[math-fun] Vector puzzle

Yes, my "V' and -V removal" ploy can fail if the set of altered vectors is half the cardinality (or more) of the full set. If the old set is -+ -- ++ +- then alter to -+ -- 0+ +0 whereupon the last three sum to 00 but no other subset works (right?). That example indicates that the puzzle cannot be solved by a simple pairing argument, something fancier is needed. If -++ -+- --+ --- +++ ++- +-+ +-- is altered to -++ -+- --+ --- 0++ 0+- +0+ +-0 then what is the subset summing to 000?