dailysudoku.com

[keith]

This one was published some time ago on another site. I still don't think I have figured it all out.

[Marty R.]

[ravel]

Hi Keith,

with 2 strong links (turbot fish) and xy-wing i came here.
I eliminated the 5 in r3c8 because of the strong link for 4 (c7) in the UR 45 in r34c78.
Then 14 from r3c1, because of the AUR 57 in r12c14 (r3c1=1 => r3c3=6 => r3c2=4 and r3c1=4 => r3c2=6 => r3c3=1), but it did not help.

[David Bryant]

The first time through this puzzle I used several double-implication chains to complete it. The second time through I found a relatively simple way to employ the "UR"s on {5, 7} to make a deduction that solved the puzzle immediately.

[Myth Jellies]

[ravel]

What i find quite interesting is that David had
r2c8 = 9 ==> r6c8 = 8 ==> {2, 5} pair in r9c28 ==> r9c9 = 9
while i read from MJ's AIC
r2c8 = 9 ==> r2c7 <> 9 ==> r9c7 = 9

So r2c7=9,which solves the puzzle :)

[Edit:] Can be done even shorter:
r9c7=9 => r2c7<>9 => r2c8=9
r9c7=9 => r9c8=8 => r6c8=9
As forcing chain:
r6c8=9 => r2c8<>9 => r2c7=9
r6c8=8 => r9c7<>8 => r9c6=8 => r2c7=9

[Chuck B]

This was interesting!! I'm a little quirky, I guess, but I generally prefer not to assume a priori that a puzzle has a unique solution. If it does, that'll come out in the wash. Consequently, I don't use UR's, but tend to use implication chains more, instead.

So, here was my approach:

Basic stuff yields:

[ravel]

[Chuck B]

Many thanks, ravel!

The ALS reference was an interesting read, too.

Cheers!
Chuck

[David Bryant]

[ravel]

[Chuck B]

Thanks for the additional info, David, and especially for that rabbit hole on "uniquity". 'Iniquity' came to my mind, too. Scary!

I''m also beginning to recognize you 'old hands' and deep thinkers here, and I certainly don't expect to contribute anything groundbreaking; at best, I'm just trying to adapt your insights into my own (fossilized?) way of thinking.

And it''s fun to reinvent a wheel or two on your own. 8)

Good stuff!

Cheers!
Chuck

[Marty R.]

What's up with this business of not assuming uniqueness? You already know the puzzle has a unique solution, so why assume otherwise? Is this just another way of saying that you prefer to solve puzzles without using URs, or is there something that I'm missing?

[Chuck B]

[keith]

I only came into becoming an "expert" at UR methods, because it turned out there were still solution methods to be discovered.

(And, I can only say, discovered among the people I know. This may be old hat to the Japanese. I work for General Motors. Never underestimate the Japanese.)

Anyway, I cannot understand the issue of not wanting to assume uniqueness, among people who do not want to solve non-unique puzzles. Chuck, et al: Try the following thread: http://www.sudoku.com/forums/viewtopic.php?t=3071

Trust me, no one is interested in these puzzles. I have tried to start threads which analyze puzzles with multiple solutions a few times. No one cares.

And, my Mother-In-Law? She never goes anywhere that involves a left hand turn. She can go most places, it is sometimes just much harder to get there.

Keith

[keith]

[Chuck B]

[Chuck B]

[ravel]

Just to throw in my two cents worth:

The main reason i use uniqueness is, that it makes solving more interesting to have also this method at hand, because many elegant solutions can be found with it, where otherwise only a couple of more or less disgusting chains help.

My argument for using them is, that it is common sense that a puzzle has to be unique.

But i also can construct this argument for not using them:
What is an accepted solution for a sudoku ? I can define it as a logical way, where every step - inserting a number - is proved. Otherwise the step would be guessed and no one likes that. Now if i make a guess and it solves the puzzle, the step is logically proved, since it must be true (and all other numbers false), because there is no other solution.

[Chuck B]

Well, I was gonna button my lip but I found another $.02 in my pocket...

Some people find snails disgusting; others consider them a delicacy. "De gustibus...", as I noted earlier. Why begrudge someone his or her poison of choice? (Not to toss in a red herring here, but I've been surprised that no one has taken issue with the non-symmetry of the puzzle in the original post. )

The arguments I've seen so far seem to belie a preference for visually cued patterns. There are, however, other patterns and structures that you can play "Where's Waldo?" with. MJ's molecular method, and Bob Hanson's "Medusa graphics" in the ALS discussion open an interesting perspective. They hint at abstract geometries, if you will, in which structure lies in the logical rather than physical relationships among cells. (math side note: The analogy here is of dual spaces in functional analysis.) Whether you find that hideous or delightful depends on the vision you choose to employ. Beauty is in the (virtual) eye of the beholder, indeed.

Anyway, for some of us, Sudoku is an interesting diversion that represents a recreational instance of more generalized analysis. One of the (admittedly anal, but sometimes necessary) customs in that larger world is to make no unnecessary assumptions. It's a principle that probably seems pointless, if not downright silly, to someone unused to formal analysis. There are more things in this world, Horatio...

And, in contrast with Keith's mother-in-law, I prefer to make only left-hand turns. It gives me a better view of the scenery along the way. It is, after all, about the journey, no? Othewise, why not just hit the "solve" button? You take the high road, and I'll take the low road... If you get there first, good on ya! As for me, I need the exercise.