favoritepuzzlesolution

CINDY'S FAVORITE PUZZLE
(PROOF THAT IT CAN'T BE DONE)

If you have an odd-sided polygon (e.g., triangle, pentagon, etc...) and you start from
outside of the polygon, when you are done drawing the line you will end up inside of the
polygon and vice versa. If, on the other hand, you have an even-sided polygon (e.g.,
rectangle, hexagon, etc...) and you start from outside of the polygon, when you are done
drawing the line you will end up outside of the polygon and in fact forms a loop.

Thus, all even-sided polygons are ?start outside, finish outside? and actually form a loop. On the
other hand, all odd-sided polygons behave: ?start outside, finish inside.? You cannot form a loop.

In fact, for our purposes, heptagon = pentagon = triangle

Interestingly, if you put two of these shapes next to each other, you will notice that a pentagon
attached next to a square (or rectangle) behaves as if the square is absent. Note how similar the
two green lines are.

So a pentagon-and-a-square can be represented by a pentagon only. The square can be ignored.

So this complex figure:

Similiar shape as the
example above.

Can be simplified to:

And further simplified to:

Which is just:

(since pentagons = triangles)

And guess what? You can?t draw a line through all sides once and only once with this simple
shape as with the original puzzle. The original puzzle therefore asks for something impossible.