MathDB

9.5

Part of 2009 All-Russian Olympiad Regional Round

Problems(1)

11 phrases written on 11 pieces of paper

Source: All-Russian MO 2009 Regional 9.5

8/27/2024
There are 1111 phrases written on 1111 pieces of paper (one per sheet):
1) To the left of this sheet there are no sheets with false statements. 2) Exactly one sheet to the left of this one contains a false statement. 3) Exactly 22 sheets to the left of this one contain false statements ... 11) Exactly 1010 sheets to the left of this one contain false statements.
The sheets of paper were laid out in some order in a row, going from left to right. After this, some of the written statements became true and some became false. What is the greatest possible number of true statements?
combinatorics