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Six real numbers with sum 10

Source: Balkan MO 1993, Problem 1

April 25, 2006
AMCUSA(J)MOUSAMOalgebra proposedalgebra

Problem Statement

Let a,b,c,d,e,fa,b,c,d,e,f be six real numbers with sum 10, such that (a−1)2+(b−1)2+(c−1)2+(d−1)2+(e−1)2+(f−1)2=6. (a-1)^2+(b-1)^2+(c-1)^2+(d-1)^2+(e-1)^2+(f-1)^2 = 6. Find the maximum possible value of ff. Cyprus
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