Sitemap Sitemap
Comment Contact
Newsletter Newsletter
Store Store
Syndication Features
Gallery Gallery
Games Games



corner top left

Previous Puzzles of the Month + Solutions

February-March 2007  
arrow back Back to Puzzle-of-the-Month page | Home arrow home


Difficulty level: bulbbulb, basic geometry knowledge.
Puzzle # 110
 Italiano italiano Français francais
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!)

puzzle 110


Someone sent us this funny solution...

fake solution

But, more seriously, the solution isn't as difficult as it appears... You have just to change your point of view (fig. 1)...

puzzle solution

... 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,
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...
puzzle solver
Puzzle Archive
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:

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

arrow back Back to Puzzle-of-the-Month page | Home arrow home

matemagica cover
MATEMAGICA Blackline masters for making over 25 funny math puzzles! A collection of incredible puzzles and optical illusions with easy-to-follow instructions (in Italian). Ideal for math workshops.
arrow More info...

Did you enjoy our puzzles and our optical illusions? You can find them every month in FOCUS Giochi magazine!

Focus Giochi

arrow More info...
Book of the Month

arrow More books...


"Please repeat this sentence once".
(if you really repeat it once, you'll in fact repeat it twice...)


Related links

Puzzles workshops for schools & museums.

Editorial content and syndication puzzles for the media, editors & publishers.

Puzzling visual illusions for everyone: beginners and experts as well!

Have a Math question?
Ask Dr. Math!
Archimedes Journal
ARCHIMEDES is an interactive review devoted to entertaining and involving its readers with puzzles, recreational mathematics and visual creativity.
archimedes review
arrow More info...
transparent gif
facebook Follow us on Facebook | comment Report any error, misspelling or dead link
Archimedes' Laboratory™ | How to contact us
| italian flag Come contattarci | francais flag Comment nous contacter
About Us | Sponsorship | Press-clippings | Cont@ct | ©opyrights | Link2us | Sitemap
© Archimedes' Lab | Privacy & Terms | The web's best resource for puzzling and mental activities
spacer spacer corner right bottom