Question 96
There is a table with $n$ rows and 18 columns. Each of its cells contains a 0 or a 1. The table satisfies the following properties:
(i) Every two rows are different.
(ii) Each row contains exactly 6 cells that contain 1.
(iii) For every three rows, there exists a column so that the intersection of the column with the three rows (the three cells) all contain 0.
What is the greatest possible value of $n$?
(i) Every two rows are different.
(ii) Each row contains exactly 6 cells that contain 1.
(iii) For every three rows, there exists a column so that the intersection of the column with the three rows (the three cells) all contain 0.
What is the greatest possible value of $n$?