[ [Properties of numbers. General properties]

In a row, numbers divisible by $9$ are written in ascending order: $9, 18, 27, 36, \ldots$. Under each number in this row, its sum of digits is written.

a) At which position will the number 81 first appear in the second row?

b) Which will appear earlier: the number 27 four times in a row or the number $36$ once?

#
a) The number 81 will first appear in the second row under the number 999999999, so its position will be $999999999: 9=111111111$.

b) The number 36 will first appear in the second row under the number 9999, the number 27 will appear four times in a row earlier, for example under the numbers $3969,3978,3987,3996$.

## Answer

a) On the $111111111-th$ place.

b) Four times in a row the number 27.