Integers on the board

For discussing Olympiad Level Combinatorics problems
tanmoy
Posts:312
Joined:Fri Oct 18, 2013 11:56 pm
Location:Rangpur,Bangladesh
Integers on the board

Unread post by tanmoy » Thu Oct 13, 2016 12:38 pm

$2016$ nonnegative integers are written on a board.In each step,you can erase two of the numbers and replace them with their sum and their difference.Is it possible,in a finite number of steps,to reach a state where at least $2015$ of the numbers are zero?
Last edited by tanmoy on Thu Oct 13, 2016 5:29 pm, edited 2 times in total.
"Questions we can't answer are far better than answers we can't question"

User avatar
Zawadx
Posts:90
Joined:Fri Dec 28, 2012 8:35 pm

Re: Integers on the board

Unread post by Zawadx » Thu Oct 13, 2016 4:33 pm

The problem actually has a mistake. The intended problem was, "Is it possible,in a finite number of steps,to reach a state where at least 2015 of the numbers are zero?"

tanmoy
Posts:312
Joined:Fri Oct 18, 2013 11:56 pm
Location:Rangpur,Bangladesh

Re: Integers on the board

Unread post by tanmoy » Thu Oct 13, 2016 5:32 pm

Zawadx wrote:The problem actually has a mistake. The intended problem was, "Is it possible,in a finite number of steps,to reach a state where at least 2015 of the numbers are zero?"
Edited.
"Questions we can't answer are far better than answers we can't question"

Post Reply