Deriving Greenberg's universal 20 and its exceptions

Of the 24 mathematically possible orders of the four elements demonstrative, numeral, adjective, and noun, only 14 appear to be attested in the languages of the world. Some of these are unexpected under Greenberg's Universal 20. Here it is proposed that the actually attested orders, and none of the unattested ones, are derivable from a single, universal, order of Merge (Dem > Num > Adj > N) and from independent conditions on phrasal movement.