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Puzzle 117.  TILES

Ryan has a set of square tiles which he arranged to form a large square.  His friend Tom came and rearrange those tiles to form fours smaller squares having different areas.  If Ryan does not have more than 100 tiles, how many tiles does he have.  If the length of the side of each tile is 1 inch, what are the areas of the four squares that Tom formed?

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Bits and Beyond...


Ranè Descartes (1596-1650) was a 17th century French philosopher and  mathematician.  He received his education in mathematics, classics, and law at La Flèche and Poitiers.  After a brief service in the military, he settled in Holland where he made significant contributions to the field of Algebra, Analytic Geometry, and Calculus.  The commonly used Cartesian Coordinate System was named after him.  His work, La géométrie, includes his contributions to algebra and geometry.


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