2010 UNCO Math Contest II Problems/Problem 10
Problem
Let where
. What is the maximum number of elements in a subset
of
,
which has at least three elements, such that
for all
in
? As an example, the subset
of
has the property that the sum of any two elements is strictly bigger
than the third element, but the subset
does not since
is
greater than
.
Since there is no subset of size
satisfying these conditions, the answer for
is
.