Recently in a contest I came across this question :

"Given N circles, defined by their x co-ordinate, y co-ordinate and radius, remove the minimum number of circles such that the remaining circles are non intersecting. Touching a circle is also considered as intersecting."

Constraints 1 <= N <= 1000 0 <= abs(X) , abs(Y) , abs(R) <= 1000

The setter solution uses a greedy solution (to remove the circle with maximum intersections everytime till all remaining are non intersecting), but this fails on a very simple test case.

Here, the greedy solution gives answer as 4, but we can do it by removing 3 circles also.