How many times will I be writing 2 if wrote down numbers from 11 to 199 ?

Options

A. 38
B. 39
C. 36
D. 37

Answer

To find out how many times the digit '2' is written when listing numbers from 11 to 199, we can break down the problem into manageable steps.

### Step-by-Step Solution:

1. **Identify the Range**: We need to count how many times '2' appears in the numbers from 11 to 199.

2. **Count occurrences of '2' in each decade**:
- **From 11 to 19**: The numbers are 11, 12, 13, 14, 15, 16, 17, 18, 19. The digit '2' appears once in 12.
- Count: 1 occurrence of '2'.

- **From 20 to 29**: The numbers are 20, 21, 22, 23, 24, 25, 26, 27, 28, 29. The digit '2' appears in every number:
- Count: 10 occurrences (20, 21, 22, 23, 24, 25, 26, 27, 28, 29).

- **From 30 to 39**: The numbers are 30, 31, 32, 33, 34, 35, 36, 37, 38, 39. The digit '2' appears once in 32.
- Count: 1 occurrence of '2'.

- **From 40 to 49**: The numbers are 40, 41, 42, 43, 44, 45, 46, 47, 48, 49. The digit '2' appears once in 42.
- Count: 1 occurrence of '2'.

- **From 50 to 59**: The numbers are 50, 51, 52, 53, 54, 55, 56, 57, 58, 59. The digit '2' appears once in 52.
- Count: 1 occurrence of '2'.

- **From 60 to 69**: The numbers are 60, 61, 62, 63, 64, 65, 66, 67, 68, 69. The digit '2' appears once in 62.
- Count: 1 occurrence of '2'.

- **From 70 to 79**: The numbers are 70, 71, 72, 73, 74, 75, 76, 77, 78, 79. The digit '2' appears once in 72.
- Count: 1 occurrence of '2'.

- **From 80 to 89**: The numbers are 80, 81, 82, 83, 84, 85, 86, 87, 88, 89. The digit '2' appears once in 82.
- Count: 1 occurrence of '2'.

- **From 90 to 99**: The numbers are 90, 91, 92, 93, 94, 95, 96, 97, 98, 99. The digit '2' appears once in 92.
- Count: 1 occurrence of '2'.

- **From 100 to 199**: We will count occurrences of '2' in the tens and units place:
- **From 100 to 199**:
- **In the hundreds place**: '2' does not appear.
- **From 100 to 199**: We can repeat the counting for each decade (100-199) similar to above.
- **From 100 to 199**: The same counts as above will apply for 120-129 (10 occurrences), 130-139 (1), 140-149 (1), 150-159 (1), 160-169 (1), 170-179 (1), 180-189 (1), 190-199 (1).
- Count: 10 (from 120-129) + 7 (1 from each of the other decades) = 17 occurrences.

3. **Total Count**: Now, we sum up all the occurrences:
- From 11 to 19: 1
- From 20 to 29: 10
- From 30 to 39: 1
- From 40 to 49: 1
- From 50 to 59: 1
- From 60 to 69: 1
- From 70 to 79: 1
- From 80 to 89: 1
- From 90 to 99: 1
- From 100 to 199: 17

Total = 1 + 10 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 17 = 34 occurrences of '2'.

### Final Answer:
The digit '2' will be written **34 times** when writing numbers from 11 to 199.