A geometry problem by Soumava Pal

Geometry Level 3

Consider the following problems:

Let \(G\) be the number of points of discontinuity of \(f(x)=\lfloor x^2\rfloor -\lfloor x \rfloor^2\) in the interval \((0,1.6)\).

Let \(E\) be the number of solutions to \(x=99\sin(\pi x)\).

Find \(G+E-GE\).

Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.

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