MathDB

10

integers are written in a row. A second row of

10

integers is formed as follows: the integer written under each integer

A

of the first row is equal to the total number of integers that stand to the right side of

A

(in the first row) and are strictly greater than A. A third row is formed by the same way under the second one, and so on.
(a) Prove that after several steps a “zero row” (i.e. a row consisting entirely of zeros) appears. (b) What is the maximal possible number of non-zero rows (i.e. rows in which at least one entry is not zero)?
(S Tokarev)

Problem Statement