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.


Inspiration.

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