Gainesville daily sun. (Gainesville, Fla.) 190?-1938, 1906-12-09

Master Magic Squares.
Probing into the secrets Of nature Is
passion with ell men, only we select
Inherent lines Of research. Men have
spent long lives IN such attempts as
10 turn the baser metals into gold, to
discover perpetual notion to End a
cure for certain malignant diseases, to
navigate the air. Some great mys-
torles have after centuries Of patient
labor been completely solved, others
are at 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 little things the conditions Of
which child can understand, though
tie greatest minds cannot master. Ev-
grybody has heard the remark, 1T Is
Is hard as squaring the circle" though
many people have very hazy notion
~ what II means. II Is thlsl If you
have a circular piece OF paper. how are
sou 10 cut out another piece In the
form OF square that shall contain
exactly the same areaY Well, II can
not be done with exactltude, though we
can get an answer near enough for all
practical purposes. because II is not
possible 20 say In exact numbers what
u the proportion OF the diameter to
the circumference. But II IL only IN
recent times that II has been proved
10 be impossible Only cranks now
waste their time in trying to solve this
venerable puzzle.
Again. we can never measure exact.
" ~ numbers the diagonal OF square.
N you have a window pane exactly
foot on each side, there IL the distance
from corner 10 corner staring you In
The face yet you can never say IN ex.
net numbers what Is the length OF that
diagonal The novice will at once sug.
geut that we might take our diagonal
hrst, sny en- exact foot, and then con.
etrnct our square Yes. you can do
ihls, but then you can never say exact.
n what n the length OF the side. You
can have Il which way you like, but
you cannot have It both ways,
But let Ne take few puzzles that
have not been proved 10 he impossible.
but which nevertheless have not been
solved, They will give the reader some
fasc' ng employment during spare
hour. { he happens 20 be fond OF lg-
urlnR First. then, take the round table
problem. Nine persons are stopping az
3 boarding house, aud they all slt down
together 60 dinner on twenty eight sue
cesslye nights az a round table. The
rule % the house h that no person shall
on any two occasions have the two
same nelghbors. How IL Il 10 bc done
n az alll
Hcrc h another poser II we write
down the number. composed OF seven
teen s--ii.iii.iil.lii,ili,lii - AMI
ask you 20 hnd some number other
than I os the number iiselr-that will
divide Il without remainder, the an.
aWer will give you considerable labor
20 discover We will however. say az
once that the only numbers that viii
divide 4 are 2,0Il.T2S and a.aCti222,.
ah1 Now ada two more ones 60 tho
number, and We cannot ten you wheth
er Il can Dc exactly divided by any
nnniber OF not. Tor nehody knows. n
you can hnd such n dlylsor you will
have done something that nobody else
n the world has yet succeeded IN DO
ing And We cannot say that Il b TN.
possible.
Every one Knows what magic
square h. Divide a square into nine
divisions. or cells, aud then place the
numbers I 90 n ono number in each
cell. - that they shall add up nfteCn
N every column. every row and Ia each
- TIE two dlagonals h 10 quite easy.
aud there d only Que way % doing h.
because Ne DO not count a. different The
arrangements obtaincd ~ mervlT furn-
sag around the square and rehessihg Il
"a q mlrrOr
Nov. N Ne wish % make a magic
square % the sixteen numhey,. 10 IA
there are iust Sss1 diHercnt ways % 90
tng a. scain n0i coUutinE rcVersals ana
rcnectiols. Ths has bcen aually PRIV
"a % racant years. hus how mans
magle squares can - turuaei NlIh the
tNeny ave numbers, % - no'soiy
knows. ana Ne shall have % eNtend
cur knswie,lgt In certaln dlrsriiasas -
foFe NE can hape o. solve fhis psrtle
hat h 10 startling 90 sad that sNacil7
fft2to sUch sQuancs rasy - forutcd Qt
ohe parJicuisf kind only- tie ba'fdtrei
sQrare 'n which fhe Inner sQgare -
slne Qc.is b ,n itsrif n.aE.e Aud ne
ffFfens write tas EhFNa bfW tltk
49,