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unique solutions
Brian
Kwon-Tom Obsessive
Puzzles: 3179
Best Total: 9m 6s
Posted - 2006.12.03 08:57:32
I was curious about this.

When I do other logic puzzles, I usually try to prove that my solution is unique. That is, if I take a fork somewhere along the way, and I find a solution on one path, then I'll go back and check that there's no solution on the other path. It gives me some sort of satisfaction, of doing things "properly".

When I first started doing slither links (kwon-tom loops or what-have-you), I did the same thing. But after a while, I realized that by assuming a unique solution, I could quickly classify some of those paths as dead-ends because on some section of the puzzle there'd be more than one solution.

Here's a simple illustration/exercise: [6 segments, assuming a unique solution]



Do most people use this reasoning? I assume so, but I'm not sure. Also, for those that do, do you feel a little dirty when you do it?
PuzzleLover
Kwon-Tom Obsessive
Puzzles: 1033
Best Total: 38m 17s
Posted - 2006.12.03 10:23:37
Yes, this forum has discussed the topic a bit, and even coined the apropos term "Highlander argument" for such considerations.  I don't have the thread pointers for the discussions, but someone can probably provide them.

People vary on how kosher they consider using Highlander arguments.  It feels like cheating to me, but with the difficulty levels of puzzles here I'll use any handle I can

Actually, foilman guarantees his puzzles have a unique solution without using Highlander arguments.  Your example doesn't fit this model because it has 3 solutions.  But I have on occasion used the idea your example represents to fill in which 2 edges diagonally connect a 2 in some of foilman's puzzles.

Quote:
Originally Posted by brian
I was curious about this.

When I do other logic puzzles, I usually try to prove that my solution is unique. That is, if I take a fork somewhere along the way, and I find a solution on one path, then I'll go back and check that there's no solution on the other path. It gives me some sort of satisfaction, of doing things "properly".

When I first started doing slither links (kwon-tom loops or what-have-you), I did the same thing. But after a while, I realized that by assuming a unique solution, I could quickly classify some of those paths as dead-ends because on some section of the puzzle there'd be more than one solution.

Here's a simple illustration/exercise: [6 segments, assuming a unique solution]



Do most people use this reasoning? I assume so, but I'm not sure. Also, for those that do, do you feel a little dirty when you do it?
Brian
Kwon-Tom Obsessive
Puzzles: 3179
Best Total: 9m 6s
Posted - 2006.12.03 16:57:55
Quote:
Originally Posted by puzzlelover
Yes, this forum has discussed the topic a bit, and even coined the apropos term "Highlander argument" for such considerations.  I don't have the thread pointers for the discussions, but someone can probably provide them.

Thanks. Now a google search gives a lot of threads. I even found a couple patterns that I hadn't exploited before!

Quote:
People vary on how kosher they consider using Highlander arguments.  It feels like cheating to me, but with the difficulty levels of puzzles here I'll use any handle I can

For me, it's also about the competition. Just add a timer and out go the morals.
Brian
Kwon-Tom Obsessive
Puzzles: 3179
Best Total: 9m 6s
Posted - 2006.12.03 17:58:36
Also, for those playing at home, my puzzle is flawed. I meant that the 2 was in a corner, but I never said so.

PuzzleLover
Kwon-Tom Obsessive
Puzzles: 1033
Best Total: 38m 17s
Posted - 2006.12.06 06:49:39
Here's a nice Highlander example from the interior left of the 11 Dec 2005 puzzle.  A Highlander deduction can fill in the ?s.

Helge
Kwon-Tom Obsessive
Puzzles: 3017
Best Total: 11m 26s
Posted - 2006.12.07 08:37:21
Great example. I love the Highlander!
Brian
Kwon-Tom Obsessive
Puzzles: 3179
Best Total: 9m 6s
Posted - 2006.12.07 17:46:37
A couple from July 2, 2005, for your enjoyment.

 
Nis
Kwon-Tom Obsessive
Puzzles: 1989
Best Total: 22m 1s
Posted - 2007.01.03 00:26:16
Quote:
Originally Posted by puzzlelover
Actually, foilman guarantees his puzzles have a unique solution without using Highlander arguments.

The above is obviously true for any puzzle of this kind - the uniqueness of the solution does not depend on which methods are used to find the solution.

Indeed, all puzzles are solvable without any arguments at all. Just try all the possible configurations one by one, testing whether they satisfy the conditions of the puzzle.
procrastinator
Kwon-Tom Obsessive
Puzzles: 1083
Best Total: 12m 56s
Posted - 2007.01.03 03:33:19
Quote:
Originally Posted by nis
Quote:
Originally Posted by puzzlelover
Actually, foilman guarantees his puzzles have a unique solution without using Highlander arguments.

The above is obviously true for any puzzle of this kind

And in fact you can't use Highlander arguments to prove a solution is unique - you'd only be showing that it's unique if it's unique.

Solving fast is fun, so I get a big kick out of finding new Highlander patterns, but I actually prefer going back through the archives and solving hard puzzles without the use of unnecessary aids (crutches ) such as Highlander, Fix Position and Xes.
Last edited by procrastinator - 2007.01.03 03:34:48
m2e
Kwon-Tom Obsessive
Puzzles: 607
Best Total: 16m 43s
Posted - 2007.01.03 04:54:09
No X's!? Sure i can do that on Mondays if i needed to, but not fridays...or the beast
m2e
Kwon-Tom Obsessive
Puzzles: 607
Best Total: 16m 43s
Posted - 2007.01.03 05:00:28
Ok i just did last friday's without X's. Quite entertaining
Para
Kwon-Tom Obsessive
Puzzles: 1911
Best Total: 19m 28s
Posted - 2007.01.03 09:46:10
What do you mean by X's and fix position?
procrastinator
Kwon-Tom Obsessive
Puzzles: 1083
Best Total: 12m 56s
Posted - 2007.01.03 09:50:52
Quote:
Originally Posted by para
What do you mean by X's and fix position?

Xes appear when you right-click or double-click on the puzzle, the Fix Current Position button is one of the yellow ones to the right of the puzzle. But you don't really need these things.
astrokath
Kwon-Tom Obsessive
Puzzles: 3093
Best Total: 13m 42s
Posted - 2007.01.03 10:20:55
Quote:
Originally Posted by m2e
No X's!? Sure i can do that on Mondays if i needed to, but not fridays...or the beast

Try it with January's beast - it's pretty straightforward this month.
Para
Kwon-Tom Obsessive
Puzzles: 1911
Best Total: 19m 28s
Posted - 2007.01.03 16:39:26
Quote:
Originally Posted by procrastinator
Quote:
Originally Posted by para
What do you mean by X's and fix position?

Xes appear when you right-click or double-click on the puzzle, the Fix Current Position button is one of the yellow ones to the right of the puzzle. But you don't really need these things.

oh lol, thought you were talking about some solving technique similar to the highlander arguement.

feeling dumb now
m2e
Kwon-Tom Obsessive
Puzzles: 607
Best Total: 16m 43s
Posted - 2007.01.04 02:05:39
Quote:
Originally Posted by astrokath
Quote:
Originally Posted by m2e
No X's!? Sure i can do that on Mondays if i needed to, but not fridays...or the beast

Try it with January's beast - it's pretty straightforward this month.
Hmm yeah so it wasn't just me thinking this month;s was unusually easy
he_he
Kwon-Tom Obsessive
Puzzles: 2001
Best Total: 14m 41s
Posted - 2007.01.04 13:34:06
Quote:
Originally Posted by m2e
Quote:
Originally Posted by astrokath
Quote:
Originally Posted by m2e
No X's!? Sure i can do that on Mondays if i needed to, but not fridays...or the beast

Try it with January's beast - it's pretty straightforward this month.
Hmm yeah so it wasn't just me thinking this month;s was unusually easy


Bugger!!!  Here's me thinking I've improved my skills and it's just because it's an easy on.  Hmph.
djpohly
Kwon-Tom Addict
Puzzles: 387
Best Total: 25m 1s
Posted - 2007.01.08 05:17:40
Quote:
Originally Posted by astrokath

Try it with January's beast - it's pretty straightforward this month.

What a self-esteem boost to have finished that X-less... thanks for the suggestion, astrokath!
astrokath
Kwon-Tom Obsessive
Puzzles: 3093
Best Total: 13m 42s
Posted - 2007.01.08 10:21:10
Glad people are stretching themselves with the beasts.


[Although I'll freely admit that I'm quite happy to keep on using my crut^H^H... x's]
Brian
Kwon-Tom Obsessive
Puzzles: 3179
Best Total: 9m 6s
Posted - 2007.02.20 03:24:05
A cool(?) highlander from Saturday, August 6th, 2005.


I think 21 lines.
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