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Last Sunday I met with Professor Knowfair at the public library. We caught up and he told me about the most recent assignment he gave his students. He said:

We had been studying medians and how they divide a triangle into two equal-area triangles. For that week's assignment, I decided to go a bit further. I asked the $n$-th student to devise a method of dissecting a triangle into $n$ equal-area triangles, using at most $n-1$ line segments.

Was the professor fair? How many students will be able to complete their tasks?

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Can't you just mark $n-1$ equally spaced spots along an edge (so that the distance between consecutive marked points and the endpoints of the edge are all equal) and draw lines from the opposite vertex to that edge? They'd all have the same area that way.

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  • $\begingroup$ And, as a result, every student can complete the task. $\endgroup$ – Joe Z. Mar 22 '16 at 0:20

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