The Worthington advance. [volume] (Worthington, Minn.) 1874-1908, 1897-08-26
FR;llEA KS OF Flou REs.

FREAKS OF FIGURES.
sPussles for s.Those VINE Find Thena,
ssIilterestinE. is
Who has not. at some period Of his
existence, been asked: IF q goose
weighs ten pounds and q half its own
weight, what Is the weight Of the.
goose ~ And who has not been tempt
ed to reply on the. instant, IS pounds.
The correct answer being, Of course, 20
pounds. Indeed, It ID astonishing what
e very simple query will sometimes
catch q wise man mapping. Even the fol-
lowing have been known to succeed:
How many days would it take to cut
up 9 piece ofcloth SO yards long, one
yard being cut OF every day?"
Or again. 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 of the post"
Or again: "A wise man having 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 ynrdswide. How was this
done 2? This is a-eatch question in ge-
ometry, as the preceding were catch
questions in sarithmetic-the 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 50 days, but
40; and to the second, not 20 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. 49,. -.ss5.ssg 4
81 A very curious number is 142,S57,
which, multiplied by !, 2, 3, 4, $ or g.,
gives the same figures in the same or
der, beginning at different point, but
if multiplied by z it gives all mines:
multiplied by / it equals AZ, S57; multi
piled by it equals 2s5,714; multiplied
by 8, equals 42s,751; multiplied by 4,
equals. 81, 42s; multiplied by $, equals
T14,265; multiplied by 6, equals 857,142;
multiplied by 2, equals 999 1899; multi
ply 142,857 by 8, and you have 1,142,s56.
Then add the first figure to the last and
you have 142,857-the original num-
Der, the figures exactly the same as at
the start. ."
The number 81 has this strange Pc
culiarity: Multiply by 3,or any multiple
of three, up to ~, it gives three figures
all alike. Thus times 81 will be III;
twice times Is times) 81 will be 222:
3 times 3 times 70 times) 81 gives three
threes; four times three times (12
times) 81, three fours; and so on.
The wonderful provocative power Of
rather, their ,accumulative
growth-has been exemplified in the ia
miliar story of the farmer undertaking
to pay his farrier 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 will 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 turn. ...
You don't think that difficult prob
lem! Well, you. may be clever math-
ematician, but it would take you about
quarter of century to work out this
simple little sum. The final product
called for contains 1859 figures, the
first of which are LAP. Allowing three
figures to an inch, the answer would be
over 1910 feet long. To perform the OPP
Grafton would require about 100000, 900
figures. If they can be made at the
rate of one minute, person working
at the rate of ten hours a day for 800
days in each year would be % years
about it. If, in multiplying, he should
1nake row of ciphers, as he does in
other figures, the number of figures
would be more than $50, 1885, 1928. This
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 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
Stunning that the cipher is used on an
average once in ten times, 5000, 000,-
900 approximates the actual number
Brooklyn Eagle.