MathDB

Let

S

be the set of points in the Cartesian plane that satisfy \Big|\big|{|x| \minus{} 2}\big| \minus{} 1\Big| \plus{} \Big|\big|{|y| \minus{} 2}\big| \minus{} 1\Big| \equal{} 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 \plus{} b.

Problem Statement