Find the sum of all 3's that are needed to write the numbers from 200 to 400.

Sure, let's break this down:

1. First, we need to identify all the numbers between 200 and 400 that have the digit 3 in them.

2. The numbers can have 3 in the hundreds place, tens place, or units place.

3. For the hundreds place, we have numbers from 300 to 399. That's 100 numbers, so we have 100 threes from this category.

4. For the tens place, we have numbers like 230, 231, ..., 239. This pattern will repeat 10 times (for 200s, 300s, and 400s). So, we have 10*10 = 100 threes from this category.

5. For the units place, we have numbers like 203, 213, 223, ..., 393. This pattern will also repeat 10 times (for 200s, 300s, and 400s). So, we have 10*10 = 100 threes from this category.

6. Adding all these up, we get 100 + 100 + 100 = 300 threes.

So, the sum of all 3's that are needed to write the numbers from 200 to 400 is 300.