sum of digits puzzle

Let the letters: A, B, C, D, E, F, G, H, and I be representative of the
numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 in no particular order. If we let
A+B+C=C+D+E=E+F+G=G+H+I=13, then what must E be?

A + B + C
        +
        D
        +
        E + F + G
                +
                H
                +
                I

Answer:

start from the maximum value = 9
and it can only be combined with 1, 3
so we have,
(1, 3, 9)

take the second maximum value = 8
possible tuples,
(1, 4, 8)
(2, 3, 8)

take the third max value = 7
(1, 5, 7)
(2, 4, 7)

take the third max value = 6
( 2, 5, 6 )
( 3, 4, 6 )

now, only C, E, F are common,
so,

Option I:

9 + 3 + 1
        +
        8
        +
        4 + 7 + 2
                +
                5
                +
                6

This is a perfectly valid arrangement

Option II:

9 + 1 +[3]
        +
        8
        +
        2 + 7 + 4
                +
                6
                +
               [3]

which is an invalid arrangement

So the required answer is 4.