# 9x9 Map Path: In and out next to each other?

This isn't something I read in a book or anything, it's more of a puzzle I thought up for myself.

However, I am unable to find a solution.

Here's my problem:

If I create a 9x9 checkerboard, and want to walk a path across it, where each block is walked upon only once, and there are only 90° turns, it's easy enough to create any path. (See first image example:)

However, if I want to create an entrance and exit point NEXT TO EACH OTHER, I am stumped. I can't do it:

Can someone help me think of a path ac cross a 9x9 area, where the entrance and exit points are directly next to each other, and yet each block is used only once and only 90° turns are used?

Thanks again.

• From a glance I believe that it is impossible to do, but I have no proof other then just my intuition. – Rewan Demontay May 22 '19 at 20:02
• I also think that it is impossible to do. From the appearance of the problem I think that there will be an elegant mathematical proof – Adam May 22 '19 at 20:07