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I came across this door on the west coast, and I thought I already understood all these puzzle elements, but I don't see any way it can be solved.

enter image description here

My understanding of the rules involved here are:

1. I must make the shapes for the yellow blocks. The one on the far right is rotatable, but the other is not.
2. The blue blocks subtract from the yellow blocks.
3. My path must go through every single black dot (so, in this case, every single intersection on the board).

I'm interested in the solution, obviously, but more so I'm interested in if I'm missing or misunderstanding some of the rules here.

  • 1
    Your understanding of the rules is correct. – Wok Feb 1 '16 at 16:54
  • I was stuck on this one for a long time. I finally drew it on paper and worked it backwards and got the solution very easily that way. – Kip Mar 29 '17 at 1:05
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There's a possible interaction between your numbers 1 and 2 that you're missing. The blue blocks only subtract from yellow blocks that are in the same space. Let's work with an example 2 box puzzle. If there's one blue block in one box, and a yellow block in the other, the solution is to go around the edge of the puzzle, not to go through the middle, splitting them up. If you cordon off the blue block from the yellow block, then the blue block doesn't do its thing, so it's not a valid puzzle solution.

So, be sure that you design a solution that has all the blue blocks in the same space as yellow blocks.

And yes, this is a super tough puzzle, it took me quite a bit of fiddling to get everything in place.

As you requested in the comments, here's a quick solution. Took me less time this time around, since I vaguely recalled some of the tricks I used in the solution.

Puzzle solution

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5

Interaction between the rules

The obvious interaction between the rules you mention is that

you must draw a shape where you subtract the blue dots from the yellow ones.

However, in the (uncommon) case where

all the yellow dots within some borders get 'eliminated' by blue ones, the shape can be totally arbitrary, as there are "no more" shapes constraining it.

This means that for this particular puzzle,

you must make a shape for the three-dot yellow piece, but connect the four dot piece in a single arbitrary border with all the blue pieces.

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