The sum of 3 numbers is 555. The 1st number is a 1-digit number, the 2nd number is a 2-digit number and the 3rd number is a 3-digit number. What is the smallest possible difference between the 2nd and 3rd number? Answer : ___

1. Express the difference in terms of the numbers and identify the condition for the minimum difference.

Let the 1-digit number be $a$, the 2-digit number be $b$, and the 3-digit number be $c$.
We are given $a + b + c = 555$.
We want to find the smallest possible difference between $c$ and $b$, which is $c - b$.
From the sum, $c = 555 - a - b$.
Substitute this into the difference: $c - b = (555 - a - b) - b = 555 - a - 2b$.
To make $555 - a - 2b$ as small as possible, we must make $a$ and $b$ as large as possible.

2. Determine the maximum possible values for the 1-digit and 2-digit numbers.

The maximum value for a 1-digit number is $a = 9$.
The maximum value for a 2-digit number is $b = 99$.

3. Calculate the 3-digit number and the minimum difference.

Using the maximum values, $c = 555 - 9 - 99 = 447$.
The difference is $c - b = 447 - 99 = 348$.
Alternatively, using the expression: $555 - 9 - 2(99) = 555 - 9 - 198 = 348$.