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Putnam 2007 B6

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December 3, 2007
Putnamlogarithmsintegrationprobabilityanalytic geometrycollege contests

Problem Statement

For each positive integer n, n, let f(n) f(n) be the number of ways to make n! n! cents using an unordered collection of coins, each worth k! k! cents for some k, 1≤k≤n. k,\ 1\le k\le n. Prove that for some constant C, C, independent of n, n, n^{n^2/2\minus{}Cn}e^{\minus{}n^2/4}\le f(n)\le n^{n^2/2\plus{}Cn}e^{\minus{}n^2/4}.
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