+216 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?
+129852 n^2 - (n -1)^2 = 2n - 1
Let's see if we can find a pattern
n n - 1 Square
1 0 1^2 = 1
5 4 3^3 = 9
13 12 5^2 = 25
25 24 7^2 = 49
41 40 9^2 = 81
Note that the diffference between n's is 4, 8, 12, 16, etc.
Following this pattern
61 60 11^2 = 121
85 84 13*2 = 169
......
And 100^2 = 10000
So.....the number of perfect squares <10000 generated this way will just be the number of odd integers between 1 and 99 inclusive that will be squared = (99 - 1) /2 + 1 = 49
