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 All things being equal ... (spoiler) by Steve Herman)

If I replace consecutive numbers I've changed the parity of the total.  

Posted by xdog on 2013-12-12 10:58:22