TWO NEW MAGIC SQUARES.
(
Magic Squares Problem.)
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.
Answer:
Here are two solutions that fulfil the conditions:--
[Illustration:
SUBTRACTING DIVIDING
11 4 14 13 36 8 54 27
16 7 1 2 216 12 1 2
6 5 3 12 6 3 4 72
9 19 8 15 9 18 24 108
]
The first, by subtracting, has a constant 8, and the associated pairs
all have a difference of 4. The second square, by dividing, has a
constant 9, and all the associated pairs produce 3 by division. These
are two remarkable and instructive squares.
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