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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    
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re: Solution Part A | Comment 2 of 7 |
(In reply to Solution Part A by Kenny M)

The boundary of the region should be considered part of the region.  This means it would not hide other parts of the region.  The S tetromino is thus star shaped as you can "see" all points from the boundary between the 2nd and 3rd square, even though you would have to sight along part of the boundary.

The formal definition in the link makes this clear as do the examples.

Edited on March 28, 2016, 7:56 pm
  Posted by Jer on 2016-03-28 16:55:49

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