The daily telegram. [volume] (Clarksburg, W. Va.) 1901-1926, 1906-11-20
I'M FIGUREs
MANY uNsoLvED MYSTERIES IN THE
WORLD OF NUMBERS.


Little Things the Conditions OF
which child Can Understand
though the Greatest Minds Cannot
oTasteP Magic Squares.
Probing into the secrets of nature is
n passion with all men, only we seiect
different lines of research Men nave
spent long lives in such attempts US
To turn the baser metals into gold, to
discover perpetual motion. to ma d
cure for certain malignant diseases to
ravirote the air. Some great mys-
tories have after centuries of patient
labor been completely solved, Others
are Mt present under investigation
while many have been demonstrated to
he quite impossible of solution.
let ms examine n few cases of un-
solved mysteries In the world of num-
,ers-little things the conditions OF
which a child can understand, though
the greatest minds cannot master. EN-
.sr-ybody has heard the remaSk, 1T Is
MS hard as sauariug the circle" though
many people have very hozy notion
Of what 1t means. 1t is this: If you
have a circular piece of paper. how are
YOU to cut out another piece in the
form of n square that shall contain
exactly the same area? Well, 1T can
not be done with eXactitude. 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 it 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
" in numbers the diagonal of square.
If you have window pane exactly Il
foot on each side, there is the distance
from corner to corner staring you IN
the face, yet you can never say in eX-
act numbers what is the length of that
diagonal. The novice will at once sug-
past that we might take our diagonal
first. saw an exnct 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 It which way you like, but
you cannot have 1t both ways
But let us tplSe a 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, II lie happens to be fond OF hg-
tIring. First. then. take the round table
problem. Nine persons are stopping at
boarding house. and they all sit down
together to dinner on twenty-eight sue
cessIve nights at round table. The
rule of the house is that no person shall
on any two occasions have the two
same nelghbors. How IS 1t to be done,
II at all?
Here is another poser. II we write
,5o,,y,, tho number comDosrd of seven
teen ones-11, III, III Ill Ill = AMI
ask you to find some numbcr-other
than / or the number itselr-tllat Will
divide 1t without remainder. the an
sver will give you considerable labor
tn discover, We viii, however. say at
once that the only numbers that viii
divide it are 2,oT1, 723 and 5,3G3,222.-
RI. Now add two more ones to the
number, and we cannot tell you wheth-
or IL can be exactly divided by any
number or not for nobody knows. II
Won can lind such n divisor you Will
hPye done something that nobody else
In the world has yet succeeded In do
ing. And we cannot say that it is Inn
possible.
every one knows what magic
square Is. Divide a square into nine
divisions, or cells, and then place the
numbers / to 0, one number In each
cen. SO that they shall add up fifteen
| in every column, every row and in each
Of the two diagonals. It is quite easy,
and there is only one way Of doing 1t,
because we do not count as different the
arrnnRements obtained by merely turn
ing around the square and rejecting It
in mirror.
now. il we wish to make a magic