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Algebra Level 3

Find the average value of ( a b ) 2 + ( b c ) 2 + ( c d ) 2 + ( d e ) 2 + ( e f ) 2 + ( f g ) 2 (a-b)^2+(b-c)^2+(c-d)^2+(d-e)^2+(e-f)^2+(f-g)^2 over all possible arrangements ( a , b , c , d , e , f , g ) (a,b,c,d,e,f,g) of the seven numbers 1 , 2 , 3 , 11 , 12 , 13 , 14 1,2,3,11,12,13,14 .


The answer is 392.

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