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

Illustration for riddle: Jenna wrote all the numbers from 300 to 400 on a piece of paper. How many times did she write the di

Jenna wrote it 120 times.

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!

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Common Wrong Answers

“100”

This guess may come from counting only the numbers that start with 3, like 300-399, without considering how many times the digit 3 appears in other positions.

“50”

This guess might reflect a misunderstanding of how often the digit 3 appears within the full range of numbers, underestimating the occurrences in both the hundreds and the tens/units places.

“30”

This guess could stem from incorrectly counting the instances of the digit 3 only in the tens place (30s) and not accounting for its appearances in the hundreds place (300s) or within other numbers.

Numbers

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