Construct a subtracting magic square with the first sixteen whole
numbers that shall be "associated" by _subtraction_. The constant is, of
course, obtained by subtracting the first number from the second in
line, the result from the third, and the result again from the fourth.
Also construct a dividing magic square of the same order that shall be
"associated" by _division_. The constant is obtained by dividing the
second number in a line by the first, the third by the quotient, and the
fourth by the next quotient.


408.--MAGIC SQUARES OF TWO DEGREES.

While reading a French mathematical work I happened to come across, the
following statement: "A very remarkable magic square of 8, in two
degrees, has been constructed by M. Pfeffermann. In other words, he has
managed to dispose the sixty-four first numbers on the squares of a
chessboard in such a way that the sum of the numbers in every line,
every column, and in each of the two diagonals, shall be the same; and
more, that if one substitutes for all the numbers their squares, the
square still remains magic." I at once set to work to solve this
problem, and, although it proved a very hard nut, one was rewarded by
the discovery of some curious and beautiful laws that govern it. The
reader may like to try his hand at the puzzle.





MAGIC SQUARES OF PRIMES.