Elegant way to eliminate values?

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Elegant way to eliminate values?

Postby brutser » Sun Nov 03, 2019 12:42 pm

This puzzle is pretty much solved, I can just test some values and find the other ones (which I already did), but I want to find/know a more elegant way to eliminate or confirm values and to logically find the correct values for the squares left over.
Can anyone help me with finding the right techniques how to do this? Thanks!

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Re: Elegant way to eliminate values?

Postby SpAce » Fri Nov 08, 2019 11:53 am

Hi brutser,

brutser wrote:This puzzle is pretty much solved, I can just test some values and find the other ones (which I already did), but I want to find/know a more elegant way to eliminate or confirm values and to logically find the correct values for the squares left over.
Can anyone help me with finding the right techniques how to do this? Thanks!

There are probably lots of different ways to solve this, but I'm too lazy to manually enter it into a software solver to see them all (it would help if you provided a text-based version of the puzzle that could be pasted).

However, it's immediately obvious that Simple Coloring would work on the 5s. Even that's not necessary as it's easy to see several individual single-digit patterns, such as this:

Skyscraper: (5)r2c4 = r6c4 - r6c8 = (5)r3c8 => -5 r2c9,r3c6

Also some easy-to-spot multi-digit patterns:

XY-Wing: (8=7)r4c1 - (7=5)r4c6 - (5=8)r6c4 => -8 r4c5,r6c1

W-Wing: (7=8)r6c1 - r6c4 = r1c4 - (8=7)r1c5 => -7 r6c5

I'm pretty sure any of those would solve the puzzle, but like I said, I haven't checked. (Added. Actually, I'm only sure of the 5s. On a closer look, it seems that the XY/W-Wing eliminations only solve r46c1 but don't propagate further. That's somewhat surprising this close to the end when pretty much any placement usually solves the whole thing.)
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Re: Elegant way to eliminate values?

Postby brutser » Fri Nov 08, 2019 12:16 pm

I will check on the 5s and what exactly you mean with the coloring. I am new to sudoku, so not really familiar with software solvers, can you recommend any that would be useful to me?
I actually noticed the multi digit patterns that you wrote, but was just unsure what to do with them. As I said, when i just assume one value for a square, most of the puzzle will either give some conflict or will be solved, so that's a brute-force way of doing it.
I just wanted to find a more elegant/logical way.

If you talk about a text-based version, is that the notation they mention here? http://forum.enjoysudoku.com/new-topics-how-to-ask-for-help-t2664.html

Thanks for your help already!
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Re: Elegant way to eliminate values?

Postby SpAce » Fri Nov 08, 2019 12:40 pm

brutser wrote:I will check on the 5s and what exactly you mean with the coloring.

If you look at the candidates of 5, most of them are paired in their houses (rows, columns, boxes) and those pairs are connected with each other too. So, if you can solve any of those pairs (i.e. eliminate one of them which makes the other true), it will propagate and solve them all, and in this case probably the rest of the grid as well.

Simple Coloring is a way to visualize such interconnected clusters of a single digit by using two colors to mark the opposite possibilities. It provides two ways to eliminate something. One, if some candidate sees other candidates with both colors it can be eliminated (because one or the other color must be true). Or two, if you end up with candidates of the same color seeing each other, you know that color must be false (because you can't have two of the same digit in one house) and the other true.

More powerful versions of coloring are very effective at solving even quite difficult puzzles manually. Simple Coloring is the simplest coloring technique, so it's a good way to start practicing the concept.

I am new to sudoku, so not really familiar with software solvers, can you recommend any that would be useful to me?

Hodoku is the best publicly available one that I know. It also has the best overall documentation of the various techniques (some of which I just linked above). You can find the download link there as well. SudokuWiki is a decent but not great web-based solver that can get you started as well. It can only show you the first technique it finds, but Hodoku will tell you everything that is available at a certain puzzle state. It also has great learning and training modes to practice specific techniques.

I actually noticed the multi digit patterns that you wrote, but was just unsure what to do with them. As I said, when i just assume one value for a square, most of the puzzle will either give some conflict or will be solved, so that's a brute-force way of doing it. I just wanted to find a more elegant/logical way.

Yes, T&E (trial and error) eventually works always, but it's not a lot of fun. When you learn to spot patterns and/or to find more generic chains, you can see those same eliminations directly. The end result is the same, but the latter is more elegant and fun, just like you seem to think already. It's usually more efficient too.

If you talk about a text-based version, is that the notation they mention here? http://forum.enjoysudoku.com/new-topics-how-to-ask-for-help-t2664.html

Basically yes. You can see more examples in the Puzzles section. You pretty much need a software solver that can export the pencilmark grid in those formats, as no one would do it manually. Both Hodoku and SudokuWiki can do that for you.

Thanks for your help already!

No problem! Ask away if you need more help with the specifics! We're all happy to help.
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