A. 409. For a positive integer m, let s(m) be the sum of the digits of m. For n2, let f(n) be the minimal k for which there exists a set S of n positive integers such that for any nonempty subset XS. Prove that there are constants 0<C1<C2 with C1log10nf(n)C2log10n.
U.S.A. Mathematical Olympiad, 2005
Deadline expired on 15 November 2006.