536 Puzzles and Curious Problems

Combinatorial & Topological Problems

384. AN IRREGULAR MAGIC SQUARE

Here we have a perfect magic square
composed of the numbers I to 16 in-
clusive. The rows, columns, and two
long diagonals all add up 34. Now,
supposing you were forbidden to use
the two numbers 2 and 15, but
allowed, in their place, to repeat any
two numbers already used, how would
you construct your square so that
rows, columns, and diagonals should
still add up 34? Your success will de-

1 14 I lZ

IS 4 9 6

10 5 16 3

8 11 2-^13

pend on which two numbers you select

as substitutes for the 2 and 15.

385. A MAGIC SQUARE DELUSION
     Here is a magic square of the fifth people who have not gone very pro-
     order. I have found that a great many foundly into these things believe that

17 2.4^1

20 5 7

4 6 1~

10 12, 19

11 18 25

B

14

20

2.1

2-

15

16

22

3

9

141

the central number in all squares of

this order must be 13. One corre-

spondent who had devoted years to

amusing himself with this particular

square was astounded when I told

him that any number from I to 25

might be in the center. I will show

that this is so. Try to form such a

magic square with I in the central cell.