Nowadays sparse systems of equations occur frequently in science and
engineering. In this contribution we deal with sparse systems common in
cryptanalysis. Given a cipher system, one converts it into a system of sparse
equations, and then the system is solved to retrieve either a key or a
plaintext. Raddum and Semaev proposed new methods for solving such sparse
systems. It turns out that a combinatorial MaxMinMax problem provides bounds on
the average computational complexity of sparse systems. In this paper we
initiate a study of a linear algebra variation of this MaxMinMax problem
