MathDB

4

Part of 2010 Flanders Math Olympiad

Problems(1)

in snack bar Pita Goras, the owner checks his accounts

Source: Flanders Math Olympiad 2010 p4

12/24/2022
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 55 adding consecutive lines, I always get a strictly positive result.” "Indeed," the accountant answers him, “but if you put the sums of 77 consecutive lines add up, you always get a strictly negative result.” How many lines are there maximum on his sheet?
combinatorics