On a generalization of the Evans Conjecture (Q942105)

Evan's Conjecture said that an \(n \times n\) square with at most \(n-1\) entries predetermined without contradiction can be completed to an \(n \times n\) Latin square. An \(r\)-multi Latin square is a square of order \(n\) where each cell has \(r\) symbols from an \(nr\)-set so that in each row and column every symbol appears exactly once. The authors show here that any partial \(r\)-multi Latin square with of order \(n\) with at most \(n-1\) cells predetermined without contradiction can be completed to an \(r\)-multi Latin square.