Shortcuts

 Sitemap Contact Newsletter Store Books Features Gallery E-cards Games

•••

 Related links Puzzles workshops for schools & museums. Editorial content and syndication puzzles for the media, editors & publishers. Numbers, just numbers... Have a Math question? Ask Dr. Math!
•••

 ••• •••

•••

 Smile! "Everything has an end -- except a sausage, which has two" "Tout a une fin, sauf le saucisson qui en a deux" "Tutto ha una fine, tranne la salsiccia che ne ha due" -- Danish quote
•••

 ••• •••

Previous Puzzles of the Month + Solutions

April - May 2010, Puzzle 124
Back to Puzzle-of-the-Month page | Home
Puzzle # 124

A chopping problem

Using the checkered pattern as a guide, cut out the board below into 7 rectangular pieces so that no piece can contain another one (for instance, a 6x8 rectangle completely covers a 4x7 rectangle).

Difficulty level: , basic geometry knowledge.
Category: dividing-the-plane puzzle.
Keywords: dissection, tiling, rectangles.
Related puzzles:
- Squared strip,
- Triangles to square.

 Français

Source of the puzzle:
You cannot reproduce any part of this page without prior written permission.
 So, each of the 7 rectangles should have one side WIDER and one side SHORTER to each other rectangle, so that neither of the rectangles can be placed inside the other one in such a way that corresponding sides are parallel. Since we have to find 7 rectangles that tile a 22 x 13 units2 rectangle, we will proceed empirically as follows: Rectangle 1: 1 x ... units2 Rectangle 2: 2 x ... units2 Rectangle 3: 3 x ... units2 Rectangle 4: 4 x ... units2 Rectangle 5: 5 x ... units2 Rectangle 6: 6 x ... units2 Rectangle 7: 7 x ... units2 Rectangle 1 should have the widest surface since it has the shortest height; however, the possible dimensions 1 x 22 and 1 x 21 should be discarted [any rectangle with sides n ≤ 13 x (22 - 21) would fit inside the latter one]... Then, proceeding by trial and error we obtain the following tiling: 1 x 18 2 x 16 3 x 13 4 x 11 5 x 10 6 x 9 7 x 7 (see image below) Aside from rotations and reflections this tiling of rectangles is unique The 5 Winners of the Puzzle of the Month are: Herbert Jones, USA - Charles F. Espenlaub, USA - Cesco Reale, Italy - Muhammad Afifi, Egypt - Martin Rick, South Africa Congratulations!
 Math fact behind the puzzle Incomparable Rectangles Two rectangles, neither of which will fit inside the other, are said to be 'incomparable' (this is equivalent to one rectangle being both longer and narrower). The minimum possible number of incomparable rectangles needed to tile a larger rectangle is 7. © 2006 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. Thanks!
 Previous puzzles of the month...
 Oct-Nov 09: The Mark of Zorro July-Sept 09: radiolarian's shell May-June 09: circle vs square Jan-Feb 09: geometric mouse Sept-Oct 08: perpendicular or not... July-Aug 08: ratio of triangles May-June 08: geometry of the bees Febr-March 08: parrot sequence... Dec 07-Jan 08: probable birthdates? Oct-Nov 2007: infinite beetle path Aug-Sept 07: indecisive triangle June-July 07: Achtung Minen! April-May 07: soccer balls Febr-March 07: prof Gibbus' angle Jan 07: triangles to square Aug-Sept 2006: 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 2005: magic star July-Aug 05: cheese! Puzzle Archive
Back to Puzzle-of-the-Month page | Home