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3

Part of 1996 Putnam

Problems(2)

Putnam 1996 A3

Source:

6/4/2014
Suppose that each of 2020 students has made a choice of anywhere from 00 to 66 courses from a total of 66 courses offered. Prove or disprove : there are 55 students and 22 courses such that all 55 have chosen both courses or all 55 have chosen neither course.
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Putnam 1996 B3

Source:

6/6/2014
Let SnS_n be the set of all permutations of (1,2,…,n)(1,2,\ldots,n). Then find : max⁡σ∈Sn(∑i=1nσ(i)σ(i+1)) \max_{\sigma \in S_n} \left(\sum_{i=1}^{n} \sigma(i)\sigma(i+1)\right) where σ(n+1)=σ(1)\sigma(n+1)=\sigma(1).
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