Difference between revisions of "2006 AIME I Problems/Problem 14"

Revision as of 14:49, 25 September 2007

Problem

Let $S_n$ be the sum of the reciprocals of the non-zero digits of the integers from 1 to $10^n$ inclusive. Find the smallest positive integer n for which $S_n$ is an integer.

Solution

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 == Problem ==
-A tripod has three legs each of length 5 feet. When the tripod is set up, the angle between any pair of legs is equal to the angle between any other pair, and the top of the tripod is 4 feet from the ground In setting up the tripod, the lower 1 foot of one leg breaks off. Let <math> h </math> be the height in feet of the top of the tripod from the ground when the broken tripod is set up. Then <math> h </math> can be written in the form <math> \frac m{\sqrt{n}}, </math> where <math> m </math> and <math> n </math> are positive integers and <math> n </math> is not divisible by the square of any prime. Find <math> \lfloor m+\sqrt{n}\rfloor. </math> (The notation <math> \lfloor x\rfloor </math> denotes the greatest integer that is less than or equal to <math> x. </math>)
+Let <math> S_n </math> be the sum of the reciprocals of the non-zero digits of the integers from 1 to <math> 10^n </math> inclusive. Find the smallest positive integer n for which <math> S_n </math> is an integer.
 == Solution ==

2006 AIME I (Problems • Answer Key • Resources)
Preceded by Problem 13	Followed by Problem 15
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Difference between revisions of "2006 AIME I Problems/Problem 14"

Revision as of 14:49, 25 September 2007

Problem

Solution

See also