Brute Force?

Algebra Level 3

π+π+16+π+26+π+36+π+46+π+56+1=? \large \left \lceil \lfloor \pi \rfloor + \left\lfloor \pi + \dfrac{1}{6}\right \rfloor + \left \lfloor \pi + \dfrac{2}{6} \right \rfloor + \left \lfloor \pi + \dfrac{3}{6} \right \rfloor + \left \lfloor \pi + \dfrac{4}{6}\right \rfloor +\left \lfloor \pi + \dfrac{5}{6}\right \rfloor \right \rceil + 1 = \, ?

Notations: \lfloor \cdot \rfloor denotes the floor function and \lceil \cdot \rceil denotes the ceiling function.


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