Difference between revisions of "1997 AIME Problems/Problem 12"
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== Problem == | == Problem == | ||
+ | Let <math>S</math> be the set of points in the Cartesian plane that satisfy <center><math>\Big|\big||x|-2\big|-1\Big|+\Big|\big||y|-2\big|-1\Big|=1.</math></center> If a model of <math>S</math> were built from wire of negligible thickness, then the total length of wire required would be <math>a\sqrt{b}</math>, where <math>a</math> and <math>b</math> are positive integers and <math>b</math> is not divisible by the square of any prime number. Find <math>a+b</math>. | ||
== Solution == | == Solution == | ||
{{solution}} | {{solution}} | ||
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== See also == | == See also == | ||
− | + | {{AIME box|year=1997|num-b=11|num-a=13}} | |
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Revision as of 15:35, 20 November 2007
Problem
Let be the set of points in the Cartesian plane that satisfy
If a model of were built from wire of negligible thickness, then the total length of wire required would be , where and are positive integers and is not divisible by the square of any prime number. Find .
Solution
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See also
1997 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |