Nine Points in a Square: Middle Secondary Mathematics Competition Question

Show that given any 9 points inside a square of side 1 we can always find 3 which form a triangle with area less than 1/8.

Junior Balkan Mathematical Olympiad 1997



You may also wish to try different numbers of points within a unit square. Start with just 3 and go all the way up to 9. As in the question above, if you are allowed to pick any 3 points from those given, such that they form a triangle with area less than x, find the minimum value of x in each case.

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