Question 17
1000 numbers are written in line 1, then further lines are constructed as follows. If the number $m$ occurs in line $n$, then we write under it in line $n + 1$, each time it occurs, the number of times that $m$ occurs in line $n$. Show that lines 11 and 12 are identical. Show that we can choose numbers in line 1, so that lines 10 and 11 are not identical.