Japt, 12 11 10 bytes

Takes input as an array of digits.

k@¬èX ÉÃrw

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Explanation

     :Implicit input of array U.
k    :Filter the array to the elements that return false when...
@    :Passed through a function that...
¬    :Joins U to a string and...
èX   :Counts the number of times the current element (X) appears in the string...
É    :Minus 1.
     :(The count of unique digits will be 1, 1-1=0, 0=false)
à   :End function.
r    :Reduce by...
w    :Getting the greater of the current element and the current value.
     :Implicit output of resulting single digit integer.

Japt -h, 12 11 10 4 bytes

I/O as a digit array.

ü l1

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#Japt, 12 11 10 bytes

Takes input as an array of digits.

k@¬èX ÉÃrw

Test it

##Explanation :Implicit input of array U. k :Filter the array to the elements that return false when... @ :Passed through a function that... ¬ :Joins U to a string and... èX :Counts the number of times the current element (X) appears in the string... É :Minus 1. :(The count of unique digits will be 1, 1-1=0, 0=false) Ã :End function. r :Reduce by... w :Getting the greater of the current element and the current value. :Implicit output of resulting single digit integer.

Japt, 12 11 10 bytes

Takes input as an array of digits.

k@¬èX ÉÃrw

Test it

Explanation

     :Implicit input of array U.
k    :Filter the array to the elements that return false when...
@    :Passed through a function that...
¬    :Joins U to a string and...
èX   :Counts the number of times the current element (X) appears in the string...
É    :Minus 1.
     :(The count of unique digits will be 1, 1-1=0, 0=false)
à   :End function.
r    :Reduce by...
w    :Getting the greater of the current element and the current value.
     :Implicit output of resulting single digit integer.

#Japt, 12 11 10 bytes

Takes input as an array of digits.

k@¬èX ÉÃrw

Test it

##Explanation :Implicit input of string U. ¬ :Split to an array. n< :Sort descending. æ :Return the first element that is true when... @ :Passed through a function that checks if... èX :The count of occurrences of the element (X) in U... ¥1 :Equals 1. :Implicit output of resulting single digit string.

#Japt, 12 11 10 bytes

Takes input as an array of digits.

k@¬èX ÉÃrw

Test it

##Explanation :Implicit input of array U. k :Filter the array to the elements that return false when... @ :Passed through a function that... ¬ :Joins U to a string and... èX :Counts the number of times the current element (X) appears in the string... É :Minus 1. :(The count of unique digits will be 1, 1-1=0, 0=false) Ã :End function. r :Reduce by... w :Getting the greater of the current element and the current value. :Implicit output of resulting single digit integer.