Removing numbers on the board
Source: 239 2013 J7
August 7, 2020
Problem Statement
Dima wrote several natural numbers on the blackboard and underlined some of them. Misha wants to erase several numbers (but not all) such that a multiple of three underlined numbers remain and the total amount of the remaining numbers would be divisible by ; but after trying for a while he realizes that it's impossible to do this. What is the largest number of the numbers on the board?