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anything else that can be done here without trial & error?
xjames
Kwon-Tom Obsessive
Puzzles: 1905
Best Total: 31m 41s
Posted - 2008.03.19 03:39:11
Hi... I almost finished this puzzle without any guessing or trial and error, but hit a snag here. I already finished after trial and error, but I was wondering if there was anything else to be done here that I missed.

Thanks for any thoughts.

Oh, I saw another non-trial and error thing that I added after I captured the screen.
prj
Kwon-Tom Obsessive
Puzzles: 2356
Best Total: 18m 20s
Posted - 2008.03.19 04:05:45
The 1 at r6c16 must have a line coming in from the top left.  Since there's a 2 there, it must also have a line coming in from its top left.  You can get 4 lines from that, and a couple more to prevent the loop from closing.
Last edited by prj - 2008.03.19 04:06:02
Naivoj
Kwon-Tom Addict
Puzzles: 314
Best Total: 33m 50s
Posted - 2008.03.19 07:34:59
Everything is forced using color and path deductions, although my last path deduction is not that easy:
   20060520SatNaivojColorTips
Last edited by Naivoj - 2008.03.19 07:53:58
xjames
Kwon-Tom Obsessive
Puzzles: 1905
Best Total: 31m 41s
Posted - 2008.03.19 11:07:54
hey guys, thanks for the thoughtful replies. I do get Prj's lines, although it took me a bit of looking to figure it out.

Naivoj, I got most of your recommendations, but I got lost with the whole colors thing. And I really appreciate the time you took to make that word doc. I studied it with care, but the whole colors bit was lost on me.

I'll look at it again tomorrow, see if a fresh mind helps... the whole thing's starting to look fuzzy to me at this late hour... lol

thanks again!
PuzzleScot
Kwon-Tom Obsessive
Puzzles: 1742
Best Total: 25m 45s
Posted - 2008.03.19 13:00:05
I'll have a go at explaining 'the colours thing' - I use colours all the time (How do I add in my message grid below?). Red for 'inside' the loop, and yellow for outside. [At the edge of the grid, there is effectively a ring of yellow grid squares, for the sake of the cases below.]

Consider the colouring of the 4 squares horizontally and vertically adjacent to our square:
Around a '3', There is 1 square matching, and 3 opposite
around a '2', 2 matching and 2 opposite
around a '1', 3 matching and 1 opposite
around a '0', 4 matching, as we all know...
(Stating the bleedin' obvious, I know, but it helps in the next bit..)eg,

If the 2 '?' squares at r3c1 and r4c2 are say both RED, then we know r2c2 and r3c3 are both YELLOW. Also, r1c3 and r2c4 are both RED.

Also, if we have r3c1/r4c2 opposite colours to each other, then we also know that r2c2/r3c3 are opposite colours, as are r1c3/r2c4

A typical example is a start grid with a 2 in the corner. It already has 2 yellow neighbours, so the remaining 2 neighbours must be red.

Similar idea with '1's - once 2 of its neighbours are of the same colour, the '1' must be that colour too. If we colour 2 neighbours opposite colours, the remaining 2 borders must be 'x'...

Hope that helps...
Alan
xjames
Kwon-Tom Obsessive
Puzzles: 1905
Best Total: 31m 41s
Posted - 2008.03.19 22:38:41
actually it does help..

I'll try doing some archives with colors to try and get the hang of it.

Thanks
Naivoj
Kwon-Tom Addict
Puzzles: 314
Best Total: 33m 50s
Posted - 2008.03.20 01:14:08
The most basic color rules are:
  - 2 adjacent squares separated by a Cross must be of the same color
  - 2 adjacent squares separated by a Line must be of opposite colors

There is a harder color pattern, I did not explained separately as a pattern in the word document, regarding the line deduction to the right of the clue 3 by the corner:

Clue 1 and 3 Same Color Pattern
  - Requirement: the two ? squares are of the same color.
  - Results= 1 Line, 2 Crosses and 1 Color

The main result is the 1 Line. Once you get that Line the other results can be deduced from simpler rule/pattern, like the "Clue 1 Opposite and Non Adjacent Color Pattern" I explained in the word document.

If the two ? squares are of opposite colors it becomes the Clue 1 and 3 Opposite Colors Pattern which gives 2 Lines, 1 Cross and 1 Color

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