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Age 14 to 16 Challenge Level:
Find the maximum of
$${1\over p} + {1\over q} + {1\over r}$$
where $p$, $q$ and $r$ are positive integers and
$${1\over p} + {1\over q} + {1\over r} < 1.$$
Prove that it is indeed a maximum.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.