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solving Archimedes' Lab™ Puzzles! 


Puzzle
#105 


Cows
and Chickens...
Knowing that 30 cows and 30 chickens graze off all the grass of a
meadow in 60 days and that 70 cows and 70 chickens could do the same job in only
24 days, how many cows and chickens are needed to clear this meadow in 96 days?
Remember, the grass grows continuously...


(Cow
and Chicken © David Feiss) 

The
initial quantity of grass of
the meadow (in square units): P
Amount of grass (in square units)
growing per day: k
One cow and one chicken eat in
one day:
a) (P + 60k)/30·60
b) (P + 24k)/70·24
c) (P + 96k)/96x
Since:
(P + 60k)/30·60
=
(P + 24k)/70·24
Then:
480k = P
Replacing
the value of P in the following
equation, we obtain:
(480k + 24k)/70·24
=
(480k + 96k)/96x
and... x = 20
20 pairs of animals are needed
to clear the meadow.
An
interesting formula
If Q denotes the
number of pairs of animals and d is
the number of days to clear the
meadow, then the general formula
is:
Q = (4800/d +
10)/3
When d is 60, Q is 30;
when d is 24, Q is 70;
when d is 96, Q is 20...


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Wunderkammer
#15: Perelman 



"Education
is not the filling of a pail,
but the lighting of a fire."
 William Butler Yeats
Our
preferred Russian Math Authors:
Yakov Isidorovich Perelman (18821942)
Yakov
I. Perelman was a JewishRussian
author of many popular science books.
Works include "Physics
Can Be Fun" and "Mathematics
Can Be Fun" (both translated
from Russian into English). His father
died when he was just one year old
and the responsibility for the children’s
education fell on mother’s
shoulders and she did well to educate
her sons despite her calamitous circumstances.
Perelman’s activity in popularizing science began at school
when in September 1899 he published an essay entitled "Concerning the fiery
rain being expected" in the newspaper Grodneriskiye guberniskiye vedomostyunder
the pseudonym "Y. P." The widely spread rumors about the advent of
Doomsday  with the exact date even fixed as 1st November  were the reasons
for his publication. The “star rain” destroying everything had to
come down upon the Earth as prophets said, exactly on that day. Perelman decided
to try to explain the forthcoming phenomenon and expose the prophets. Drawing
upon historical scientific data Perelman told his readers about the Leonids meteorite
showers which regularly visited the Earth and concluded that the "fiery
rain" was a regular natural phenomena posing no danger to the citizens of
Earth.
The publication
of this article inspired Yakov to study
more and on leaving school he enrolled
in the St Petersburg Forestry Institute
in August 1900, which in addition to
specialist studies provided an excellent
higher education, affording Perelman
exposure to advanced studies in Physics
and Mathematics. However paying for this
education was a struggle for Yakov for
by this time his mother was ill and could
not support him as before, so the young
man decided to try his hand at journalism,
publishing an article called “The
Century of Asteroids” in Nature
and People in 1901 again using his "Y.
P." nom de plume.
In July 1913 the first part of Perelman’s book "Entertaining
Physics" was published and was not only a stunning publishing success but
provoked also the interest of other physicists.
Perelman contributed to Nature and People in total for 17 years publishing
over 500 articles. Thanks to him, collections of short stories entitled "The
World of Adventure" appeared as a free and very popular supplement to the
journal from 1910 until 1928 including works by writers in English such as Wells,
Conan Doyle and Poe.
After the October Socialist Revolution Nature and People was closed
down and Perelman devoted his energies to teaching, being accepted as an inspector
at a Department of United Labour School in February 1918. Here he worked on new
textbooks and learning programmes on physics, maths, and astronomy teaching these
subjects in various different educational establishments at the same time.
Then an idea to establish the first Soviet scientificpopular journal
came to him since all the preRevolutionary ones had ceased publication. So in
the Spring of 1919 the new "In Nature’s Workshop" appeared and
he continued to edit this until 1929, publishing the work of many remarkable
scientists.
During the World War II, Perelman read dozen of lectures to soldiers
and sailors working on themes which could be of practical help in warfare.
However the strengths of a now elderly man were gradually depleting
by the hunger and cold of blockaded Leningrad and his wife Anna died in January
1942 from exhaustion whilst on duty at the hospital. Yakov outlived his wife
only for a further two months dying of hunger on 16th March 1942 in the besieged
city.
Despite his death, his books continued to be read and have been republished
over 300 times reaching nearly 15 billion copies in Russia alone! They have been
translated into many languages such as German, French, English, in fact most
European languages.
Yakov Isidorovich Perelman didn’t invent nor did he discover
anything in the Scientific or Technical area  he had no scientific title or
degree, but was devoted to science and brought the joy of science to the people
for over four decades.
Related Book 

The
Chicken from Minsk
Yuri
Cherniak, Robert Rose
The 99 brainy and infuriatingly
funtosolve problems that have
kept the best Russian math and
physics students biting their
pencils as far back as the time
of the czars...


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ORIGINAL Wunderkammer fact 





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•••
Smile!
According to George Gobol, if
it weren't for electricity we'd all be watching television
by candlelight.
•••
Math
Gems
(111+1)/(1+1)=56
(222+2)/(2+2)=56
(333+3)/(3+3)=56
...
(999+9)/(9+9)=56
•••


