perplexus.info :: Numbers : Last but not the least

Last but not the least (Posted on 2013-12-12)

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.

Submitted by Ady TZIDON

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Solution: (Hide)

The replacement operation preserves the parity of the sum, so the last number left cannot be even.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Gilding the Lily	Steve Herman	2013-12-13 10:07:21
re(5): All things being equal ... (spoiler)	Ady TZIDON	2013-12-13 02:08:02
re(4): All things being equal ... (spoiler)	Ady TZIDON	2013-12-13 02:04:50
re(4): All things being equal ... (spoiler)	Charlie	2013-12-13 01:54:49
re(3): All things being equal ... (spoiler)	xdog	2013-12-12 18:19:21
re(2): All things being equal ... (spoiler)	Charlie	2013-12-12 11:13:20
re: All things being equal ... (spoiler)	xdog	2013-12-12 10:58:22
All things being equal ... (spoiler)	Steve Herman	2013-12-12 10:02:57

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