[Illustration: SIMPLE]

[Illustration: SEMI-NASIK]

[Illustration: ASSOCIATED]

[Illustration: NASIK]


I published in _The Queen_ for January 15, 1910, an article that would
enable the reader to write out, if he so desired, all the 880 magics of
the fourth order, and the following is the complete classification that
I gave. The first example is that of a Simple square that fulfils the
simple conditions and no more. The second example is a Semi-Nasik, which
has the additional property that the opposite short diagonals of two
cells each together sum to 34. Thus, 14 + 4 + 11 + 5 = 34 and 12 + 6 +
13 + 3 = 34. The third example is not only Semi-Nasik but also
Associated, because in it every number, if added to the number that is
equidistant, in a straight line, from the centre gives 17. Thus, 1 + 16,
2 + 15, 3 + 14, etc. The fourth example, considered the most "perfect"
of all, is a Nasik. Here all the broken diagonals sum to 34. Thus, for
example, 15 + 14 + 2 + 3, and 10 + 4 + 7 + 13, and 15 + 5 + 2 + 12. As a
consequence, its properties are such that if you repeat the square in
all directions you may mark off a square, 4 × 4, wherever you please,
and it will be magic.

The following table not only gives a complete enumeration under the four
forms described, but also a classification under the twelve graphic
types indicated in the diagrams. The dots at the end of each line