Give the vectors back to your child, and tell them they can {play WII | have dessert} only after finding some vectors that add up to zero. Kids are smart (-: On Fri, Jun 22, 2012 at 5:03 PM, Dan Asimov <dasimov@earthlink.net> wrote:
I recently heard this cute puzzle:
<< For some integer n > 0 you have all 2^n vectors of dimension n whose entries are +1 or -1. Of course the sum of all 2^n of these vectors is the 0 vector.
Then your three-year-old child changes some of the entries of some of these vectors to 0.
Show that there is still a nonempty subset of the new set of 2^n vectors that sums to the 0 vector.
--Dan
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