What is this formula?

This formula is used to find the sum of all possible $n$-digit numbers that can be formed using a specific set of $n$ non-zero digits (without repetition).

$\text{Sum} = (n-1)! \times (\text{Sum of given digits}) \times (\underbrace{111...1}_{n \text{ times}})$

Component	Meaning
$(n-1)!$	The number of times each digit appears in each position (units, tens, hundreds, etc.).
$(\text{Sum of digits})$	The sum of the specific numbers you are given to work with.
$(111...1)$	The place value factor (e.g., $111$ for a 3-digit number).

Example: Find the sum of all 3-digit numbers formed using digits 1, 2, and 3:

• $n = 3$, so $(n-1)! = 2! = \mathbf{2}$
• Sum of digits = $1 + 2 + 3 = \mathbf{6}$
• Place value factor = $\mathbf{111}$

$\text{Sum} = 2 \times 6 \times 111 = \mathbf{1,332}$

Note: If a digit is repeated in the given set (e.g., using digits 1, 1, 2), you must divide the final result by the factorial of the number of repetitions (in this case, $2!$), as noted in the handwritten "divide if digits is repeated" comment.