All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Rectangle Color Rigor (Posted on 2014-09-23) Difficulty: 3 of 5
Some unit squares on an infinite sheet of squared paper are colored green such that:

Every 2x3 rectangle contains precisely two green squares, and:
Every 3x2 rectangle contains exactly two green squares.

How many green squares are there in a 9x11 rectangle?

*** Based on a Russian Math Olympiad problem.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution a diagram | Comment 3 of 4 |
The below pattern follows the rules of formation, is 9x11 and has 33 green (g) squares. It can be seen that the pattern can continue indefinitely beyond the bounds of the shown rectangle and still fill the conditions.

Also when shifted to the right or left the same number of g squares replace the ones disappearing on the trailing edge.

+---+---+---+---+---+---+---+---+---+---+---+
| g |   |   | g |   |   | g |   |   | g |   |
+---+---+---+---+---+---+---+---+---+---+---+
|   |   | g |   |   | g |   |   | g |   |   |
+---+---+---+---+---+---+---+---+---+---+---+
|   | g |   |   | g |   |   | g |   |   | g |
+---+---+---+---+---+---+---+---+---+---+---+
| g |   |   | g |   |   | g |   |   | g |   |
+---+---+---+---+---+---+---+---+---+---+---+
|   |   | g |   |   | g |   |   | g |   |   |
+---+---+---+---+---+---+---+---+---+---+---+
|   | g |   |   | g |   |   | g |   |   | g |
+---+---+---+---+---+---+---+---+---+---+---+
| g |   |   | g |   |   | g |   |   | g |   |
+---+---+---+---+---+---+---+---+---+---+---+
|   |   | g |   |   | g |   |   | g |   |   |
+---+---+---+---+---+---+---+---+---+---+---+
|   | g |   |   | g |   |   | g |   |   | g |
+---+---+---+---+---+---+---+---+---+---+---+


  Posted by Charlie on 2014-09-23 12:37:28
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information