MathDB

At first all

2^n

rows of a

2^n \times n

table were filled with all different

n

-tuples of numbers

+1

and

-1

. Then some of the numbers were replaced by Os. Prove that one can choose a (non-empty) set of rows such that:
(a) the sum of all the numbers in all the chosen rows is

0

;
(b) the sum of all the chosen rows equals the zero row, that is, the sum of numbers in each column of the chosen rows equals

0

.
(G Kondakov, V Chernorutskii)

Problem Statement