# 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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