# Floor Functions

**Algebra**Level 5

\[\large \lfloor x\rfloor+\lfloor 2x\rfloor+\lfloor 4x\rfloor+\lfloor 8x\rfloor+\lfloor 16x\rfloor+\lfloor 32x\rfloor=12345\]

What is the number of integral values of \(n\) such that \(\dfrac{n}{1729}\) satisfies the equation above?

**Details and assumptions**

- \(\lfloor x\rfloor\) represents the greatest integer function.