MathDB

0-1 matrix w/ rows & cols having the same number of 0s or 1s

Source: XVII Olimpíada Matemática Rioplatense (2008)

July 25, 2011

linear algebramatrixcombinatorics unsolvedcombinatorics

Problem Statement

In each square of a chessboard with

a

rows and

b

columns, a

0

1

is written satisfying the following conditions. [*]If a row and a column intersect in a square with a

0

, then that row and column have the same number of

0

s. [*]If a row and a column intersect in a square with a

1

, then that row and column have the same number of

1

s. Find all pairs

(a,b)

for which this is possible.