Let $n$ points with integer coordinates be given in the $xy$-plane. What is the minimum value of $n$ which will ensure that three of the points are the vertices of a triangel with integer (possibly, 0) area?
1. **Assume a point at the origin:**
   Without loss of generality, we can assume that one of the points is at the origin, \( O(0,0) \). This is because we can always translate the entire set of points such that one of them is at the origin.

2. **Area formula for a triangle:**
   If \( A(a,b) \) and \( B(x,y) \) are two points, the area of triangle \( OAB \) is given by:
   \[
   \text{Area} = \frac{1}{2} \left| ax - by \right|
   \]
   For the area to be an integer (possibly zero), \( \left| ax - by \right| \) must be an even integer.

3. **Coordinate parity analysis:**
   - If one of the points, say \( A \), has both coordinates even, then \( a \) and \( b \) are even. Thus, \( ax \) and \( by \) are even for any integer coordinates \( x \) and \( y \). Therefore, \( \left| ax - by \right| \) is even, ensuring the area is an integer.
   - If two points, say \( A \) and \( B \), have all their coordinates odd, then \( a, b, x, \) and \( y \) are all odd. The product of two odd numbers is odd, so \( ax \) and \( by \) are odd. The difference of two odd numbers is even, ensuring \( \left| ax - by \right| \) is even.
   - The same logic applies if two points have coordinates of the form \( (o,e) \) or \( (e,o) \), where \( e \) stands for even and \( o \) stands for odd.

4. **Conclusion from parity analysis:**
   If a set of integer points does not contain three points which are the vertices of a triangle with integer area, then this set must have at most 4 elements. This is because there are only 4 possible combinations of parity for the coordinates: \( (e,e), (e,o), (o,e), (o,o) \).

5. **Existence of a set with 4 elements:**
   Consider the four vertices of a unit square: \( (0,0), (1,0), (0,1), (1,1) \). None of these points form a triangle with integer area, as the area of any triangle formed by these points is either \( \frac{1}{2} \) or 0.

Therefore, the minimum value of \( n \) which ensures that three of the points are the vertices of a triangle with integer area is 5.

The final answer is \(\boxed{5}\).