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.

Amusements in Mathematics · 第 943 / 970 题