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rioplatense(2005/6)

Source:

September 3, 2006

integrationcombinatorics unsolvedcombinatorics

Problem Statement

Let

k

be a positive integer. Show that for all

n>k

there exist convex figures

F_{1},\ldots, F_{n}

and

F

such that there doesn't exist a subset of

k

elements from

F_{1},..., F_{n}

and

F

is covered for this elements, but

F

is covered for every subset of

k+1

elements from

F_{1}, F_{2},....., F_{n}

.

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