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Victor · Joined: 29 Sep 2005 Posts: 207 Location: NI

Found this puzzle - M5281753 (118) - hard to solve by 'standard' techniques:

keith · Posted: Fri Mar 28, 2008 2:03 am Post subject:

Victor,

Am I being blamed for this? I do not see a way forward. (But, I have not looked very hard, yet.)

You amaze me at your willingness to attack these. I usually do not try any puzzle higher than 30.

Keith

Marty R. · Posted: Fri Mar 28, 2008 3:53 am Post subject:

ravel · Joined: 21 Apr 2006 Posts: 536

Victor · Joined: 29 Sep 2005 Posts: 207 Location: NI

Keith / Marty. I think I explained before that, having done VHs / Brainbashers SHs / etc. for some time, I wanted to expand my range & try some slightly harder puzzles. IF I'd found a site that produced puzzles that needed a few extra techniques like skyscrapers & ERs I'd have stuck with it: but I haven't found one, and I don't think anyone else has? I totally agree that Menneskes can be too difficult at quite a low quoted difficulty level, but they do have the advantage that I feel able to report an interesting problem because (a) they've been around a long time (c. 3 yrs) and (b) there's no attached forum. If you guys know of a good site I'd love to hear about it: yes, it is a bit tedious wading through a puzzle only to come up against a blank wall.

As regards this puzzle, I love Ravel's expo, but I did see it in a simple sort of way. Frivolous hint for Nataraj. Iron Monkey says 'Consider x = 64K ^ .25' . Drunken Monkey adds 'and add on x^0.' And Hidden Tiger finishes off "And times that by x^.5'

PS I'll post a quite straightforward M with a highish rating (which I know proves nothing useful).

nataraj · Posted: Fri Mar 28, 2008 5:35 pm Post subject:

nataraj · Posted: Fri Mar 28, 2008 7:12 pm Post subject:

Victor · Joined: 29 Sep 2005 Posts: 207 Location: NI

Apologies for silly joke, Nataraj. (My only excuse is that some of us Irish get imbued on St Patrick's day by impishness, which can take some time to dissipate).

Consider these small thought processes.
(a) Looking for M-wings etc., I noticed that the two 68s (marked # in Ravels' diagram) are indeed related - both 6s or both 8s, as explained by Keith once upon a time. Let me call the left-hand one (in box 1) A, the other B. So A = 8 => B=8. But of course you can instantly see that A = 8 => B <> 8 (because now the 8 in box 2 must be in r1). Ergo A = 8 is false. Etc. Now, in a sense that conclusion was reached fairly and squarely, apparently no more T & E than say finding an XY-wing.

(b) However, a moment's thought shows that this is actually just a forcing chain (as I understand the term): either number in A forces a 6 into B. So it's bad after all! (I don't like forcing chains in general, and never search for them.)

(c) So maybe I should set this out more stylishly as some sort of AIC? (No doubt not as nicely as Ravel has done it, but still adequately.) Bur wouldn't that be faintly dishonest? - less honourable even than a forcing chain.

OMG - it's almost philosophical.

nataraj · Posted: Sun Mar 30, 2008 11:50 am Post subject:

No need to apologize, Victor! I liked the joke and it wasn't silly at all.
It is probably no coincidence that Leprechauns live in Ireland and not so much here on the continent. We got other spirits here, some no less mischievous than yours, I guess.

And I am glad, indeed, you did give me that push I needed to post my solution path and the qualms I have with it, too.

I used to resort to forcing a lot before I lerned techniques like x-wing, xy-wing, UR, you name it. Basically, whenever I was stuck, I'd start with a (random) bi-value cell, take one of the two possibilities and see where it leads. If it leads to a contradiction, good. I solved one cell fair and square. But the whole process is deeply unsatisfying.

I am very happy I found sites like this one here on the internet where people introduced me to advanced methods that allow me to solve a whole new range of puzzles without falling back on that search strategy.

That is the beauty with ravel's solution, here. It shows some "inner structure", a relationship between two cells that can be exploited to solve another cell (or at least reduce the number of possibilities for that other cell). This inner structure is not something unique to the puzzle in question but can be generalized. And by this process of generalization becomes a useful tool in the bag for solving other puzzles as well.

I am not sure whether the difference is only psychological or if there is something else: on one hand, we have a solving strategy that looks at results and tries to establish a proof for the result (like this or any xy, xyz, w-wing: two pincers, could remove a candidate, lets see if we can connect the pincers) and another strategy that looks at possible starting points and tries to find possible useful consequences.

As a metaphor, take searching for oil (which I know nothing about!): start at random places, think "this looks like a great spot" and drill. Or: look at geological data, satellite images, seismic record, develop a theory and test it by drilling.

I just feel more comfortable with the latter way.

___

P.S. Some of the DP-based solutions in the "other" category present the same dilemma. No problem with the well established patterns of type 1, type 2, etc. They give you immediate solutions or virtual cells or other eliminations right away. Big problem with the ad-hoc resoning. Why is it better to start with a bifurcation ("either xx=6 or yy=8") resulting from a DP than to start with ANY bi-value cell in the grid ("either xx=6 or xx=8")?