Bulldozer on the coordinate plane

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Phlembac Adib Hasan
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Bulldozer on the coordinate plane

Unread post by Phlembac Adib Hasan » Mon Nov 07, 2016 10:17 pm

On the coordinate plane, there are finitely many walls, (= disjoint line segments) none of which are parallel to either axis. A bulldozer starts at an arbitrary point and moves in the $+x$ direction. Every time it hits a wall, it turns at a right angle to its path, away from the wall, and continues moving. (Thus the bulldozer always moves parallel to the axes.)

Prove that it is impossible for the bulldozer to hit both sides of every wall.
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