Problem

Source: Dutch NMO 2018 p1

Tags: number theory, Digits, divisible



We call a positive integer a shuffle number if the following hold: (1) All digits are nonzero. (2) The number is divisible by $11$. (3) The number is divisible by $12$. If you put the digits in any other order, you again have a number that is divisible by $12$. How many $10$-digit shuffle numbers are there?