eleven wrote:denis_berthier wrote:.There has never been any "tridagon search hype" - because there has never been any tridagon search at all.
What there has been is a search for T&E(3) puzzles
Are you kidding, is there any T&E(3) puzzle without a tridagon ? So how do you think did they search for T&E(3) puzzles ?
Twisted logic!
There's no (known) T&E(3) puzzle without a tridagon, and that's a very interesting
result.
In the same way, there are only 3 known puzzles with BxB ≥7 and without a tridagon, and that's also a very interesting
result for T&E(2).
And the converses of both are false. There are puzzles with a tridagon and with lower classifications.
As mith says, before finding Loki, he searched for high clue and high SER puzzles and that's how he found a few with the pattern. After Marek identified the pattern, mith may have specifically looked for it and found a few more that way; it seems we'll never know for sure how Loki appeared (even mith has been unable to track its origin).
But the fact is, the millions of puzzles with a tridagon have been found by mith after Loki, after I found it was in T&E(3) and after mith started using T&E(3) as his main search criterion. mith has always been clear about this. So clear that he discarded all the T&E(2) or T&E(1) puzzles he must have found by his vicinity search (even those that must have had a tridagon).
[mith also refers to tridagons in old puzzles by dobrichec (SE 11.0) - but these have been in the ph2010 database for 10+ years before being noticed as having a tridagon. The beast was there, but no one knew it. Do you count this as part of a search for tridagons?]
eleven wrote:(many are easy, did not see one, which was not solved manually in a few steps).
As that's obviously false, there's no need for an answer.
Very hard puzzles with a tridagon have been proposed in the Puzzles section. And I have precise stats showing the easy ones are not so frequent.
The tridagon is probably the most beautiful pattern ever found, due to its symmetry and its simplicity. I can compare it only to Subset patterns (invented by nobody knows whom, probably many times independently) and to sk-loops (which are more complex - but have also played some role in the search for hard puzzles, long ago).
What's unique with tridagons is
- they fall out by millions from a type of vicinity search (T&E(3)) that doesn't search for them,
- they are extremely resistant to perturbations (addition/deletion of clues)
- they have opened the whole new world of the T&E(3) and BxB > 6 puzzles, and this world remains open to more explorations than have been done until now (e.g. what I started to do in [HCCS2] and in this thread:
http://forum.enjoysudoku.com/the-layered-structure-of-t-e-depth-d-t45647.html.
