Problem

Source: X International Festival of Young Mathematicians Sozopol 2019, Theme for 10-12 grade

Tags: combinatorics, counting



Let $A$ be the number of 2019-digit numbers, that is made of 2 different digits (For example $10\underbrace{1...1}_{2016}0$ is such number). Determine the highest power of 3 that divides $A$.