Suppose in a given collection of $2016$ integer, the sum of any $1008$ integers is positive. Show that sum of all $2016$ integers is positive.
Problem
Source:
Tags: Sum, number theory, algebra
09.08.2019 16:08
Isn't that obvious? Take a set of 1008 numbers. Take the set of the other 1008 numbers. Use closure property of natural numbers BTW,my 2500th post yeah!!
18.08.2019 18:27
Someone who can find a mistake in my solution? Cuz it does not seem to be convincing that it is an RMO problem
18.08.2019 19:56
Math-wiz wrote: Isn't that obvious? Take a set of 1008 numbers. Take the set of the other 1008 numbers. Use closure property of natural numbers BTW,my 2500th post yeah!! Well, I thought the same thing on seeing the problem. Seems like some data is wrong or missing.
18.08.2019 20:35
this is my source for the problem, the wording is as the source's
18.08.2019 22:52
I agree with mathwiz, and I think this is pretty trivial. I mean just choose any arbitrary $1008$ numbers, their sum must be positive. The other $1008$ numbers must also sum to be a positive number, so adding the two sums yields a positive number.