Question 180
For each positive integer $n$ denote $x_n$ the number of the positive integers with $n$ digits, divisible by $4$, formed with digits $2$, $0$, $1$ or $6$.
a) Compute $x_1$, $x_2$, $x_3$ and $x_4$.
b) Find $n$ so that
$$
1 + \left\lfloor \frac{x_2}{x_1} \right\rfloor + \left\lfloor \frac{x_3}{x_2} \right\rfloor + \left\lfloor \frac{x_4}{x_3} \right\rfloor + \dots + \left\lfloor \frac{x_{n+1}}{x_n} \right\rfloor = 2016.
$$
a) Compute $x_1$, $x_2$, $x_3$ and $x_4$.
b) Find $n$ so that
$$
1 + \left\lfloor \frac{x_2}{x_1} \right\rfloor + \left\lfloor \frac{x_3}{x_2} \right\rfloor + \left\lfloor \frac{x_4}{x_3} \right\rfloor + \dots + \left\lfloor \frac{x_{n+1}}{x_n} \right\rfloor = 2016.
$$