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Highlander rule & locked edges
v_e_e_n_c_a
Kwon-Tom Obsessive
Puzzles: 930
Best Total: 38m 37s
Posted - 2008.08.18 13:08:12
Is there anybody who can explain to me the princip of the highlander rule. I have read the hint but I didn't discovered any edges unfortunatlly (i know that there should be only one solution). Please show me the affected edges and explain why they are affected. And the second question is how to use locked and anti-locked edges in solving (i understand the princip of them), but i don't know how i would gather some result (x's or lines).. If i can gather something without guessing.. Thanks very much and exuse my english...
MondSemmel
Kwon-Tom Obsessive
Puzzles: 3888
Best Total: 7m 47s
Posted - 2008.08.18 14:56:22
I'll try to answer your questions, but I'm not sure whether I've understood all of them correctly, so my answers might not be entirely complete.

First of all, the highlander rule:
The highlander rule (the name comes from the quote "There can only be one!") works like this: All puzzles on kwontomloop.com (and most puzzles everywhere, actually) only have one unique solution - there are no alternatives anywhere. Every line can only be on one exact place.
Because of this, the highlander rule states that while solving, if there is ANY situation where more than one possibility exists, all those possibilities are wrong.
[Actually this sentence looks really awkward - English is a foreign language for me, too. Sorry about that.)
Anyway, here's the most basic example of the highlander rule:


Empty squares are empty, ? squares can be anything.
The basic 2 corner pattern results in


There are only two possibilities for the 2:
a)

b)

Suppose a) is correct. In that case, you could always use b) instead. If that were the case, the puzzle would have two solutions - and that's impossible as stated above: All puzzles have one unique solution.
The ONLY unique solution for this case (which is the highlander pattern) is this:


As you can see, the highlander pattern in this case are the two lines at the right top of the 2. If these aren't there, the puzzle has two solutions, which is impossible.

I don't think I'll try to answer the other part, though - I guess my English isn't good enough to explain it as simple as it actually is. If nobody else answers it, I might do that too, though.
v_e_e_n_c_a
Kwon-Tom Obsessive
Puzzles: 930
Best Total: 38m 37s
Posted - 2008.08.18 15:53:26
Thanks MondSemmel for explanation. I want to ensure that I understood it well. So for this highlander pattern:

it should be like this:

is this right?

And can anybody help me with my second question - about locked and unlocked edges? Thanks for help.. I am working on this topic because it is my bachelor's theme..
MondSemmel
Kwon-Tom Obsessive
Puzzles: 3888
Best Total: 7m 47s
Posted - 2008.08.18 16:30:14
Yes, that's right. This is the most basic highlander pattern. It simply works on the presumption that the puzzle has one unique solution (this is something you have to know beforehand, but it's true for every puzzle on this website, as far as I know) - therefore, if there are two equivalent possibilities to solve part of a puzzle, they are both invalid.
In symmetrical puzzles with unique solutions, applying highlander is even easier.


I'll try to give you some stuff to think about for your secon question, but you should probably have somebody else explain them for you:

Consider this for unlocked (? I call them differently, but the principle remains the same) edges:






And this for locked (?) edges:



Also, this:

and this:


Basically, this is the most important principle in Slither Link in my opinion, certainly more important than patterns etc. There should already be some threads in the forum about this topic, though.
Last edited by MondSemmel - 2008.08.18 16:32:05
v_e_e_n_c_a
Kwon-Tom Obsessive
Puzzles: 930
Best Total: 38m 37s
Posted - 2008.08.19 08:07:45
Yes, I think that I understood locked and unlocked edges and by the way I have been using them but I didn't know that this technique is called like this. I thought that I understood highlander as well. But then I was reading one thread there on forum, and I wasn't able to deduce some of them. For example:



and these two (in both cases i should be able to deduce 6 lines and 4 crosses, but i deduced only 4 lines and 4 crosses in both puzzles)





Thanks for help.
Last edited by v_e_e_n_c_a - 2008.08.19 09:20:52
Jankonyex
Kwon-Tom Obsessive
Puzzles: 3723
Best Total: 9m 35s
Posted - 2008.08.19 11:18:52
4 lines, 2 x's:

the middle blank should be larger than or equal to 2.
Last edited by Jankonyex - 2008.08.19 11:32:58
v_e_e_n_c_a
Kwon-Tom Obsessive
Puzzles: 930
Best Total: 38m 37s
Posted - 2008.08.19 14:58:17
And I have a last question - and it is the counting topic. This technique is mentioned here on the forum by Jankonyex. I wanted to learn it but in the section, where he is decribing it, there are no pictures - but only some "ugly characters".. Please, can someone explain me counting technigue??
Last edited by v_e_e_n_c_a - 2008.08.19 14:59:24
Jankonyex
Kwon-Tom Obsessive
Puzzles: 3723
Best Total: 9m 35s
Posted - 2008.08.19 15:05:58
here
Jankonyex
Kwon-Tom Obsessive
Puzzles: 3723
Best Total: 9m 35s
Posted - 2008.08.19 16:03:14
this is recommended,
there're mainly two types of puzzles named [jcsl##] or [jsl##].
[jsl##] was written by me, and nearly all of them are logically solvable. Solutions are given by me. [jcsl##] was written by computer, and also, solutions are given.
My solutions include no highlander technique, but many logical analysis, where some of them have not been discussed yet.

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