Evening journal., 1897-09-01
FREAKS OF FIGURES.
rnrzles for Taosc who Find Them
Interesting.

Who has not, at some period of his |
existence, been asked: "If a goose |
weighs ten pounds and half its own |
weight. what is the weight Of the
goose?" And who has not bgen tempt |
ed to reply on the instant, IS pounds.
The correct answer being, Of course, 20 !
pounds Indeed, il is astonishing what |
a very simple query win sometimes
catch a wise man mapping. Even the fol-
lowing have been known to succeed:
How many days would it take to cut
up piece Of cloth so yards long, one
yard being cut OF every day?"
Or again. "A snail climbing up q
post 20 feet high ascends five feet
every day and slips down four feet
every night; how long will the snail
take to reach the top CT the post?"
Or again "A wise nan having q win
dow one yard high and one yard wide,
and, requiring more light. enlarged the
window to twice its former size; yet the
window was still only one yard high
and one yard wide How was this
done?" This is catch question in ge
ometry, as the preceding were catch
questions in arithmetic-th window
being diamond shaped at first and aft
erward made square.
As to the two former, it is scarcely
necessary seriously to point out that The
the answer to the first is not so days, but
40; and to the second, not 90 days. but
16-since the snail, who gains one foot
each day for IS days, climbs on the
sixteenth day on the top of the pole and
there remains.
A very curious number is 142,s57,
which, multiplied by /, 2, 3, 4. 8 or G,
gives the same figures in the same or
der, beginning at different point, but
if multiplied by it gives all mines;
multiplied by ii equals 142, ,s57; multi
piled by it equals 2s5,714; multiplied
by 3. equals 42s,751; multiplied by 4,
equals 571 ,42s; multiplied by 5, equals
714,2S5; multiplied by 6, equals s57,142;
multiplied by z, equals 100000; multi
ply 142, s57 by s, and you have 1,142,s56.
Then add the first figure to the last and
you have 142,s57-the original num-
ber, the figures exactly the same as at
the start.
The number 81 has this strange pc
culiarity: Multiply by S,orany multiple
of three up to 27. it gives three figures
all alike. Thus 3 times 81 will be III;
twice times 6 times) 81 will be 222;
3 times 3 times @ times) 81 gives three
threes; four times three times C2
times) 81, three fours and so on.
The wonderful provocative power OF
figures-or, rather, their accumulative
growth-has been exemplifed in the IA
miliar story of the farmer undertaking
TO pay his farricr one grain of wheat
for the first nail, two for the second, and
so on, and found that he had bargained
TO give the farrier more wheat than was
grown in all England.
Here is another example, Take the
number IS. we viii say; multiply that
by itself, and you get 225 Now multi
ply 225 by itself, and so on until IS prod
ucts have been multiplied by them
selves in tern.
You don't think that a difficult prob
lem! Wen, you may be a clever math-
cmatician, but it would take You about
quarter of a century 30 work out this
simple little sum. The final product
called for contains 3s,5s9 figures, the
first Of which are ], ,442. Allowing three
/ figures to an inch, the answer would be
over 1,07O feet long. To perform the op-
Grafton would require about 50o,0O0,000
figures. If they can be made at the
rate of one q minute, person working
at the rate of ten hours day for 300
days In each year would be 2S years
about it. If, in multiplying, he should
make a row of ciphers, as he does in
other figures, the number of figures
would be moro than 523,939,22s. Thu
would be the precise number Of figures
used if the product of the left hand fig
ure in each multiplicand by each fig
ure of the multiplier was always a sin
gle figure; but. as is most frequent,and
yet not always two figures, the method
employed TO obtain the foregoing re
suit cannot be accurately applied. As
suming that the cipher is used on al
average once in ten times, 475,oO0,0oO,
600 arproNimates the actual number
Brooklyn Eagle.