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25 March 2011 @ 12:37 am
Friday Puzzle #94 - Borderlines  
Last week I explored a simple loop variation that was (as I expected) received as a bit "easy". One commenter noticed that the rules, which gave a strict count on unused loop segments, made the type essentially a slitherlink variant with fixed but unprinted numbers and I totally agree. I could not use the experimental Nikoli formula to make interesting puzzles because it is simply a bit too limiting. But the concept was inspiring which is why I played with its construction for awhile.

Having shown you the "simple" form, I now want to introduce my own variation called "Borderlines". This is still a puzzle about irregular regions and loop constraints regarding the borders. However, the rules now requires you to either use a total length N, or to not use a total length N, around each region of size N and this increased flexibility leads to a whole new set of properties. There are a few logical "rules" to discover in the puzzles below, and they should certainly be harder than last week's.

Rules: Draw a single closed loop that does not intersect itself using just the dotted lines of the grid. Each colored tile of area N must have either a total length of used dotted segments of exactly N or a total length of unused dotted segments of exactly N along its border.


Puzzle 1:

Puzzle 2:
MellowMelonMellowMelon [wordpress.com] on March 25th, 2011 05:33 am (UTC)
I remember seeing your comment last week suggesting this change, but I'm amazed at how well it actually worked. Certainly a tougher challenge than what was had last week, but it still feels like there's a relatively low ceiling for how hard this could get.

It also seems like there's a ton of ways you could put a spin on this type. Without thinking too hard, one could try to drop the region sizes and instead make the only constraint that no two adjacent regions can have the same number of touching segments, or if that's not strong enough require them to differ by at least two.
(Anonymous) on March 25th, 2011 12:43 pm (UTC)
I keep getting a contradiction fairly early on in the second puzzle. Is there a mistake, or do I keep missing something?
(Anonymous) on March 25th, 2011 12:50 pm (UTC)
Wait, nevermind, I was overapplying a rule I had figured out. I see what has to happen.
(Anonymous) on March 26th, 2011 04:40 pm (UTC)
I had some trouble to break in the puzzles, but once done they became moderately difficult. Still, this rule clearly improves the original idea - which was predictible, but you confirm it nicely.

Palmer's suggestions are also interesting. I would surely like to see what one you two (or both...) could do with them.

spheniscine on April 28th, 2011 03:02 pm (UTC)
Ssssssss... boom!

Can't believe no one has made that reference yet...