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2012 AMC 10A Problems/Problem 25

Revision as of 19:12, 8 February 2012 by Mattchu386 (talk | contribs) (Created page with "== Problem 25 == Real numbers <math>x</math>, <math>y</math>, and <math>z</math> are chosen independently and at random from the interval <math>[0,n]</math> for some positive in...")
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Problem 25

Real numbers $x$, $y$, and $z$ are chosen independently and at random from the interval $[0,n]$ for some positive integer $n$. The probability that no two of $x$, $y$, and $z$ are within 1 unit of each other is greater than $\frac {1}{2}$. What is the smallest possible value of $n$?

$\textbf{(A)}\ 7\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 9\qquad\textbf{(D)}\ 10\qquad\textbf{(E)}\ 11$

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