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

Source: XII Cono Sur Mathematical Olympiad (2001)

July 28, 2011
combinatorics unsolvedcombinatorics

Problem Statement

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.
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