Question 1
Given is a table with $n$ rows and $12$ columns. Each cell in it contains a $0$ or a $1$. The table has the following properties:
a. Every two rows are different.
b. Every row contains exactly $4$ entries equal to $1$.
c. For every $3$ rows there is a column that intersects them at three entries equal to $0$.
Find the greatest $n$ for which such a table exists.
a. Every two rows are different.
b. Every row contains exactly $4$ entries equal to $1$.
c. For every $3$ rows there is a column that intersects them at three entries equal to $0$.
Find the greatest $n$ for which such a table exists.