# Solve the equation: $f(n)=\left\lfloor \frac n2\right\rfloor$

Let $A \in \mathbb N$ and $A=\overline{a_1a_2...a_{n-1}a_n}$. Consider the function $f(A)=\overline{a_na_{n-1}...a_2a_1}$. For example, $f(123)=321, f(100)=1$. Solve the equation: $$f(n)=\left\lfloor \frac n2\right\rfloor$$ where $n \in \mathbb N$.

### My work so far:

I found one such number. $n=73$. $$f(73)=37; \left\lfloor \frac {73}2\right\rfloor=\left\lfloor 37,5\right\rfloor=37$$

• You've made a mistake. $$f(73) = 37$$. But, $$\left\lfloor \frac {73}2\right\rfloor=\left\lfloor 36.5\right\rfloor=36$$ – JDF Sep 8 '16 at 12:32
• @JDF: Yes, I made a mistake – Roman83 Sep 8 '16 at 12:42