MathDB

Let

n>2

be an integer. A deck contains

\frac{n(n-1)}{2}

cards,numbered

1,2,3,\cdots , \frac{n(n-1)}{2}

Two cards form a magic pair if their numbers are consecutive , or if their numbers are

1

and

\frac{n(n+1)}{2}

. For which

n

is it possible to distribute the cards into

n

stacks in such a manner that, among the cards in any two stacks , there is exactly one magic pair?

9