Question 174
Given a stripe $1 \times n$, $n \ge 4$. One wrote a positive integer in each cell of it (the numbers are not obliged to be equal). After under each number one writes a positive integer which is equal to the quantity of such integers in the previous row. (i.e. if $10$ was written in the previous row three times then under each of the numbers $10$ one writes $3$ in the next row). After the procedure repeats.
a) Prove that after a finite number of steps the rows will not change.
b) How long can the next row differ from the previous one if $n=2016$ and if $n$ is arbitrary?
a) Prove that after a finite number of steps the rows will not change.
b) How long can the next row differ from the previous one if $n=2016$ and if $n$ is arbitrary?