If you write down all the numbers from 1 to 100, then how many times do you write 3?

Question

If you write down all the numbers from 1 to 100, then how many times do you write 3?

1. A. 11
2. B. 18
3. C. 20 (Correct answer)
4. D. 21

Correct Answer

Option C — 20

Detailed Solution & Explanation

The correct answer is 20.

Key Points

• Count the digit 3 in the units place: 3, 13, 23, 33, 43, 53, 63, 73, 83, 93 — that is 10 occurrences.
• Count it in the tens place: 30 to 39 — another 10 occurrences.
• Total = 10 + 10 = 20.

Additional Information

• The number 33 contains the digit twice and is correctly counted once in each place — it is not double-counting, and treating it as such is the usual error that yields 19.
• The same method gives 20 occurrences for every digit from 1 to 9 in the range 1-100; only 0 differs, appearing 11 times.
• For a range 1-1000, each non-zero digit appears 300 times.