067: Quasigroup Completion

Proposed by Gilles Pesant

An order $m$ quasigroup is a Latin square of size $m$. That is, a $m$ by $m$ multiplication table in which each element occurs once in every row and column. For example,

1        2       3       4
4        1       2       3
3        4       1       2
2        3       4       1

is an order 4 quasigroup.

Problem 3 of the CSPlib asks about the existence of quasigroups. This variant asks to complete a quasigroup given some of its entries. For example, partially specified quasigroup

1                        4
                 2        
3                1        
         3                

could be completed as the first example above.