MathDB

Let

A

and

B

be unit hexagons that share a center. Then, let

\mathcal{P}

be the set of points contained in at least one of the hexagons. If the maximum possible area of

\mathcal{P}

X

and the minimum possible area of

\mathcal{P}

Y,

then the value of

Y-X

can be expressed as

\tfrac{a\sqrt{b}-c}{d},

where

a,b,c,d

are positive integers such that

b

is square-free and

\gcd(a,c,d)=1.

Find

a+b+c+d.

Problem Statement