536 Puzzles and Curious Problems

344 Answers

384. AN IRREGULAR MAGIC SQUARE

If for the 2 and 15 you substitute 7 bers can be arranged to form a magic
and 10, repeated, the square can be square if they can be written in this
formed as shown. Any sixteen num- way, so that all the horizontal differ-

1 10

l~^10

8 3

12 11

9

5

16

4

14-

6

'7

'1

ences are alike and all the vertical

differences also alike. The differences

here are 3 and 2:

I 4 7 10

3 6 9 12

5 8 11 14

7 10 13 16

385. A MAGIC SQUARE DELUSION

If you make nine squares precisely

similar to this one and then place them

together to form a larger square, then

you can pick out a square of 25 cells

in any position and it will always be a

magic square, so it is obvious you can

arrange for any number you like to be

in the central cell. It is, in fact, what

is called a Nasik square (so named by

the late Mr. Frost after the place in

9

3

12

2.1

20

11

25

19

S

2-

(^18 5) :22
1 14<i^16
(^1) 2~ 10
IS 11 4
(^24 6) I?>
India where he resided), and it is only can be treated in the manner de-
perfect squares of this character that scribed.

386. DIFFERENCE SQUARES

The three examples I give are, I believe, the only cases possible. The differ-
ence throughout is 5.

(^2 1 4) S 1 4 2 1 6
?, 5 7 3 S 1 3 5 '1
6 9 S 6 9 2. -it 9 S