1998 OIM Problems/Problem 3

Problem

Find the minimum natural number $n$ with the following property: among any $n$ different numbers belonging to the set ${1, 2, \cdots , 999}$ you can choose four different numbers $a$, $b$, $c$, $d$, such that $a + 2b + 3c = d$.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

https://www.oma.org.ar/enunciados/ibe13.htm