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

Home > Shapes
Touching polygons (Posted on 2013-02-27) Difficulty: 3 of 5
1a. What is the least number of identical squares that can be placed in a plane such that each shares a side with exactly two others?

1b. What is the least number of identical squares that can be placed in a plane such that each shares a side with at least one other and they form a contiguous region with no rotation or reflection symmetry?

1c. What is the least number of identical squares that can be placed in a plane such that each shares a side with exactly two others and they form a contiguous region with no rotation or reflection symmetry?

2a-c. Same as 1a-c. but replace 'squares' with 'equilateral triangles.'

3a-c. Same as 1a-c. but replace 'squares' with 'regular hexagons.'

See The Solution Submitted by Jer    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Hexagonal reply (partial spoiler) | Comment 3 of 5 |
3a) 3, all sharing a common vertex

3b) 4. Start with the three above, and add a 4th hexagon than shares a side with only one of the others

  Posted by Steve Herman on 2013-02-27 23:30:17
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 (3)
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