MathDB
2017 PUMaC Team 9

Source:

September 20, 2019
floor functionceiling function

Problem Statement

The set {(x,y)∈R2∣⌊x+y⌋⋅⌈x+y⌉=(⌊x⌋+⌈y⌉)(⌈x⌉+⌊y⌋),0≤x,y≤100}\{(x, y) \in R^2| \lfloor x + y\rfloor \cdot \lceil x + y\rceil = (\lfloor x\rfloor + \lceil y \rceil ) (\lceil x \rceil + \lfloor y\rfloor), 0 \le x, y \le 100\} can be thought of as a collection of line segments in the plane. If the total length of those line segments is a+bca + b\sqrt{c} for cc squarefree, find a+b+ca + b + c. (⌊z⌋\lfloor z\rfloor is the greatest integer less than or equal to zz, and ⌈z⌉\lceil z \rceil is the least integer greater than or equal to zz, for z∈Rz \in R.)
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