Using Excel, the numbers are: 616, 637, 677 and 696. This sums to 2626. So the answer is 626.
/* I know this approach was not what you were looking for, but can't resist using Excel when I have a spreadsheet open. :-) */
See question on Quora
Consider all three-digit numbers that are greater than the sum of the squares of their digits by exactly 543. What are the last three digits of the sum of these numbers?
Using Excel, the numbers are: 616, 637, 677 and 696. This sums to 2626. So the answer is 626.
/* I know this approach was not what you were looking for, but can't resist using Excel when I have a spreadsheet open. :-) */
See question on Quora