In the multiplication indicated in the figure on the side, the asterisks represent digits, which may or may not be the same. What is the sum of the numbers that were multiplied?
A) 82
B) 95
C) 110
D) 127
E) 132

![](https://cdn.mathpix.com/cropped/2024_05_01_984603b876c0bc28095bg-03.jpg?height=245&width=166&top_left_y=820&top_left_x=1616)
Solution

## ALTERNATIVE C

The number 1656 is the result of the product of two two-digit numbers. Let's factorize 1656 to see all the possibilities for these two numbers. We have that $1656=2 \times 2 \times 2 \times 3 \times 3 \times 23$; thus the possibilities are $1656=72 \times 23, 1656=24 \times 69, 1656=36 \times 46$, and $1656=92 \times 18$.

Now observe the vertical calculations:
![](https://cdn.mathpix.com/cropped/2024_05_01_984603b876c0bc28095bg-20.jpg?height=378&width=968&top_left_y=2280&top_left_x=454)

The only one that satisfies the statement is the one in which the second addend of the sum does not have three digits, that is, it is the last calculation in the first line. Therefore, the numbers that were multiplied are 92 and 18, and the sum sought is $92+18=110$.