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2012 AMC 10A Problem 25

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2012 AMC 10A Problem 25AMC 10 Step by Step

Name: Date: September 13, 2026

Geometric Probability · difficulty 5 of 5 · about 10 min · position P21-25

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 $n$ ?

A)
$7$
B)
$8$
C)
$9$
D)
$10$
E)
$11$

2012 AMC 10A Problem 25

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