Problem

Source: 2021 Dürer Math Competition Finals Day2 E4 https://artofproblemsolving.com/community/c2749870_

Tags: Digits, number theory



What is the number of $4$-digit numbers that contains exactly $3$ different digits that have consecutive value? Such numbers are for instance $5464$ or $2001$. Two digits in base $10$ are consecutive if their difference is $1$.