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Tournament Of Towns
1993 Tournament Of Towns
(383) 1
(383) 1
Part of
1993 Tournament Of Towns
Problems
(1)
TOT 383 1993 Autumn A J1 rows of 10 integers
Source:
6/12/2024
10
10
10
integers are written in a row. A second row of
10
10
10
integers is formed as follows: the integer written under each integer
A
A
A
of the first row is equal to the total number of integers that stand to the right side of
A
A
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)
combinatorics
algebra