Conjecture:
"For any $N$ number of points placed arbitrarily in the plane, the minimum number of lines need to bound each point in a separate polygon(which we will call B), is equal to: 2+ ceiling($n/2$),regardless of the placement of the $N$ Points."
Restrictions:
- $N$ is an integer greater than 2
2.All of the points together may not be co-linear (Although subgroups of points may be co-linear)
3.You may only use straight lines
4.Lines drawn may not intersect your starting points
The questions is, Can you prove or disprove the Conjecture above, and if it is false, What is the formula for finding B?
Here's an Example using three points in an orderly arrangement:
In the example, $N=3$ and $B=4$, as we were able to bound each of the individual three points into heir own separate polygon using the minimum number of lines:$4$
Example of what was said in comment, n=10,b=8, formula holds
Counter example to all co linear but one: