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

Home > Shapes
Union of squares (Posted on 2014-07-09) Difficulty: 3 of 5
For what number of non-overlapping unit squares can a figure be formed whose perimeter is numerically equal to the area?

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

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution re: Partial solution - another part | Comment 4 of 10 |
(In reply to Partial solution by tomarken)

Right after posting I realized that an odd number can't be possible.  Consider a single unit square.  Its perimeter is 4.  If we append another square, we are adding 4 sides to the total perimeter, minus 2x however many sides it's touching.  This will always be the case, so the perimeter of the resulting shape will always be even, and thus the area must also be even.  So we can never make a shape satisfying the conditions of the puzzle with an odd number of unit squares.

  Posted by tomarken on 2014-07-09 12:15:47

Please log in:
Remember me:
Sign up! | Forgot password

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

Copyright © 2002 - 2020 by Animus Pactum Consulting. All rights reserved. Privacy Information