin24

Posts: 2
Joined: 13 March 2006

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
TKiel

Posts: 209
Joined: 05 January 2006

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
QBasicMac

Posts: 441
Joined: 13 July 2005