2007 Cyprus MO/Lyceum/Problem 10
Problem
The volume of an orthogonal parallelepiped is and its dimensions are integers. The minimum sum of the dimensions is
Solution
, so we want to minimize the sum of three integers whose product is . To do this, the factors must be as close together as possible. Therefore, none of the factors will be , and one will likely be . This implies that the factors are minimized when they are , and the answer is .
See also
2007 Cyprus MO, Lyceum (Problems) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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