Question 2
(CAN) Let $R_1,R_2,\ldots$ be the family of finite sequences of positive integers defined by the following rules: $R_1=(1)$, and if $R_{n-1}=(x_1,\ldots,x_s)$, then
$$R_n=(1,2,\ldots,x_1,1,2,\ldots,x_2,\ldots,1,2,\ldots,x_s,n).$$
For example, $R_2=(1,2)$, $R_3=(1,1,2,3)$, $R_4=(1,1,1,2,1,2,3,4)$. Prove that if $n>1$, then the $k$th term from the left in $R_n$ is equal to $1$ if and only if the $k$th term from the right in $R_n$ is different from $1$.
$$R_n=(1,2,\ldots,x_1,1,2,\ldots,x_2,\ldots,1,2,\ldots,x_s,n).$$
For example, $R_2=(1,2)$, $R_3=(1,1,2,3)$, $R_4=(1,1,1,2,1,2,3,4)$. Prove that if $n>1$, then the $k$th term from the left in $R_n$ is equal to $1$ if and only if the $k$th term from the right in $R_n$ is different from $1$.