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up to now, this is the most beautiful puzzle I've created.
Jankonyex
Kwon-Tom Obsessive
Puzzles: 3815
Best Total: 9m 35s
Posted - 2006.06.18 16:23:42
I write it before a half an hour and I don't want to delete any numbers because it's already great.

6x6:a1b2a2a22a1a2112b2112a1a22a2a2b1a

here's my solution
Last edited by Jankonyex - 2006.06.24 12:08:41
mathmaniac
Kwon-Tom Obsessive
Puzzles: 1198
Best Total: 20m 57s
Posted - 2006.06.18 18:19:07
can you make that a real puzzle so that we can see it? Or maybe foilman can put it online.
procrastinator
Kwon-Tom Obsessive
Puzzles: 1083
Best Total: 12m 56s
Posted - 2006.06.18 18:42:22
It _was_ pretty while it lasted, wasn't it? But yer still a Nazi.
Last edited by procrastinator - 2006.06.18 18:42:34
procrastinator
Kwon-Tom Obsessive
Puzzles: 1083
Best Total: 12m 56s
Posted - 2006.06.18 18:44:12
Yes, I spent all my money on beer tonight instead of buying off refs. We've much to learn from the Brazilians. FWIW, Jankonyex's Jago was far more Bonita.
Jankonyex
Kwon-Tom Obsessive
Puzzles: 3815
Best Total: 9m 35s
Posted - 2006.06.19 09:57:46
I think that should be the last puzzle which is completely written by me,
because I've found a more better way to create a puzzle - computer.

Here's few puzzles imagine by me and simplified by computer:


solution


solution


solution


solution

Also:
6x6:b222a22222b2222a2b22a2a222b2a22a
7x7:a22222a2a22222a22222a22222a2222a22d2222d2b
9x9:i222c222222c222b1c1b222c222a1b0b1aa222a222aa222a222ac222c worse solution
Last edited by Jankonyex - 2006.06.24 12:09:28
procrastinator
Kwon-Tom Obsessive
Puzzles: 1083
Best Total: 12m 56s
Posted - 2006.06.19 13:34:02
The symmetry makes these puzzles very easy, I'm afraid: When you place (or assume) a line, you can immediately place (or assume) all other symmetric lines.
Jankonyex
Kwon-Tom Obsessive
Puzzles: 3815
Best Total: 9m 35s
Posted - 2006.06.19 15:33:03
Quote:
Originally Posted by procrastinator
The symmetry makes these puzzles very easy, I'm afraid: When you place (or assume) a line, you can immediately place (or assume) all other symmetric lines.
When solving a puzzle, its uniqueness can never been deduced until you've finished the analysises, non-reasonablely conluding uniqueness is already a wrong thought, therefore we cannot simultaneously assuming factors symmetrically by just looking at its symmetric pattern, we can only skip the known and possible disproofs and make inferences symmetrically in a symmetric pattern. The statement: "symmetric solution must have symmetric pattern" is not reversible.
tilps
Kwon-Tom Obsessive
Puzzles: 4320
Best Total: 20m 22s
Posted - 2006.06.20 00:10:30
Quote:
Originally Posted by jankonyex
The statement: "symmetric solution must have symmetric pattern" is not reversible.
The statement isn't true, to start with.

However the reverse isn't required to be true, given a large enough lack of clues.  There is however a requirement that for every non-symmetrical solution, there exists a symmetrical solution where the only parts which  change are non-constrained. (At least, I'm pretty sure there is... Edit: - teach me to be pretty sure about anything see below)
Therefore, if there are multiple asymetric solutions, there are also multiple symmetric solutions, by holding different sections of the asymetric constant.  Therefore, you can prove uniqueness of the puzzle, by only investigating symmetric solutions.
Last edited by Tilps - 2006.06.20 03:53:59
PuzzleLover
Kwon-Tom Obsessive
Puzzles: 1033
Best Total: 38m 17s
Posted - 2006.06.20 03:29:27
Quote:
Originally Posted by tilps
Therefore, if there are multiple asymetric solutions, there are also multiple symmetric solutions, by holding different sections of the asymetric constant.
Umm, not true.  Diagonally symmetric clues with a 3 or 1 on the diagonal can't have any diagonally symmetric solutions.
Tilps
Kwon-Tom Obsessive
Puzzles: 4320
Best Total: 20m 22s
Posted - 2006.06.20 03:51:42
Quote:
Originally Posted by puzzlelover
Quote:
Originally Posted by tilps
Therefore, if there are multiple asymetric solutions, there are also multiple symmetric solutions, by holding different sections of the asymetric constant.
Umm, not true.  Diagonally symmetric clues with a 3 or 1 on the diagonal can't have any diagonally symmetric solutions.

Hrmm, I was about to say this is a good point, and it is - but in that situation, you are gauranteed no symmetrical solutions, and multiple asymetrical solutions - meaning that solvability of symmetric does correspond to solvability for all cases. (but not multiple solutions corresponding to multiple solutions as I originally conjectured)

However,

has only one symmetric solution, and multiple asymmetric solutions.
Which does render my point completely invalid.  At least for mirror symmetry.

Edit: and there goes rotational symmetry ... I think...

Last edited by Tilps - 2006.06.20 06:12:26
Jankonyex
Kwon-Tom Obsessive
Puzzles: 3815
Best Total: 9m 35s
Posted - 2006.06.20 05:42:31
symmetric solution must "have" symmetric pattern.
I'm sorry for my poor English...
I meant "symmetric pattern can be formed if the solution is symmetric"
procrastinator
Kwon-Tom Obsessive
Puzzles: 1083
Best Total: 12m 56s
Posted - 2006.06.20 07:57:04
Quote:
Originally Posted by jankonyex

When solving a puzzle, its uniqueness can never been deduced until you've finished the analysises

Sure it can - that's the rules. Your first puzzle was the first non-unique one I've seen, and for good reason:

You can't solve a non-unique puzzle logically if the two solutions are different enough to prevent you reading one possibility all the way to the end. The rest of your puzzle wasn't ruined because it was so small and the deductions so localised, but for non-trivial puzzles uniqueness is a must. This makes the rule necessary.

If the puzzle is small and localised enough that you can follow a path to the end, then it will be easy to put in some information to force uniqueness (perhaps at the cost of symmetry, but hey - noone said composing these was easy). This makes the rule viable.

Since the rule is necessary for serious puzzles and viable for trivial ones, it's been universally accepted by composers. So it's definitely reasonable to assume uniqueness for a given puzzle unless the poser specifically states otherwise.
Jankonyex
Kwon-Tom Obsessive
Puzzles: 3815
Best Total: 9m 35s
Posted - 2006.06.20 15:00:47
Quote:
Originally Posted by procrastinator

You can't solve a non-unique puzzle logically if the two solutions are different enough to prevent you reading one possibility all the way to the end.
Why can't I solve a non-unique puzzle logically?
How can a puzzle prevent people to read through all possibilities?
Or am I misunderstanding your meaning?
Last edited by Jankonyex - 2006.06.20 18:11:23

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