Problem A. 409. (October 2006)
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
(5 pont)
Deadline expired on November 15, 2006.
Sorry, the solution is available only in Hungarian. Google translation
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Statistics:
13 students sent a solution. 5 points: Dobribán Edgár, Fischer Richárd, Gyenizse Gergő, Hujter Bálint, Kisfaludi-Bak Sándor, Kónya 495 Gábor, Korándi Dániel, Lovász László Miklós, Nagy 224 Csaba, Nagy 235 János, Nagy 314 Dániel, Sümegi Károly, Tomon István.
Problems in Mathematics of KöMaL, October 2006