MathDB

Let

n{}

and

k{}

be natural numbers, with

n > 2k

. In the deck of cards, each card contains a subset of the set

\{1, 2, \ldots , n\}

consisting of at least

k+1

, but no more than

n-k

elements. Each

m

-element set is written exactly on

m-k

cards. Is it possible to split these cards into

n- 2k

stacks so that in each stack all subsets on the cards are different, and any two of them intersect?

Problem Statement