Numbers 1, 2, 3, ... 2014 are written on
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: All things being equal ... (spoiler)
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