By mixed monotone method, the existence and uniqueness are established for singular (k, n - k) conjugate boundary value problems. The theorems obtained are very general and complement previous known results.

A mathematical puzzle from a recent issue of the New Scientist magazine is solved by combining the theory of permutations with Prologʹs symbolic and other computational facilities. The scheme studied is interesting because it shows that the power of the generate-and-test approach, a rather crude approach known from Artificial Intelligence, is greatly enhanced if it is supplemented by some topical knowledge from the field of study. The puzzle involves searching for matrices with certain patterns, leading to the study of permutation types. The suggested route allows for the solution of a generalized version of the original puzzle.