Puzzle of the Month, February 99

1) 3=7, a square root problem

(Click on the button below to begin)

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2) Square to smithereens...
• Two squares to one: cut the large darkgrey square shown in fig.a) below into 3 pieces (yes, three pieces), so that you obtain a bigger square when you reassemble its pieces with the small darkgrey square.
• A rectangle to two squares: cut the darkgrey rectangle shown in fig.b) into 4 pieces in order to form 2 squares with its pieces.

Print this page and make an enlarge copy of the diagrams shown in fig. a) and b). Then, try to solve the puzzle according to the terms above.

©96-99, Sarcone & Waeber, Lausanne

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Solutions

1) 3=7, a square root problem
Remember that the square root of any number has always 2 solutions: a positive, and also a negative one!
E.g.: the square root of 4 is +2 and -2. If you forget it, when resolving quadratic equations or identities, you may get paradoxical results, like 3 = 7 !

2) Solutions of the square cutouts

 

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