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corner top left Previous Puzzles of the Month + Solutions  
October-November 2003  

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logo puzzle of the month 1 Puzzle #92
Quiz/test #2 logo pzm 2
logo pzm 3 W-kammer #2
   Enjoy solving Archimedes' Lab™ Puzzles!

Solution
to puzzle #92
Send us your comments on this puzzle
Prove empirically (without measuring or cutting) that Area of square A = Area of rectangle B puzzle 92
francais/italiano


Report rectangle B on a vertex of square A as shown, and draw lines to extend the sides of both quadrilaterals to form a larger rectangle R whose height is the sum of the heights of A and B, and whose width is the sum of the widths of A and B.
If the diagonal connecting the corners of R that are not touched by A and B goes through the point where A and B meet, they have the same area.
For more info see "Visual proof", April 2001.
solution puzzle 92
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Quiz #2
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Test your math knowledges online
1. N is an integer, then N2 - N is... 2. Place the operational signs x, +, : or - between the 3s to make the identity true. 3. This exclamation has unexpectedly _ "s", _ "i", _ "x" !!! (complete)
a) divisible by 2
b) a prime
c) odd number
complete
a) 3, 3, 2
b) 6, 6, 6
c) 3, 2, 1

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Puzzle #3, logic, by Kh. Guili
Why is it very common to have a 9 minute snooze interval on alarm clocks and not 10 instead?
Rate: •• Solution #3

Puzzle #4, logic, by Augusto P.
50 ants are dropped on a 2-meter stick. Each one of them is traveling either to the left or to the right with constant speed of 1 meter per 1/2 minute. When 2 ants meet, they bounce off each other and reverse direction. When an ant reaches an end of the stick, it falls off. What is the longest amount of time to wait that the stick has no more ants?
Rate: •• Solution #4

Wunderkammer #2
Puzzling facts

early square root symbolsThe Radical Symbol
A square root of x is a number r such that r2 = x. Square roots are also called radicals or surds. Any positive real number has two square roots: one positive and one negative. For example, the square roots of 9 are 3 or -3.
Before symbols, the words "roots" or "side" were commonly used for the square root of a number. Arab writers thought of a square number as growing out of a root, so Arabs often used the word radix, "extracting", or pulling out, the root. Latin writers thought of it as "finding" the latus, or side of a square.
Late medieval Latin writers turned radix into a single symbol Rx. This symbol was introduced by Leonardo Fibonacci (1170) and was used for more than two hundred years. The French writer Nicolas Chuquet (1484) sometimes used Rx2 for Rx, Rx3 and Rx4 for cube and fourth roots, respectively.
The symbol square root was introduced by Christoff Rudolff in 1525 in his book Die Coss (the reason for this strange book title is that cosa, an Italian word, is a thing which was used for the unknown. Algebraists were called "cossists", and algebra the "cossic art", for many years!). It is believed this symbol was used because it resembled a small r (radix) at the time.
Rudolff's symbol was not immediately used. The letter l (latus, "side") was often used. For example the square root of 4 was l4 and the third root of 5 was lc5. By the seventeenth century, the square root symbol was being used regularly even though there were many ways the indices were written for higher roots.
To conclude, here are some abbreviations in use in the XVth century for the various powers of the unknown, namely:
"cosa" = r (= x),
"censo" = c (= x2),
"cubo" = b (= x3),
"censo di censo" = cc (= x4),
"cubo relato cosa" = br (= x5),
and "cubo di cubo cosa" = bb (= x6).

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•••
Month's Quotes

Life looks like 2 locked boxes, each containing the others key...
•••

"Always live within your income, even if you
have to borrow money to do so."
Josh Billings
•••

Math Gems

(1+5)/2 =1.618...
Golden number
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