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Interior / exterior
Kwon-Tom Obsessive
Puzzles: 826
Best Total: 30m 18s
Posted - 2005.12.25 05:45:01
Hi!  I'm brand new to doing these puzzles on the internet (as can be seen by my incerdibly long amount of time to solve them...).  I've been doing them under the name fences on paper recently; and the greatest tool I've used is the consider the interior and exterior of the loop as seperate areas.  To this effect, I've been using different colours (or patterns) for the intrior and exterior, to form one connected area in the middle.  You can't seem to do it on computer, but it opens up a lot of new patterns.  You should print some out and try it, it means (almost) no guessing - even on really big puzzles.
Kwon-Tom Obsessive
Puzzles: 3004
Best Total: 22m 33s
Posted - 2006.01.05 18:41:58
I printed out today's (Thursday, so hardish) puzzle, and tried using just colours for inside / outside squares, ignoring all the lines / crosses patterns that I know.  I used just a couple of simple rules basically along the lines of: a '0' is adjacent to 4 squares of the same colour, a '1' has 3 squares the same and 1 different, a '2' has 2 squares the same, 2 different, and a '3' has just 1 square the same and 3 different, putting a line between squares if they are of different colours (obviously), and I solved it .... eventually ... !

It's a really interesting different way to look at the puzzles, as the core rules seem simple, though I suspect can be expanded for bigger patterns.  It's the same puzzle with the same clues and solution, but a fundamentally different approach to solving it.  Isn't maths great..?!  (rhetorical) (actually, I'm inclinded to wonder if there is an obvious proof to show that all solvable puzzles by one method are solvable by the other...)

Foilman- would it be possible to setup some sample puzzles where you can click on a square to mark it inside / outside / unknown, with lines appearing automatically between inside and outside squares?  I think it could be an interesting alternative style to play with.  There may even be some way of integrating the line / cross and inside/outside methods into one, eventually. hmmm.

What do you think?
Kwon-Tom Obsessive
Puzzles: 1292
Best Total: 31m 39s
Posted - 2006.01.06 23:15:29
I agree with AmyR, a lot of things become obvious deductions when you combine the line-based logic with interior/exterior 2-colouring.  Another simple observation is that the board cannot contain a 2x2 checkerboard pattern of colours, and that if a "1" has 2 of the same colour adjacent then it inherits that colour.

I think it would be cool if we could click on the interiors of each square to toggle the colour between blank, and say, yellow for inside and green for outside.
Kwon-Tom Obsessive
Puzzles: 826
Best Total: 30m 18s
Posted - 2006.01.07 19:30:24
In my experience, solving using a combination of lines and colours is most efficient...  I agree that adding some colour to the code would be good.  I also agree with Erick's choice of green and yellow... 
Kwon-Tom Admin
Puzzles: 1720
Best Total: 24m 8s
Posted - 2006.01.10 09:34:14
I'll have a look at adding this at some point. Unfortunately it's not as easy as it sounds!
Kwon-Tom Obsessive
Puzzles: 1083
Best Total: 12m 56s
Posted - 2006.01.12 06:35:47
Originally Posted by amyr
In my experience, solving using a combination of lines and colours is most efficient...

Really? I've had a bit of a go at using colours, but haven't been able to find a situation where it showed me anything the lines didn't. I can sort of imagine that sometimes it might let you locally detect potential loops and stray ends rather than having to check the rest of the board, but I'm not sure you'd ever need to do that often enough to make up for the time lost colouring it in - but of course you would be much quicker with the colouring patterns than me. Might you give an example of a situation in which using colours speeds up your solution?

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