Consider the set

S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 23, 24, 25 ... 123456789}

which consists of all positive integers whose digits strictly increase from left to right. This set is finite. What is the 100th smallest element of the set?

Guest May 7, 2021