Philosophy of Nice Loops, or When Is It Guessing?

Advanced methods and approaches for solving Sudoku puzzles

Philosophy of Nice Loops, or When Is It Guessing?

Postby ramdeuja » Sat Apr 15, 2006 5:50 pm


this is not so much about a technique as about the philosophy of what makes sudoku fun and what is "pure" solving.

i'm new to all this forum stuff and the lingo, but recently I've been trying to learn the advance techniques to tackle Vidar's Monster #4 (which someone in this forum deviously supplied).

What I know, I've gotten from the definitions on (no offense to everyone here, but the graphic illustrations are much clearer than notation).

When I got to nice loops and tried looking for one, it felt to me like it was basically guessing. If the puzzle had a nice clear rectangular loop that led fairly directly to a contradiction-- something one could learn to see without drawing lines first-- it would feel like a valid technique. But when you go far down a chain of "it this is that, then this is that, so this must be that..." until you get a contradiction, couldn't that be called guessing?

My whole enjoyment of sudokus is that it can be done without guessing, otherwise it's just rote busywork.

Now the philosophical part.... "Guessing" itself is a form of logical conclusion: you pick on candidate value, then follow the logic until you either come to a contradiction, a deadend, or a complete solution. Other techniques are the same, they just form a more recognizable pattern than the convoluted chain of implications you get from guessing.

To me, it comes down to the "recognizable pattern." If you can learn to see a pattern in the grid, without really digging for it, if it jumps out at you, that's satisfying and valid. If elaborate patterns involving a dozen cells with multiple candidate values jump out at you, congratulations, you're a genius. But if it takes a loop that's long and has no recognizable pattern, it just doesn't feel right an it's not satisfying.

just a thouht

So I guess I'm just curious for people to weigh in on what constitutes "pure solving" to them.

(this is what happens when you do puzzles too late and your brain starts wandering....."
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Postby TKiel » Sun Apr 16, 2006 1:37 am


Deciding whether something is logical or illogical on the basis of it fitting a recognizable pattern doesn't seem to hold much water. If you accept the logic behind an xy-wing (a four cell forcing chain) then why would the logic be any less applicable for a forty-four cell forcing chain?

To choose not to use the technique is a different matter entirely. I don't generally use forcing chains that don't fit a recognizable pattern because I'm not good at spotting where to start a chain and not good at realizing when I've circled back to my starting cell to make a possible exclusion. To me they also feel like guessing, but I don't doubt the logic behind them one bit.

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Postby ramdeuja » Mon Apr 17, 2006 2:56 am

i agree. i wasn't saying that it's not logical, only that it feels like guessing, so i'll get no satisfaction out of finishing a puzzle that requires it.

(and i suppose the unspoken hope is that someone will tell me Vidar's Monster No. 4 is such a puzzle, thereby relieving me of my struggle to solve it....)
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Postby Myth Jellies » Mon Apr 17, 2006 4:30 am

Just curious...

If it is okay to look at a naked pair one way and expand it from ab-ab to abc-abc-abc and beyond and get all your naked sets as big as you want them.

It should also be okay to look at a naked pair as a bi-value chain, ab-ba, and then expand it to ab-bc-ca (xy-wing), and beyond (ab-bc-...-xy-ya) as big as you want it. Is it just the potential unlimited size of the chain pattern that freaks people out, or are they not really looking for the "pattern" and are mixing up valid chains with a brute force method instead?

A similar comparison can be made for hidden pairs and hidden sets versus bi-location chains.

To solve the toughest puzzles, like Vidar #4, you probably are going to have to open yourself up to learning and using some of the more advanced methods such as chains, multi-digit coloring, almost locked sets, subset counting and others. There are lots of methods out there. If you really learn one and find it doesn't satisfy your personal ethics, then there are several more basically equivalent choices that might be more acceptable.
Myth Jellies
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