# The ceiling is breaking

Algebra Level 5

$\large \left \lceil \dfrac n2 \right \rceil + \left \lceil \dfrac n3 \right \rceil + \left \lceil \dfrac n6 \right \rceil = n+1$

How many positive integers $$1\leq n \leq100$$ satisfy the equation above?

Notation: $$\lceil \cdot \rceil$$ denotes the ceiling function.

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