Consider the set S={1,2,3,4,5,6,7,8,9,12,13,14,15,16,17,18,19,23,24, .............. ,123456789}, which consists of all positive

Question

sergiy2304 [10]

3 years ago

11

Consider the set S={1,2,3,4,5,6,7,8,9,12,13,14,15,16,17,18,19,23,24, .............. ,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?

Mathematics

1 answer:

jarptica [38.1K] · Answer 1 · 2022-02-17T14:23:42+03:00

Answer:

12345

Step-by-step explanation:

The number of numbers with n digits is the same as the number of combinations of n things taken from 9. That means as many numbers have 5 or more digits as have 4 or fewer, with the exception that the number 123456789 is not matched by the number 0 (or a number with no digits). There are 256 numbers with 5 or more digits, but only 255 with 4 or fewer.

So, the median number is the first number with 5 digits:

12345