  We introduce a condition on arrays in some way maximally distinct from Latin
square condition, as well as some other conditions on algebras, graphs and
$0,1$-matrices. We show that these are essentially the same structures,
generalising a similar collection of models presented by Knuth in 1970.
  We find ways in which these structures can be made more specific, relating to
existing investigations, then show that they are also extremely general; the
groupoids satisfy no nontrivial equations. Some construction methods are
presented and some conjectures made as to how certain structures are preserved
by these constructions. Finally we investigate to what degree partial arrays
satisfying our conditions and partial Latin squares overlap.
