I have found three such subsets (admittedly with brute-force search), Tom's and -+- --+ 0+- +0+ +-0 -++ --- 0+- +0+ +-0 Christoph
I think this subset works for that example:
-+- --- 0++ +0+ +-0
Tom
Warren Smith writes:
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 -++ -+- --+ --- +++> -++ -+- --+ --- 0++ 0+- +0+ +-0 ++- +-+ +-- is altered to -++ -+- --+ --- 0++ 0+- +0+ +-0 then what is the subset summing to 000?There are three such subsets, the other two being