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

Home > Shapes
Star-shaped polyominos (Posted on 2016-03-28) Difficulty: 3 of 5
A star-shaped polygon is a polygon that contains at least one point from which the entire polygon boundary is visible. The set of all such points is called the kernel.

A) Find the smallest polyomino that is not star-shaped.
B) Find the smallest polyomino whose kernel is a single point.
C) Find the smallest polyomino whose kernel is a line segment.
D) Find the smallest polyomino whose kernel is precisely half the area of the polyomino.

E) Prove or disprove: For every rational number, Q, where 0≤Q≤1 there is a polyomino whose kernel is Q times the area of the polyomino.

Note: smallest refers to the number of squares comprising the polyomino.

No Solution Yet Submitted by Jer    
No Rating

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionPart EBrian Smith2016-03-29 10:43:39
Some ThoughtsParts A through DBrian Smith2016-03-28 23:18:44
A, B, C (Do Re Mi)Steve Herman2016-03-28 21:03:31
re(3): Solution Part AJer2016-03-28 19:57:28
Questionre(2): Solution Part ASteve Herman2016-03-28 18:03:47
re: Solution Part AJer2016-03-28 16:55:49
Solution Part AKenny M2016-03-28 16:12:19
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 (1)
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