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Previous Puzzles of the Month + Solutions
October-November 2003

 Puzzle #92 Quiz/test #2 W-kammer #2
Enjoy solving Archimedes' Lab™ Puzzles!

Solution
to puzzle #92
Prove empirically (without measuring or cutting) that Area of square A = Area of rectangle B

 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.
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Previous puzzles of the month...

 August 98: the irritating 9-piece puzzle September 98: the impossible squarings October 98: the multi-purpose hexagon November 98: the incredible Pythagora's theorem December 98: the cunning areas January 99: less is more, a square root problem February 99: another square root problem... March 99: permutation problem... April 99: minimal dissections July 99: jigsaw puzzle August 99: logic? Schmlogic... September 99: hexagon to disc... Oct-Nov 99: curved shapes to square... Dec-Jan 00: rhombus puzzle... February 00: Cheeta tessellating puzzle... March 00: triangular differences... Apr-May 00: 3 smart discs in 1... July 00: Funny tetrahedrons... August 00: Drawned by numbers... September 00: Leonardo's puzzle... Oct-Nov 00: Syntemachion puzzle... Dec-Jan 01: how many squares... February 01: some path problems... March 01: 4D diagonal... April 01: visual proof... May 01: question of recflection... June 01: slice the square cake... July 01: every dog has 3 tails... Aug 01: closed or open... Sept 01: a cup of T... Oct 01: crank calculator... Nov 01: binary art... Dec 01-Jan 02: egyptian architecture... Feb 02: true or false... March 02: enigmatic solids... Apr 02: just numbers... May 02: labyrinthine ways... June 02: rectangle to cross... July-Aug 02: shaved or not... Sept 02: Kangaroo cutting... Oct 02: Improbable solid... Dec-Jan 03: Hands-on geometry Feb-Mar 03: Elementary my dear... Apr-May 03: Granitic thoughts June-July 03: Bagels... September 03: Larger perimeter...

Quiz #2
 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

 Everyone has at least one logic or math puzzle that is his or her favorite. Send us yours and let all our readers enjoy them!

Posted puzzles
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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
 The 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 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). Suggest an ORIGINAL Wunderkammer fact

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 ARCHIMEDES is an interactive review devoted to entertaining and involving its readers with puzzles, recreational mathematics and visual creativity. More info...
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 Everyone has at least one logic or math puzzle that is his or her favorite. Send us yours and let all our readers enjoy them!
 ••• 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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