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Last but not the least (Posted on 2013-12-12) Difficulty: 2 of 5
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.

See The Solution Submitted by Ady TZIDON    
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re(2): All things being equal ... (spoiler) | Comment 3 of 8 |
(In reply to re: All things being equal ... (spoiler) by xdog)

If you've replaced consecutive numbers, you've replaced an odd and an even. You've replaced them with an odd. The parity is still the same, not different.
  Posted by Charlie on 2013-12-12 11:13:20

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