2018 OIM Problems/Problem 3

Problem

In a plane we have $n$ lines without two being parallel, nor two perpendicular, nor three concurrent. A system of Cartesian axes is chosen with one of the $n$ straight lines as the axis of the abscissa. A point $P$ is located at the coordinate origin of the chosen system and begins to move at constant speed along the positive side of the $x$-axis. Every time $P$ arrives at the intersection of two lines, continue along the line just reached in the direction that allows the value of the abscissa of $P$ to always be always increasing. Show that you can choose the Cartesian system axes so that $P$ passes through points of the $n$ lines.

Note: The abscissa axis of a plane coordinate system is the axis of the first coordinate or $x$-axis.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

OIM Problems and Solutions