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. 🙂 */

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Continue reading about 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?