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' appears when writing all the numbers from 11 to 199, we can break down the problem into several steps.

### Step 1: Count occurrences of '2' in the tens place
We need to analyze the numbers from 11 to 199 and check how many times '2' appears in the tens place.

- The tens place will have '2' in the numbers from 20 to 29.
- The numbers are: 20, 21, 22, 23, 24, 25, 26, 27, 28, 29.
- There are 10 occurrences of '2' in the tens place (20 to 29).

### Step 2: Count occurrences of '2' in the units place
Next, we will count how many times '2' appears in the units place.

- The units place will have '2' in the following ranges:
- From 11 to 19: Only 12 (1 occurrence)
- From 20 to 29: 20, 21, 22, 23, 24, 25, 26, 27, 28, 29 (10 occurrences)
- From 30 to 39: 32 (1 occurrence)
- From 40 to 49: 42 (1 occurrence)
- From 50 to 59: 52 (1 occurrence)
- From 60 to 69: 62 (1 occurrence)
- From 70 to 79: 72 (1 occurrence)
- From 80 to 89: 82 (1 occurrence)
- From 90 to 99: 92 (1 occurrence)
- From 100 to 199: 102, 112, 122, 132, 142, 152, 162, 172, 182, 192 (10 occurrences)

Now, let's sum these occurrences:
- From 11 to 19: 1 occurrence
- From 20 to 29: 10 occurrences
- From 30 to 39: 1 occurrence
- From 40 to 49: 1 occurrence
- From 50 to 59: 1 occurrence
- From 60 to 69: 1 occurrence
- From 70 to 79: 1 occurrence
- From 80 to 89: 1 occurrence
- From 90 to 99: 1 occurrence
- From 100 to 199: 10 occurrences

Total occurrences in the units place = 1 + 10 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 10 = 27.

### Step 3: Combine the counts
Now we will combine the counts from the tens place and the units place:
- Tens place: 10 occurrences
- Units place: 27 occurrences

Total occurrences of '2' = 10 + 27 = 37.

### Final Answer
Therefore, the digit '2' will be written **37 times** when writing down the numbers from 11 to 199.

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