in snack bar Pita Goras, the owner checks his accounts
Source: Flanders Math Olympiad 2010 p4
December 24, 2022
combinatorics
Problem Statement
In snack bar Pita Goras, the owner checks his accounts. He writes on every line either a positive amount in case of an income or a negative amount in case of an expense. He says to his accountant, “If I change the amounts of random adding consecutive lines, I always get a strictly positive result.” "Indeed," the accountant answers him, “but if you put the sums of consecutive lines add up, you always get a strictly negative result.” How many lines are there maximum
on his sheet?