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Find the number of solutions to the equation ⌊n2⌋+⌊n3⌋+⌊n6⌋=n \large \left \lfloor \dfrac n2 \right \rfloor + \left \lfloor \dfrac n3 \right \rfloor + \left \lfloor \dfrac n6 \right \rfloor =n ⌊2n⌋+⌊3n⌋+⌊6n⌋=n
where nnn is a natural number such that 1≤n≤1001\leq n \leq 1001≤n≤100.
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