MathDB

Six decks of

n

cards, numbered from

1

n

, are given. Melanie arranges each of the decks in some order, such that for any distinct numbers

x

y

, and

z

\{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.

Problem Statement