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Problem of the Week
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 400th 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, \(214\,578=9 \times 23\,842.\)