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Combinatorics.

Source: Baltic Way 2015

November 8, 2015
combinatoricsBaltic Way

Problem Statement

Let n>2n>2 be an integer. A deck contains n(n−1)2\frac{n(n-1)}{2} cards,numbered 1,2,3,⋯ ,n(n−1)21,2,3,\cdots , \frac{n(n-1)}{2} Two cards form a magic pair if their numbers are consecutive , or if their numbers are 11 and n(n+1)2\frac{n(n+1)}{2}. For which nn is it possible to distribute the cards into nn stacks in such a manner that, among the cards in any two stacks , there is exactly one magic pair?
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