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Define omega

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September 2, 2010
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Problem Statement

Let SS be a set of positive integers n1,n2,⋯ ,n6n_1, n_2, \cdots, n_6 and let n(f)n(f) denote the number n1nf(1)+n2nf(2)+⋯+n6nf(6)n_1n_{f(1)} +n_2n_{f(2)} +\cdots+n_6n_{f(6)}, where ff is a permutation of {1,2,...,6}\{1, 2, . . . , 6\}. Let Ω={n(f)∣f is a permutation of {1,2,...,6}}\Omega=\{n(f) | f \text{ is a permutation of } \{1, 2, . . . , 6\} \} Give an example of positive integers n1,⋯ ,n6n_1, \cdots, n_6 such that Ω\Omega contains as many elements as possible and determine the number of elements of Ω\Omega.
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