Can you solve it?

Algebra Level 4

\[ \large \left \lfloor \dfrac x{1!} \right \rfloor + \left \lfloor \dfrac x{2!} \right \rfloor + \left \lfloor \dfrac x{3!} \right \rfloor +\cdots + \left \lfloor \dfrac x{10!} \right \rfloor =1001\]

Find the integer value of \(x\) satisfying the equation above.

Notations:

  • \( \lfloor \cdot \rfloor \) denotes the floor function.

  • \(!\) denotes the factorial notation. For example, \(8! = 1\times2\times3\times\cdots\times8 \).

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