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This is basically what the image looks like, and yes it is impossible. If you look, you'll see any rectangle has either 4 or 5 sides (even or odd). Now if you were to start inside an odd one, you eventually would have to end up on the outside and if there were two odd box's it would be fine but there are three... it's hard to explain, but it's impossible. I actually devised a way to find out whether or not a puzzle like this is impossible or possible. First add up all the rectangles with even "doorways" and odd ones. Cancel every even with every even, and every odd with every odd. I found that's it's not possible if you end up with an odd. It's possible: if they all cancel out, if you have a remaining even. However there is a special case if you end up with 1 even and 1 odd; If you have an odd amount of odds (3, 5, 7...) then it's not possible, But it is for 1.
As I read over that, it's a little difficult to understand, read it carefully.
So if we look at the original we see that we have 3 odds and 2 evens:
o oo ee . The paired ones cancel out so we have an o remaining. If you look back at my list, a remaining odd is...Not Possible, hence the puzzle is unsolvable.
Note: I haven't showed this mathematically, I made puzzle types a bunch of times and tried them, the ones that weren't possible and the ones that were possible had the same properties, that's what this is based upon. You can try it yourself.
