Question 1096948
The above is incorrect.  Sorry, Jorrell.
<pre><font size=4><b>
If the hundreds digits could be 0's, the problem would be much
easier.  So let's begin by pretending that the hundreds digits
can be 0, and finding that sum first.  Then we will find the
sum of those with 0's as the hundreds digit, and subtract.

Suppose we had them all listed to add like this:

 012
 013
 014
 ...
 ...
 098
 102
 103
 ...
 ...
 ...
 986
+987
----
 sum

There are 10*9*8 = 720 numbers in that list.  There are an
equal number of each digit in each column, so there are 720/10
or 72 of each digit in each column.  Since the sum of the digits
0+1+2+3+4+5+6+7+8+9 = 45, the sum of each of the three columns
of digits is 45*72 = 3240.

The hundreds column will contribute 324000 toward the sum, the 
tens column will contribute 32400, and the ones column will 
contribute 3240, so the sum is 324000+32400+3240 = 359640.  That 
would be the answer if 0 could be used as the hundreds digit of 
a 3 digit number.  But alas, it cannot!  :)

So now we calculate how much we must subtract from the 359640.

We must now find the sum of this list:


 012
 013
 014
 ...
 ...
 098
----

Since the hundreds digits are all 0's there are no 0's in the
tens or ones digit columns.  So there are 9*8 = 72 numbers in 
that list.  There are an equal number of each digit, 1 though
9 in each of the tens and ones columns, so there are 72/9 or 
8 of each digit 1 thru 9 in the tens and ones columns.  Since 
the sum of the 9 digits 1+2+3+4+5+6+7+8+9 = 45, 
the sum of each of the two columns of digits is 45*8 = 360.  

The tens column will contribute 3600 toward the sum, and the 
ones column will contribute 360, so the sum is 3600+360 = 3960.  

So we subtract that from 359640.

Answer = 359640-3960 = 355680

Edwin</pre></b></font>