MathDB

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Part of 2001 Cono Sur Olympiad

Problems(2)

Distinct row & column sums in 2000x2000 array of 0s, 1s, -1s

Source: XII Cono Sur Mathematical Olympiad (2001)

7/28/2011
Each entry in a 2000×20002000\times 2000 array is 00, 11, or −1-1. Show that it's possible for all 40004000 row sums and column sums to be distinct.
combinatorics unsolvedcombinatorics
Distance between two points in a polygon in a square

Source: XII Cono Sur Mathematical Olympiad (2001)

7/28/2011
A polygon of area SS is contained inside a square of side length aa. Show that there are two points of the polygon that are a distance of at least S/aS/a apart.
geometryanalytic geometrygeometry unsolved