Problem E

Wipe Away 3

Tyra writes consecutive positive integers on a whiteboard starting
with the integer \(1\). However, when
she writes a number that is a multiple of \(9\), or contains the digit \(9\), Juliana immediately erases it. If they
continue this for a long time, what is the 400^{th} number that
Juliana will erase?

Note: In solving this problem, it may be helpful to use the fact that a number is divisible by \(9\) exactly when the sum of its digits is divisible by \(9\). For example, the number \(214\,578\) is divisible by \(9\) since \(2+1+4+5+7+8 = 27\), which is divisible by \(9\). In fact, \(214\,578=9 \times 23\,842.\)