## 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.