Floor Functions With Unlucky 13
Algebra
Level
4
\[\begin{eqnarray} \text{ Equation 1 }: &&\quad \lfloor x \rfloor + \lfloor 2 x \rfloor + \lfloor 4x \rfloor = 13 \\ \text{ Equation 2 }: &&\quad \lfloor x \rfloor + \lfloor 2 x \rfloor + \lfloor 4x \rfloor+ \lfloor 8x \rfloor = 13 \end{eqnarray} \]
Do the equations above have real solutions?
Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.
by
Denton Young