Math puzzle for you math nerds out there...

Test Preparation
1

<p>As a function of n, find the sum of the digits of the following:</p>

<p>9 x 99 x 9999 x .... x (10^(2^n) - 1)</p>

<p>also, figure out a way to determine how many of each digit the product would have...(being very general for example, the number 194829318 has two 1s, two 9s, two 8s, one 2, one 3, and one 4)...</p>

2

<p>do NOT advertise on my post…either solve my puzzle or screw off…</p>

3

<p>is this a AIME problem?</p>

4

<p>USAMO actually…</p>