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PutnamSuperchallengeIntegrals I: Feynman's Trick

Integrals I: Feynman's Trick · Superchallenge problem

How many ordered quadruples of integers (a,b,c,d)(a, b, c, d) with 0≤a,b,c,d≤100 \le a, b, c, d \le 10 satisfy a+b+c+d=30a + b + c + d = 30?