RU-ALLRUSSIAN 1976 Problem 2

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 $\mathrm{n + 1}$ , 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.