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Previous Puzzles of the Month + Solutions
December 2003-January 2004

 Puzzle #93 Quiz/test #3 W-kammer #3
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Solution
to puzzle #93
 Send us your comments on this puzzle
Prove empirically (without measuring or superimposing any shape on the other one) that Area of curvilinear shape A = Area of cross-shaped figure B
click to enlarge
 The curvilinear shape (A) is equidecomposable to 2 squares and the cross-shaped figure (B) to a larger square. We can then demonstrate thanks to the Pythagorean Theorem that they are of the same area, as shown in the figure below. During this operation no pieces are superimposed nor placed side by side! See also the neat solution sent by Micheal Baldus.
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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 reflection... 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... Oct-Nov 2003: square vs rectangle

Quiz #3
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 Test your math knowledges online 1. I buy a watch for 100 \$, then I sell it at 120 \$. I repurchase my watch for 140 \$ and, finally, I sell it again at 160 \$. How much did I earn? 2. The area of a square of 100 is equal to 2 smaller squares. The side of one is 1/2+1/4 the side of the other. Find the side of both squares... 3. 80% of 125% is... a) 30 \$ b) 10 \$ c) 40 \$ complete a) 100% b) 95% c) 105%

 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
 Submit a puzzle
 Puzzle #1, logic, by G. Kan Is it cheaper to invite (assuming you are paying...) one friend to the movies twice, or two friends to the movie at the same time? Rate: ••• Solution #1 Puzzle #2, logic, by Theresa Walt During a racing, you passes the runner who is in the second place. Then, what is now your current rank? Rate: •• Solution #2

Wunderkammer #3
 Puzzling facts

Wasan puzzles
During the Edo period (l603-1867), when Japan was almost completely cut off from the western world, a distinctive style of mathematics, called Wasan (和算; "native Japanese mathematics" in contrast to yosan, "Western mathematics"), was developed.
Results and theorems were originally displayed in the form of problems, sometimes with answers but with no solutions, inscribed on wooden boards and accompanied by beautiful coloured figures. These problems dealt predominantly with Euclidian geometry and, true to wasan preferences, mostly dealt with circles and ellipses.
These boards (see an example below), known as Sangaku (算額; "mathematical tablet"), were hung under the eaves in shrines and temples. Later, books appeared, either handwritten or printed from hand-carved wooden blocks, containing collections of sangaku problems with solutions. The earliest known Sangaku tablet was created in 1683.
The samurai remained the dominant creators of sangaku, consistent with their status of the educated and artistic caste in Japan.  A majority of sangaku are inscribed in Kambun (漢文), an archaic Japanese dialect related to Chinese. Kambun was the equivalent of Latin in Europe, used during the Edo period for scientific works and known predominantly by only the most educated castes.

 A sangaku tablet and some typical problems
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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!
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