In mathematics, the theory of Latin squares is an active research area with many open problems.
As in other areas of mathematics, such problems are often made public at professional conferences and meetings.
Describe how all Latin subsquares in multiplication tables of Moufang loops arise.
A partial Latin square has Blackburn property if whenever the cells (i, j) and (k, l) are occupied by the same symbol, the opposite corners (i, l) and (k, j) are empty.
What is the highest achievable density of filled cells in a partial Latin square with the Blackburn property?