Unformatted text preview: es whose centers are 10 units
apart, and whose radii are 1 and 3. Find, with proof, the
locus of all points for which there exists points on
and on
such that
is the midpoint of the line
segment
. minimal selﬁsh sets, that is, selﬁsh sets none of whose
proper subsets is selﬁsh. x ¢ (r Y 3r ¢ fr '"DbY r ¤ r Y ¤ r ¢ r
r
e Yaaa d
Q
hy
y
y xxx Q v H r xxx r r
S&qu...
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 Fall '08
 Staff
 Math, Real Numbers, Natural number, William Lowell Putnam Mathematical Competition

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