Daily press. [volume] (Newport News, Va.) 1896-current, 1906-11-22

Though the Grcntcst Minda Cannot
Master Magic Squares.
Probing into the secrets of nature is
II passion with all men, only we select
different lines OF research. Men have
spent long lives in such attempts us
10 turn the bascr metals into gold, to
discover perpetual motion, to find
cnrc for certain malignant diseases, to
navigate the air. Some great mys-
tcrics have after centuries of patient
labor been completely solved, others
are ut present under investigation.
while many have been demonstrated to
be quite impossible OF solution.
Let us examine a few cases of un-
solved mysteries in the world of num-
bcrs-littlc things the conditions Of
which n child cnn understand, though
the greatest minds cannot muster. Ev-
crybody hns heard the remark, at Is
us hard ms squarng the circle" though
many people have Il very hazy notion
Of what it means. 1t Is this: If you
have circular piece of paper, how are
you TO cut out another piece in the
form of square that shall contain
exactly the same urea? Well, 1t can
not lie done With cXactitudc, though we
can get an answer near enough for all
practical purposes. because 1t is not
possible TO say In exact numbers what
is the proportion of the diameter to
the circumference. But 1t Is only In
recent times that 1t has been proved
to be impossible. Only cranks now
waste their time in trying to solve this
venerable puzzle.
Again, we can never measure exact
ly IN numbers tho diagonal OF a square.
IL you have II window pane exactly n
foot on each side, there Is the distance
from corner to corner staring you In
the face. yet you can never say in cx-
net numbers what is the length of That
diagonal. The novice will at once sug-
gcst that we might take our diagonal
first. say an exact foot, and then con-
struct our square. Yes, you can do
this. but then YOU can never say exact
~ what Is the length OF the side. You
can have 1t which way You like, but
you cannot have it both ways.
But let us take q few puzzles that
have not been proved to be impossible,
but which nevertheless have not been
solved. They Will give the reader some
fascinating employment during spare
hours. If lie happens to be fond Of fig
uring. First, then, take the round table
problem. Nine persons are stopping ut
boarding house, and they all sit down
together to dinner on twcnty-eight sue
ccSSive nights mt round table. The
rule of the house is that no person shall
on any two occasions have the two
same ncIghbors. How Is 1t to be done.
IL at all?
Here is another poser. If we write
down the number. composed of seven
teen oncs-1l, 1,111.1 1,111.111 = and
ask you to find some number-othcr
than l or the number itself-that will
divide it without remainder, the an
swer will give YOU considerable labor
to discover We WILL however, shy Mt
once that the only numbers TINT will
divide II are 2,0Il.T23 and $500, 2o2.-
35I. Now add two more ones TO the
number, and we cannot tell you wheth-
err 1t can lie exactly divided by any
number or not. for nobody knows. IF
YOU can find such IL divisor you will
have done something that nobody else
In the world has yet succeeded in do.
Ing. And we cannot say that it Is i'm
possible.
Every one knows what magic
square is. Divide IL square into nine
divisions. Or cells, and then place the
numbers ! TO 0, one number in each
cell, SO that they shall add up fifteen
In every column, every row and in each
of the two diagonnls. 1t is quite easy,
and there Is only one way Of doing It.
because we do not count MS different the
arrangements obtained by merely turn
ing around the square and rejecting 1t
In q mirror
Now. if we wish to make magic
square of the ei1teen numbers, to 1G,
there are just $50 different ways of do
Ing 1t, again not counting reversals and
reflections. This has been finally prov
cd Of recent years. But how many
magic squares can he formed with the
twenty-five numbers. to %, nobody
knows, and we shall have to extend
our knowledge In certain directions be-
fore we can hope to solve this puzzle
But 1t Is startling to find that exactly
174.240 such squares may be formed of
one particular kind only-the bortlered
square, in which the inner square Of
nine cells is In itself magic And the
present writer has shown how this
number may ut once be doubled by
merely converting every bordercd
square by simple rule into a non
bordered one.
Vain attempts have been made to
construct a magic squire by what Is
cnlled knights tour" over the chess
board. numbering each square that tho