Many mathematical problems require counting possibilities, but advanced aptitude tests often demand the total sum of those possibilities instead. This requires a shift from simple permutation logic to aggregate summation within strictly defined numerical boundaries.

To solve these problems, one must first establish fixed positional constraints, such as fixing a digit in the thousands place to maintain a specific magnitude. Following this, non-repetition rules are applied to the remaining positions to systematically reconstruct and add every valid resulting number.,,

• Apply magnitude requirements by fixing specific digits in the highest available place value positions.
• Determine the count of valid permutations based on rules that prevent digit repetition.
• Execute the actual summation of all valid combinations rather ...