What is the sum of the digits used to form the integers from 45 to 100,
inclusive? 

There are 5 4's used for first digits of the numbers from 45 thru 49,
inclusive.  That's 20.

The second digits of those numbers are 5+6+7+8+9 or 35.  That's 55 so far.

There are 10 5's used for the first digits of the numbers from 50 thru 59,
inclusive,  That's 50 more, or 105 so far

The second digits of those numbers are 0+1+2+3+4+5+6+7+8+9 or 45.  That's 150
so far.

There are 10 6's used for the first digits of the numbers from 60 thru 69,
inclusive,  That's 60 more, or 210 so far

The second digits of those numbers are 0+1+2+3+4+5+6+7+8+9 or 45.  That's 255
so far.

There are 10 7's used for the first digits of the numbers from 70 thru 79,
inclusive,  That's 70 more, or 325 so far

The second digits of those numbers are 0+1+2+3+4+5+6+7+8+9 or 45.  That's 370
so far.

There are 10 8's used for the first digits of the numbers from 80 thru 89,
inclusive,  That's 80 more, or 450 so far

The second digits of those numbers are 0+1+2+3+4+5+6+7+8+9 or 45.  That's 495
so far.

There are 10 9's used for the first digits of the numbers from 50 thru 59,
inclusive,  That's 90 more, or 585 so far

The second digits of those numbers are 0+1+2+3+4+5+6+7+8+9 or 45.  That's 630
so far.

The sum of the digits of 100 is 1+0+0 or 1.  So that's a grand total of 631, if
I added correctly.