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# Previous Puzzles of the Month + Solutions

February-March 2007
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Difficulty level: , basic geometry knowledge.
Puzzle # 110
Italiano Français
Prof. Gibbus' Angle

Help Prof. Gibbus find the angle a in the diagram below (solve this puzzle using just basic geometry, no sines or cosines allowed!)

 Someone sent us this funny solution... But, more seriously, the solution isn't as difficult as it appears... You have just to change your point of view (fig. 1)... ... and look beyond the boundaries of the problem (fig. 2), as suggested in our tips to puzzle solving. Actually, you can find the solution without any calculation! Just extend the grid and draw two lines as shown in the picture, and you'll form a right isosceles triangle having two opposite angles of 45 degrees. The base (or the hypothenuse) of the triangle is parallel to the diagonal (the red line in fig. 2) of the previous 1x3 rectangle. One leg of the right triangle 'intersects' both parallels. A transversal line which intersects a pair of parallel lines produces pairs of alternate interior angles which are EQUALS. So, angle a worths 45 degrees. The winner of the puzzle of the month is: John REIDY, Australia. Congratulations John! © 2002 G. Sarcone, www.archimedes-lab.org You can re-use content from Archimedes’ Lab on the ONLY condition that you provide credit to the authors (© G. Sarcone and/or M.-J. Waeber) and a link back to our site. You CANNOT reproduce the content of this page for commercial purposes. You're encouraged to expand and/or improve this article. Send your comments, feedback or suggestions to Gianni A. Sarcone.

Previous puzzles of the month...
 Jan 07: triangles to square Aug-Sept 06: balance problem June-July 06: squared strip Apr-May 06: intriguing probabilities Febr-March 06: cows & chickens Dec 05-Jan 06: red monad Sept-Oct 05: magic star July-Aug 05: cheese! May 05: stairs to square Febr 05: same pieces Sept-Oct 04: odd triangles June 04: pizza's pitfalls May 04: Pacioli puzzle... April 04: inscribed rectangle March 04: magic 4-T's Febr 04: a special box Dec-Jan 04: curvilinear shape... Oct-Nov 03: same area? well... Sept 03: square vs rectangle June 03: magic bagel

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