# Sotiri's Doku Squares

**Discrete Mathematics**Level 4

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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