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ILL 1987 Problem 67

    If a,b,c,da, b, c, d are real numbers such that a2+b2+c2+d2≤1a^2 + b^2 + c^2 + d^2 \leq 1 , find the maximum of the expression (a+b)4+(a+c)4+(a+d)4+(b+c)4+(b+d)4+(c+d)4.(a + b)^4 + (a + c)^4 + (a + d)^4 + (b + c)^4 + (b + d)^4 + (c + d)^4.

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