Report on the 64th Annual International Mathematical Olympiad

Summary

We present the problems and solutions to the 64th Annual International Mathematical Olympiad.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Note that the online version of this article has color diagrams.

This statement easily follows from the fact that the maximal elements of the poset form an antichain. The dual statement, that the size of the largest antichain equals the minimum number of chains that can partition the poset, is known as Dilworth’s theorem, and is considerably harder to establish.

The proof can be readily established using the Cartesian coordinate system by noticing that for a point $P=(x,y)$ and a circle ω, $\mathit{\text{Pow}}(P,\omega )=x^2+y^2+\mathit{\text{Ax}}+\mathit{\text{By}}+C$, where A, B, and C depend on the center and radius of ω.

Additional information

Notes on contributors

Béla Bajnok

BÉLA BAJNOK (MR Author ID: 314851) is a Professor of Mathematics at Gettysburg College and the Director of the American Mathematics Competitions program of the MAA.

Evan Chen

EVAN CHEN (MR Author ID: 1158569) is a former co-Editor-in-chief of the USAMO, and one of the United States coaches for the International Math Olympiad.

Enrique Treviño

ENRIQUE TREVIÑO (MR Author ID: 894315) is an Associate Professor of Mathematics at Lake Forest College and the co-Editor-in-chief of the USAMO.