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Interesting ordered quadruples

Source: 2011 AIME II #6

March 31, 2011
probabilityAMCAIME

Problem Statement

Define an ordered quadruple of integers (a,b,c,d)(a, b, c, d) as interesting if 1≤a<b<c<d≤101 \le a<b<c<d \le 10, and a+d>b+ca+d>b+c. How many ordered quadruples are there?
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