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Previous Puzzles of the Month + Solutions

February - March 2006  

thinking man
logo puzzle of the month 1 Puzzle #105
Quiz/test #15 logo pzm 2
logo pzm 3 W-kammer #15
   Enjoy solving Archimedes' Lab™ Puzzles!

triangle-square 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
(Cow and Chicken © David Feiss)

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meadowThe 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

(P + 60k)/30·60 =
(P + 24k)/70·24
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...

Previous puzzles of the month...
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circle-triangle Quiz/Test #15 TOP
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Numbers and Spellings
Which number is spelled with 15 letters? Which number is spelled with 25 letters? In which singular word ‘okc’ occurs once?
the number is
the number is

Wunderkammer #15: Perelman TOP
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"Education is not the filling of a pail,
but the lighting of a fire.

- William Butler Yeats

Our preferred Russian Math Authors:
Perelman yakov isidorovich
Yakov Isidorovich Perelman (1882-1942)

yakov perelman  Yakov I. Perelman was a Jewish-Russian 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 scientific-popular journal came to him since all the pre-Revolutionary 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.

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