Grid without lines

Can you remove the least number of points from this diagram, so no three of the remaining points are in a straight line?
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Problem

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Grid without Lines

The diagram shows nine points in a square array.

What is the smallest number of points that need to be removed in order that no three of the remaining points are in a straight line?



 

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.