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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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Solution Part A | Comment 1 of 7
If I understand all the definitions correctly,

All dominos and trominos are star-shaped, but there is one tetromino that is not.  If each square is represented by an "X", it is shaped like this

    XX
      XX

I believe there is no point inside this shape that can "see" 100% of each of both the far left side and far right side of the figure.



  Posted by Kenny M on 2016-03-28 16:12:19
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