Question 39
In a certain game, the number $1$ is written on the board. At any moment, an allowed move consists of replacing the number written on the board by its double or by another number that has the same digits as it. For example, if the number $137$ is written on the board, an allowed move consists of replacing it by $137 \cdot 2 = 274$ or by $173$, $317$, $371$, $713$ or $731$. Determine whether, after a finite number of operations, it is possible to obtain the following numbers:
a) $10^{3}$.
b) $10^{9}$.
c) $9876543210$.
a) $10^{3}$.
b) $10^{9}$.
c) $9876543210$.