Six decks of n cards, numbered from 1 to n, are given. Melanie arranges each of the decks in some order, such that for any distinct numbers x, y, and z in {1,2,...,n}, there is exactly one deck where card x is above card y and card y is above card z. Show that there is some n for which Melanie cannot arrange these six decks of cards with this property. combinatoricsnumber theory