Christof wrote: << So we have n x 2^n numbers and the child sets any *arbitrary* (not necessarily small) subset of those to zero, correct? regarding the 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.
Yes, exactly. Any subset of the n(2^n) components of the original 2^n vectors may be changed to 0's. The problem is to show there is always some nonempty subset of the resulting set of 2^n vectors that sums to the 0 vector. --Dan ________________________________________________________________________________________ It goes without saying that .