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Compute the area of the union of all squares

Source: Austrian Mathematical Olympiad 2003, Part 2, D1, P3

June 18, 2011

geometrynumber theory unsolvednumber theory

Problem Statement

For every lattice point

(x, y)

with

x, y

non-negative integers, a square of side

\frac{0.9}{2^x5^y}

with center at the point

(x, y)

is constructed. Compute the area of the union of all these squares.