I know that the difference of two consecutive perfect squares is always odd, because (n+1)^2 - n^2 = 2n + 1. So I need to find how many odd perfect squares are less. than 10,000. The largest odd perfect square less than 10,000 is 99^2, which is 9,801. The smallest odd perfect square is 1^2, which is 1. There are 50 of them. So there are 50 perfect squares less than 10,000 that can be represented as the difference of two consecutive perfect squares. 
Recall that a perfect square is the square of some integer.  How many perfect squares less than 10,000 can be represented as the difference of two consecutive perfect squares?