How many times the keys of a typewriter have to be pressed in order to write numbers from 121 to 1346?

Options

A. 3675
B. 4018
C. 4021
D. 4025

Answer

To solve the problem of how many times the keys of a typewriter have to be pressed in order to write the numbers from 121 to 1346, we can break it down into steps:

### Step 1: Identify the range of numbers
We need to write numbers from 121 to 1346.

### Step 2: Count the 3-digit numbers
The 3-digit numbers in this range are from 121 to 999.

To find the total number of 3-digit numbers:
- The first 3-digit number is 121.
- The last 3-digit number is 999.

Using the formula for counting numbers in a range:
\[ \text{Total 3-digit numbers} = 999 - 121 + 1 = 879 \]

### Step 3: Calculate key presses for 3-digit numbers
Each 3-digit number requires 3 key presses (one for each digit). Therefore, the total key presses for 3-digit numbers is:
\[ \text{Key presses for 3-digit numbers} = 879 \times 3 = 2637 \]

### Step 4: Count the 4-digit numbers
The 4-digit numbers in this range are from 1000 to 1346.

To find the total number of 4-digit numbers:
- The first 4-digit number is 1000.
- The last 4-digit number is 1346.

Using the formula for counting numbers in a range:
\[ \text{Total 4-digit numbers} = 1346 - 1000 + 1 = 347 \]

### Step 5: Calculate key presses for 4-digit numbers
Each 4-digit number requires 4 key presses. Therefore, the total key presses for 4-digit numbers is:
\[ \text{Key presses for 4-digit numbers} = 347 \times 4 = 1388 \]

### Step 6: Calculate the total key presses
Now, we add the key presses from both 3-digit and 4-digit numbers:
\[ \text{Total key presses} = 2637 + 1388 = 4025 \]

### Final Answer
The total number of times the keys of the typewriter have to be pressed to write the numbers from 121 to 1346 is **4025**.

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