10.6

Part of 2011 All-Russian Olympiad Regional Round

Problems(1)

Smallest number of zeros

Source: Problem 6 of Russian Regional Olympiad 2011 grade 10 day 2

2011 numbers are written on a board. For any three numbers, their sum is also among numbers written on the board. What is the smallest number of zeros among all 2011 numbers? (Author: I. Bogdanov)

algebra proposedalgebracombinatorics