MathDB

Let

n{}

be a positive integer, and let

\mathcal{C}

be a collection of subsets of

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

satisfying both of the following conditions: [*]Every

(2^n-1)

-element subset of

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

is a member of

\mathcal{C}

, and [*]Every non-empty member

C

\mathcal{C}

contains an element

c

such that

C\setminus\{c\}

is again a member of

\mathcal{C}

. Determine the smallest size

\mathcal{C}

may have.
Serbia, Pavle Martinovic ́

Problem Statement