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?
Age
11 to 14
Challenge level
Problem
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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.
Student Solutions
At least one point must be removed from each of the three horizontal lines; so at least three points need to be removed.
Removing the three points lying on either diagonal does what is required.
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