AT-OEMO-REG 2020 Problem 2

The set $M$ consists of all $7$ -digit positive integer numbers that contain (in decimal notation) each of the digits $1, 3, 4, 6, 7, 8$ and $9$ exactly once. (a) Find the smallest positive difference $d$ of two numbers from $M$ . (b) How many pairs $(x, y)$ with $x$ and $y$ from M are there for which $x - y = d$ ?

(Gerhard Kirchner)