Difference between revisions of "1993 AIME Problems/Problem 7"
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== Problem == | == Problem == | ||
| + | Three numbers, <math>a_1\,</math>, <math>a_2\,</math>, <math>a_3\,</math>, are drawn randomly and without replacement from the set <math>\{1, 2, 3, \dots, 1000\}\,</math>. Three other numbers, <math>b_1\,</math>, <math>b_2\,</math>, <math>b_3\,</math>, are then drawn randomly and without replacement from the remaining set of 997 numbers. Let <math>p\,</math> be the probability that, after a suitable rotation, a brick of dimensions <math>a_1 \times a_2 \times a_3\,</math> can be enclosed in a box of dimensions <math>b_1 \times b_2 \times b_3\,</math>, with the sides of the brick parallel to the sides of the box. If <math>p\,</math> is written as a fraction in lowest terms, what is the sum of the numerator and denominator? | ||
== Solution == | == Solution == | ||
| + | {{solution}} | ||
== See also == | == See also == | ||
| − | + | {{AIME box|year=1993|num-b=6|num-a=8}} | |
Revision as of 23:10, 25 March 2007
Problem
Three numbers, 
, 
, 
, are drawn randomly and without replacement from the set 
. Three other numbers, 
, 
, 
, are then drawn randomly and without replacement from the remaining set of 997 numbers. Let 
be the probability that, after a suitable rotation, a brick of dimensions 
can be enclosed in a box of dimensions 
, with the sides of the brick parallel to the sides of the box. If is written as a fraction in lowest terms, what is the sum of the numerator and denominator?
Solution
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See also
| 1993 AIME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
