# Sotiri's Doku Squares

A Doku Square is an $$n \times n$$ array containing all integers from $$0$$ to $$n-1$$ exactly once in each column and each row. The entry in the $$i$$th row and $$j$$th column of Doku Square $$A$$ is denoted by $$A_{i,j}$$.

We call two $$n \times n$$ Doku Squares $$A$$ and $$B$$ friendly if all $$n^2$$ ordered pairs $$(A_{i,j},B_{i,j})$$ are distinct.

What is the maximum number of $$73 \times 73$$ Doku Squares, such that any two of them are friendly?

This problem is shared by Sotiri K.

Details and assumptions

As an explicit example, the two squares $\begin{array} { | l | l | } \hline 0 & 1 & 2 \\ \hline 1 & 2 & 0 \\ \hline 2 & 0 & 1 \\ \hline \end{array}$ and $\begin{array} { | l | l | } \hline 0 & 1 & 2 \\ \hline 2 & 0 & 1 \\ \hline 1 & 2 & 0 \\ \hline \end{array}$

are 2 friendly $$3 \times 3$$ Doku squares.

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