The Lando Trick

Lando trick is a  novel way to surprise friends or an audience by generating a super magic square of a certain sum while an arbitrary numeral is placed in an arbitrary cell.  After an introduction in the first section of the course, the second section outlines a recipe for performing the Lando trick in two steps.  The square is divided into four corners, and in the first step, two opposite corners are filled.  In the second step, the remaining two corners are filled. Finally, four placeholders are replaced by four respective calculated numbers to get the desired sum. This section concludes with several tips for performing the Lando trick in front of an audience.  Also, an example is demonstrated.  In the last section of the course, The third section of the course justifies the recipe by a discussion of a 4X4 diagonal mutually orthogonal Latin square or MOLS. It is shown that the super magic square implements a diagonal MOLS. Then, relocating an arbitrary entry of the diagonal MOLS to an arbitrary cell is performed in two steps, without recalculation of the entries.  It is shown that in the second step, may necessitate flipping of opposite corners.  That ability in diagonal MOLS justifies the recipe for Lando trick.