Difference between revisions of "2007 Cyprus MO/Lyceum/Problem 10"
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==Solution== | ==Solution== | ||
| − | <math>\displaystyle V = lwh</math>, so we want to minimize the sum of three integers whose product is <math>\displaystyle 132 = 2^ | + | <math>\displaystyle V = lwh</math>, so we want to minimize the sum of three integers whose product is <math>\displaystyle 132 = 2^2\cdot3\cdot11</math>. To do this, the factors must be as close together as possible. Therefore, none of the factors will be <math>2</math>, and one will likely be <math>11</math>. This implies that the factors are minimized when they are <math>3,\ 4,\ 11</math>, and the answer is <math>3 + 4 + 11 = 18 \Longrightarrow \mathrm{D}</math>. |
==See also== | ==See also== | ||
Latest revision as of 15:47, 6 May 2007
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 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
