Can the line intersect all segments?
Algebra
Level
3
A closed path is made up of line segments. Can one line, not containing a vertex of the path, intersect each of its segments?
No
Yes
It depends
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1 solution
Every time the line crosses one of the line segments, the line passes from being inside the closed path to being outside, or vice versa. Since an infinite line must both start and finish outside the closed path, it must change from being inside to being outside the path an even number of times. It is not possible to do this if the number of inside/outside changes is 2 0 1 9 , an odd number.