intersecting features, problems with arcmap v9.

I have a problem with intersecting features,

I have a point file with 1000's of data points
a buffer file around these points
a square grid which I am attempting to determine how many buffer zones are in each grid
I used the intersect tool and it not only did the intersect of buffer to grid but also intersecting buffers to buffers
I want to know how to make Arcmap only took for intersections between grid and buffer.

I am attempting to create a score for each grid best on how many buffers are in each, if it includes buffer buffer intersections then the score is over exaggerated.

I would also like to do this without using code because I don'y know how to implement code to ArcMap.

Thanks,

Andrew