MathDB

Let

R

be the set of points

(x, y)

such that

x

and

y

are positive,

x + y

is at most 2013, and

\lceil x \rceil \lfloor y \rfloor = \lfloor x \rfloor \lceil y \rceil.

Compute the area of set

R

. Recall that

\lfloor a \rfloor

is the greatest integer that is less than or equal to

a

, and

\lceil a \rceil

is the least integer that is greater than or equal to

a

Problem Statement