Difference between revisions of "1997 AIME Problems/Problem 12"

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== Problem ==
 
== Problem ==
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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 ==
 
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== See also ==
 
== See also ==
* [[1997 AIME Problems/Problem 11 | Previous problem]]
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{{AIME box|year=1997|num-b=11|num-a=13}}
* [[1997 AIME Problems/Problem 13 | Next problem]]
 
* [[1997 AIME Problems]]
 

Revision as of 15:35, 20 November 2007

Problem

Let $S$ be the set of points in the Cartesian plane that satisfy

$\Big|\big||x|-2\big|-1\Big|+\Big|\big||y|-2\big|-1\Big|=1.$

If a model of $S$ were built from wire of negligible thickness, then the total length of wire required would be $a\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime number. Find $a+b$.

Solution

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See also

1997 AIME (ProblemsAnswer KeyResources)
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
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