2012 AMC 10A Problems/Problem 25: Difference between revisions
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== Problem | == Problem == | ||
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 integer <math>n</math>. The probability that no two of <math>x</math>, <math>y</math>, and <math>z</math> are within 1 unit of each other is greater than <math>\frac {1}{2}</math>. What is the smallest possible value of <math>n</math>? | 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 integer <math>n</math>. The probability that no two of <math>x</math>, <math>y</math>, and <math>z</math> are within 1 unit of each other is greater than <math>\frac {1}{2}</math>. What is the smallest possible value of <math>n</math>? | ||
<math> \textbf{(A)}\ 7\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 9\qquad\textbf{(D)}\ 10\qquad\textbf{(E)}\ 11 </math> | <math> \textbf{(A)}\ 7\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 9\qquad\textbf{(D)}\ 10\qquad\textbf{(E)}\ 11 </math> | ||
==Solution== | |||
== See Also == | |||
{{AMC10 box|year=2012|ab=A|num-b=24|after=Last Problem}} | |||
Revision as of 15:42, 11 February 2012
Problem
Real numbers 
, 
, and 
are chosen independently and at random from the interval ![$[0,n]$](http://latex.artofproblemsolving.com/1/1/e/11ef480c3077b93f3ac006b998c520ece6100116.png)
for some positive integer 
. The probability that no two of , , and are within 1 unit of each other is greater than 
. What is the smallest possible value of ?
Solution
See Also
| 2012 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 24 |
Followed by Last Problem | |
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| All AMC 10 Problems and Solutions | ||
