MathDB

11.6

Part of I Soros Olympiad 1994-95 (Rus + Ukr)

Problems(1)

triangular table of 0s ans 1s

Source: I Soros Olympiad 1994-95 Ukraine R2 11.6 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

6/6/2024
A natural number nn is given and written in a row of nn numbers, each of which is equal to 00 or 11. Then n−1n - 1 numbers are written below in a row - one number under each pair of adjacent numbers of the first row. At the same time, 00 is written under a pair of identical numbers. and under a pair of different ones 11. Then, under the second row, the third of n−2n- 2 numbers is similarly written, etc., until we get a triangular table with nn rows. For a given nn, find the largest possible number of units in such a table.
combinatorics