23 Jun
2012
23 Jun
'12
7:38 a.m.
* Dan Asimov <dasimov@earthlink.net> [Jun 23. 2012 07:47]:
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
This will work only for some definition of "some": if the evil kid removes, for example, the j-th component in all but one vector then I cannot non-emptily sum to the 0 vector.
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