Help with next step

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Help with next step

Postby Serenity's Embrace » Mon Jan 16, 2017 7:06 am

Can't figure out what technique to use next. Where do I go from here?
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Re: Help with next step

Postby JasonLion » Mon Jan 16, 2017 12:51 pm

I see a Hidden Unique Rectangle and a Sashimi Swordfish right off, though neither of them looks like they will get you very far. You will almost certainly need chains to make real progress.


2.658....83...46.5.5.36....59..23168.238.65496.89...7...2.38.56.65......38.6..7..
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Postby Pat » Mon Jan 16, 2017 1:59 pm

Serenity's Embrace, you have somehow excluded 9 at r3c3,
this is wrong and you will be unable to solve the puzzle
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Re: Help with next step

Postby nedBlake » Fri Feb 17, 2017 1:52 am

The puzzle does have a single solution, but it's a tough one to find. I couldn't see anyway to begin to solve it, and so exported it to www.sudokuwiki.org. If you step through the solution at that site, you will see it solved by applying about a dozen strategies. The first step I have drawn out below:
Extreme50 puzzle.png
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Assuming that 4 is the solution at row 7 col 2, a chain of implications shows that it cannot be a solution since it would imply that the 4 in the cell above would also be one. Therefore 4 at (7,2) can be removed:

+4(7,2) -7(7,2) +7(1,2) -7(2,3 & 3,3) +7(4,3) +7(4,3) -4(4,3) +4(6,2)

What makes this chain work is that although there are three 7's in column 3, there is a strong link between two of them and the third one below the two. This is true because when there are n possibles in a unit, and n-1 of them are the same color, then the one with the single color must be the solution.

Most of the other strategies used in this puzzle are digit, or cell, or unit forcing strategies. I am still looking at them.
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Re: Help with next step

Postby pjb » Fri Feb 17, 2017 5:05 am

Agree with Jason. After the sashimi swordfish elimination of 7 from r7c4 and the 1 from r9c5 due to the hidden UR, it only requires simple AICs. (I will list them if you want).
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