2011 AIME II Problem 6

Define an ordered quadruple of integers (a, b, c, d) as *interesting* if 1 \le a<b<c<d \le 10, and a+d>b+c. How many interesting ordered quadruples are there?

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.