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

Count the digit 3 in each position, not the numbers that contain a 3. Numbers 1 to 100 are the two-digit numbers 01 to 99 plus 100, and 100 has no 3.

Units place: 3, 13, 23, 33, 43, 53, 63, 73, 83, 93. That gives 10 occurrences, one in each decade.

Tens place: 30 to 39 gives 10 more, since every number in that block has a 3 in the tens position.

Total is 10 + 10 = 20, so option A is correct. The number 33 carries two 3s, one in each place, and both are counted.

• Option B (11) and option D (10) undercount, usually by missing one of the two blocks or the double 3 in 33.
• Option C (21) overcounts, typically by adding a stray 3 that does not exist in the range.

Core concept: digit frequency across place values. The same positional logic drives counting questions and number-pattern problems in reasoning, so work systematically block by block rather than guessing.

Trap: Counting how many numbers contain a 3, which gives 19 because 33 is one number, instead of counting how many times the digit is written, which gives 20.