How many 3's you have to write down while writing the numbers from 3301 to 3401 ?

Options

A. 220
B. 218
C. 198
D. none of these

Answer

To find out how many times the digit '3' appears while writing the numbers from 3301 to 3401, we can break down the problem into manageable steps.

### Step 1: Identify the range of numbers
We need to consider the numbers from 3301 to 3401. This includes all numbers from 3301, 3302, ..., up to 3401.

### Step 2: Count the occurrences of '3' in the thousands and hundreds places
- In the range from 3301 to 3399, the thousands place is always '3'.
- This means for every number from 3301 to 3399 (which is a total of 99 numbers), '3' appears in the thousands place 99 times.
- In the hundreds place, from 3300 to 3399, the hundreds digit is also '3' for all 100 numbers (3300 to 3399).
- Therefore, '3' appears in the hundreds place 100 times.

**Count so far:**
- Thousands place: 99 times
- Hundreds place: 100 times

Total from these two places: 99 + 100 = 199 times.

### Step 3: Count the occurrences of '3' in the tens and units places
Now we need to check the tens and units places for the numbers from 3301 to 3399.

#### Tens Place:
- The tens digit will be '3' for the numbers 3330 to 3339.
- This gives us 10 occurrences of '3' in the tens place (3330, 3331, 3332, ..., 3339).

#### Units Place:
- The units digit will be '3' for the numbers ending in '3' from 3301 to 3399.
- The numbers are: 3303, 3313, 3323, 3333, 3343, 3353, 3363, 3373, 3383, 3393.
- This gives us 10 occurrences of '3' in the units place.

**Count so far:**
- Tens place: 10 times
- Units place: 10 times

Total from these two places: 10 + 10 = 20 times.

### Step 4: Add all occurrences together
Now we add the occurrences from all digit places:
- From thousands and hundreds: 199 times
- From tens and units: 20 times

Total occurrences of '3' from 3301 to 3399 = 199 + 20 = 219 times.

### Step 5: Include the number 3400 and 3401
- In the number 3400, '3' appears once in the thousands place.
- In the number 3401, '3' appears once in the thousands place.

Adding these two occurrences:
219 + 1 (from 3400) + 1 (from 3401) = 221 times.

### Final Answer
Thus, the total number of times '3' is written while writing the numbers from 3301 to 3401 is **221**.

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