1. Find the sum of all three-digit numbers that can be written using the digits $1,2,3$ such that all digits in each number are different.
1. Let's first determine the three-digit numbers that can be formed using the digits $1,2,3$ such that all digits in each number are different.
![](https://cdn.mathpix.com/cropped/2024_05_21_e53d4ff4f2278a1c0d12g-053.jpg?height=388&width=1062&top_left_y=500&top_left_x=496)

Thus, we have the following numbers that satisfy the condition of the problem: $123,132,213,231,312,321$. Let's find their sum.

$$
123+132+213+231+312+321=1332
$$

Answer: 1332.