142 Combinatorial & Topological Problems
- DIFFERENCE SQUARES
(^4 3 2)
7 1 9
6 5 8
Can you rearrange the nine digits
in the square so that in all the eight
directions the difference between one
of the digits and the sum of the re-
maining two shall always be the same?
In the example shown it will be found
that all the rows and columns give
the difference 3; (thus 4 + 2 - 3, and
I + 9 - 7, and 6 + 5 - 8, etc.), but
the two diagonals are wrong, because
8 - (4 + I) and 6 - (I + 2) is not
allowed: the sum of two must not be
taken from the single digit, but the
single digit from the sum. How many
solutions are there?
- SWASTIKA MAGIC SQUARE
A correspondent sent me this little
curiosity. It is a magic square, the
rows, columns, and two diagonals all
adding up 65, and all the prime num-
bers that occur between I and 25
(viz., 1,2,3,5,7, II, 13, 17, 19,23) are
to be found within the swastika ex-
cept II. "This number," he says, "in
occult lore is ominous and is asso-
ciated with the eleven Curses of Ebal,
so it is just as well it does not come
into this potent charm of good
fortune."
He is clearly under the impression
that II cannot be got into the swastika
with the other primes. But in this he
is wrong, and the reader may like to
try to reconstruct the square so that
the swastika contains all the ten prime
numbers and yet forms a correct
magic square, for it is quite possible.8 t.2
16 15
- IS IT VERY EASY?
Here is a simple magic square, the three columns, three rows, and two
diagonals adding up 72. The puzzle is to convert it into a multiplying magic