The sum of the squares of five real numbers equals . Prove that the least of the numbers , where and , does not exceed
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The sum of the squares of five real numbers $a_1, a_2, a_3, a_4, a_5$ equals $1$. Prove that the least of the numbers $(a_i - a_j)^2$, where $i, j = 1, 2, 3, 4,5$ and $i \neq j$, does not exceed $\frac{1}{10}.$
Izvor: Međunarodna matematička olimpijada, shortlist 1974
Školjka 
equals 
. Prove that the least of the numbers 
, where 
and 
, does not exceed 