MathDB

Ziquan makes a drawing in the plane for art class. He starts by placing his pen at the origin, and draws a series of line segments, such that the

n^{th}

line segment has length

n

. He is not allowed to lift his pen, so that the end of the

n^{th}

segment is the start of the

(n + 1)^{th}

segment. Line segments drawn are allowed to intersect and even overlap previously drawn segments. After drawing a finite number of line segments, Ziquan stops and hands in his drawing to his art teacher. He passes the course if the drawing he hands in is an

N

N

square, for some positive integer

N

, and he fails the course otherwise. Is it possible for Ziquan to pass the course?

Problem Statement