MathDB

m \times n

table is filled with signs

"+"

and

"-"

. A table is called irreducible if one cannot reduce it to the table filled with

"+"

, applying the following operations (as many times as one wishes).

a)

It is allowed to flip all the signs in a row or in a column. Prove that an irreducible table contains an irreducible

2\times 2

sub table.

b)

It is allowed to flip all the signs in a row or in a column or on a diagonal (corner cells are diagonals of length

1

). Prove that an irreducible table contains an irreducible

4\times 4

sub table.

Problem Statement