2 Explanation added
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Pyth, 11 bytes

h.MsZ.TmjdT

A program that takes input of a list of integers on STDIN and prints a list.

Try it online

[Explanation coming later]How it works

h.MsZ.TmjdT  Program. Input: Q
        j T   Yield the base-10 representation, giving a list of digits
       m d   Map that over Q (implicit input fill)
     .T      Justified transpose, giving each column as a list
 .MsZ        Filter the above by maximum sum
h            First element of above
             Implicitly print

Pyth, 11 bytes

h.MsZ.TmjdT

A program that takes input of a list of integers on STDIN and prints a list.

Try it online

[Explanation coming later]

Pyth, 11 bytes

h.MsZ.TmjdT

A program that takes input of a list of integers on STDIN and prints a list.

Try it online

How it works

h.MsZ.TmjdT  Program. Input: Q
        j T   Yield the base-10 representation, giving a list of digits
       m d   Map that over Q (implicit input fill)
     .T      Justified transpose, giving each column as a list
 .MsZ        Filter the above by maximum sum
h            First element of above
             Implicitly print
1
source | link

Pyth, 11 bytes

h.MsZ.TmjdT

A program that takes input of a list of integers on STDIN and prints a list.

Try it online

[Explanation coming later]