Jenna wrote all the numbers from 300 to 400 on a piece of paper. How many times did she write the digit 3?

Why this works

To solve this riddle, we need to consider how many times the digit '3' appears in each position (hundreds, tens, and units) for the numbers from 300 to 400. 1. **Hundreds Place**: Every number from 300 to 399 has a '3' in the hundreds place. Since there are 100 numbers in this range (300 to 399), '3' appears 100 times here. 2. **Tens Place**: The tens digit can be '3' in the range from 330 to 339, which includes 10 numbers (330, 331, 332, ..., 339). So, '3' appears 10 times in the tens place. 3. **Units Place**: The digit '3' appears in the units place for the numbers 303, 313, 323, 333, 343, 353, 363, 373, 383, and 393 – a total of 10 occurrences. Adding these together: 100 (hundreds) + 10 (tens) + 10 (units) equals 120. Thus, Jenna wrote the digit '3' a total of 120 times!