Karyobin wrote:Has the tipping-point moved - absolutely, and it's been fun to watch. Still, for the time being Forcing Chains are about as far down the T & I road as I'd like to go.

Me too I suppose. Supercoloring and Magic are indistinguishable to me.

Karyobin wrote:As the eye of the beholder becomes trained, what was ugly may become beautiful.

Well my eye's going to have to become pretty trained in order for me to appreciate the kind of "Oh well, it's one of two options so off we go..." T & I approach that I envisaged when I wrote that!

However, bearing in mind the invention and undeniable practical use of

Forcing Chains and

Turbot Fish, amongst others, I do wonder whether the problem with genuine T & I lies in the fact that 'normal' people can't hold all the steps in their minds at any single point (possibly because it's impossible to know how many steps will/won't lead to a result). This may lead to a feeling that one has somehow lost touch with the puzzle in a way that does not occur with the other more defined /refined strategies.

Jelly Beans in a Glass Jar -- if there are 5, you can count them, if there are 1000 you must estimate them. I maintain that it is impossible to draw a line that separates the two situations. Maybe I can count to 20, you can count to 25.

Also, not much has been posted on tactics of *finding* forcing chains. Though you *could* just search blindly, there are various ways of narrowing the possibilies so that you won't feel like it could be any number of steps. I’m trying to put together a post that describes how I look for chains in *some* limited situations -- not neccessarily to supply a tool for doing so, but to show that there is logic behind the proof.

My favorite Sudoku end up with a large number of 2-candidate cells from which I’m able to produce a forcing chain while completely ignoring the cells with more than 2 candidates. It may very well be possible to intentionally create puzzles of this type that require longer and longer chains that are nevertheless, easy to find once you know how to look.

When I first heard of Swordfish, I tried to solve several problems using the tactic -- it doesn't work unless there is a Swordfish to be found! I did a lot of searching for nothing. T&E? I dunno. I had to learn when and how to look for them. How I do it is probably NOT how you do it.

It's all a matter of degree, a sliding scale. That's my point. Any line drawn will be arbitrary and personal -- and will change over time.

-- 1 inch sided square

-- whole number sided square

-- square

-- rectangle

-- parallelogram

-- convex quadrilateral

-- convex polygon

-- polygon

Shapes as metaphorical Sudoku patterns -- proofs being closed lines.

Towards the top of the list, the patterns are very specific. But the number of separate descriptions required to cover everything we see is very high. They are very useful if we find them, very easy to create a (computer or human) search that will identify them -- but we cannot find them if they aren’t there, and any one specific shape will probably NOT be there. (We can also easily create a search that tells us that as well.)

Towards the bottom, the patterns become more and more general, requiring fewer and fewer rules to encompass the all we see. They are much more likely to be found, though they may become more difficult to identify. Searches of any kind are more difficult to construct, either to find or exclude the existence of the patterns. Imagine 100 sided non-convex polygon drawn on a large piece of paper with many other open ended segmented lines -- hard to see, but undeniable once found.

As a human solver, I want to work as far down the list as is comfortable AND appropriate.

Switching metaphors, it seems that my argument that elephant guns are fair is often met with the reply that it makes hunting ducks too easy and no fun. But I’m clearly not suggesting that you use an elephant gun for ducks! Only that birdshot will not bring down and elephant, sometimes there *are* elephants, elephant hunting is a qualitatively different experience from duck hunting, I like elephant meat -- and hope we don't run out of elephants!

(No animals were harmed in this post, though by dogs need to be taken for a walk badly.)