Killer Math Problem With An Unbelievably Elegant Solution

Did you know some math problems were used to discriminate against groups of people? This is one such problem, and it stumped me! But it has an unbelievably elegant solution. Take any equilateral triangle and pick a random point inside the triangle. Draw from each vertex a line to the random point. Two of the three angles at the random point are known, let’s say angles x and y. If the 3 line segments from each vertex to the random point were removed out of the original triangle to form a new triangle, what would the new triangle’s angles be?

Thanks to Daniel E for sharing this puzzle! Also do check out these sources for the historical background to this problem and other similar “killer problems” that are easy to state and nearly impossible to solve unless you know the trick (in which case they are readily solvable problems).

My blog post for this video:
https://wp.me/p6aMk-5pw

Sources and historical background
Gold Plated Goof video on “coffin problems” – Simple Math Problems To Fool The Best. The triangle problem is the third problem presented (around 5:33)

Tanya Khovanova, and Alexey Radul. “Jewish Problems.”
https://arxiv.org/abs/1110.1556v2

Originally published as: Tanya Khovanova, and Alexey Radul. “Killer Problems.” The American Mathematical Monthly, vol. 119, no. 10, 2012, pp. 815–823. JSTOR, JSTOR, www.jstor.org/stable/10.4169/amer.math.monthly.119.10.815.

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