I find an equivalence for a linear algebra problem which seems not easy.
Consider the vector space $$ \mathbb{Z}_2^n $$ for a natural number n. We want to partition $$ \mathbb{Z}_2^n \setminus\{(0,\dots.0)\} $$ into the subsets with the property that if $x,y,z$ are in the same group, then we have $ x+y+z \neq 0 $. The question is that can the number of partition groups be $ o(n) $? But I still can't find an example with less than $n$ groups(partition into n groups in easy).