It’s hard to miss the hype for the Rio Olympics, writes Michael Mazenko on A Teacher’s View. But very few know that U.S. mathletes won the 2016 International Math Olympiad in Hong Kong last month. For the second year in a row. U.S. students beat competitors from China (Shanghai), South Korea, Singapore and Japan.
This is “just one more example of how in America we are ignoring our best and brightest,” writes Mazenko.
“This year’s IMO featured an unusually large number of non-standard problems which combined multiple areas of mathematics into the same investigation,” Po-Shen Loh, coach of the U.S. team, wrote in the New York Times:
The most challenging problem turned out to be #3, which was a fusion of algebra, geometry, and number theory. On that question, the USA achieved the highest total score among all countries, ultimately contributing to its overall victory — a historic repeat #1 finish (2015 + 2016), definitively breaking the 21-year drought since the last #1 finish in 1994, and the first consecutive #1 finish in the USA’s record.
Here’s IMO 2016 Problem 3:
Let P = A1 A2 … Ak be a convex polygon on the plane. The vertices A1, A2, …, Ak have integral coordinates and lie on a circle. Let S be the area of P. An odd positive integer n is given such that the squares of the side lengths of P are integers divisible by n. Prove that 2S is an integer divisible by n.
It’s as impossible for me as the gymnastics floor exercise. Does anyone have a clue how to tackle this problem?