MathDB

How Many Ones?

Source: Spring 2006 Tournament of Towns Junior A-Level #5

April 15, 2015

Problem Statement

Numbers

0, 1

and

2

are placed in a table

2005 \times 2006

so that total sums of the numbers in each row and in each column are factors of

3

. Find the maximal possible number of

1

's that can be placed in the table.
(6 points)