The Four-Digit Password

Difficulty: Hard · Topics: Discrete Mathematics, Sets, Word Problems

Each place of a 4-digit password holds one digit. Reading from left to right, the set of the digits in the first two places is A, the set of the digits in the middle two places is B and the set of the digits in the last two places is C, with

A=C, A≠ B.

The set of all digits \0,1,2,…,9\ is the universal set, and the elements of A' add up to 37.

What is the sum of the digits of the password?