Consider the set

\(S=\{1,2,3,4,5,6,7,8,9,12,13,14,15,16,17,18,19,23,24,\ldots,123456789\},\)which consists of all positive integers whose digits strictly increase from left to right. This set is finite. What is the median of the set?

Guest Jul 22, 2018

#1**0 **

I will take a crack at this one!.

If you look carefully, you should notice that ALL terms beyond 89 cancel out leaving you with the following 45 terms:

(1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 23, 24, 25, 26, 27,** 28**, 29, 34, 35, 36, 37, 38, 39, 45, 46, 47, 48, 49, 56, 57, 58, 59, 67, 68, 69, 78, 79, 89)

**Therefore, the median of the set is 28.**

Guest Jul 22, 2018