Numbers 1, 2, 3, ... 2014 are written on a board.
You are allowed to replace any two of these numbers by a new number, which is either the sum or the difference of these numbers.

Show that after 2013 times performing this operation, the only number left on the board cannot be zero.

(In reply to re(2): All things being equal ... (spoiler) by Charlie)

My reading of the problem conditions is that I must replace both selected numbers with the same number, either the sum or difference.  If instead the sum replaces one and the difference replaces the other, then I agree with Steve Herman's answer.

Posted by xdog on 2013-12-12 18:19:21