2011 AIME II Problems/Problem 6

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


There is probably some really complicated formula for this, but as I didnt know it and had 3 hours to "do my best", I listed all possible combinations out. The answer is 80.