3 Quick Questions from the Hardest Math Test in the World

Author(s): SPX

Originally published on Towards AI.

Can you solve any of these questions from the William Lowell Putnam Mathematical Competition?

Source

Question 1.

Determine all possible values of the expression A³ + B³ + C³ — 3ABC where A, B, and C are nonnegative integers.

Question 2.

In triangle ∆ABC, let G be the centroid, and let I be the center of the inscribed circle. Let α and β be the angles at the vertices A and B, respectively. Suppose that the segment IG is parallel to AB and that β = 2 tan^-1 (1/3). Find α.

Question 3.

Let f be a continuous real-valued function on R³. Suppose that for every sphere… Read the full blog for free on Medium.

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Published via Towards AI