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Rajat noticed an interesting pattern: sometimes, when you add the digits of different numbers,
the sums are the same.

For example:

 68: 6 + 8 = 14

 176: 1 + 7 + 6 = 14

 545: 5 + 4 + 5 = 14

All these numbers have a digit sum of 14!

Digit Detectives

Mahi had a curious thought: how often does the digit ‘7’ appear when writing all the numbers
from 1 to 100 or even 1 to 1000?

 1 to 100: The digit ‘7’ appears in the 7th, 17th, 27th, 37th, 47th, 57th, 67th, 70-79 (10
times), and 87th, 97th. This totals to 20 times.

 1 to 1000: The digit ‘7’ will appear more frequently in three positions (hundreds, tens,
and units) across all numbers from 1 to 1000. Calculating this for each position involves
counting how often ‘7’ appears in each digit place:
 Units place: 100 times (7, 17, 27...997)

 Tens place: 100 times (70-79 in each hundred)

 Hundreds place: 100 times (700-799)

 So, the digit ‘7’ appears 300 times between 1 and 1000.

Question: What is the total number of five-digit numbers?
A. 90,000 B. 10,000 C. 9,000 D. 1,00,000
Explanation
B. 10,000
To calculate the total number of five-digit numbers, we need to consider the range from 10,000
to 99,999.
- Subtract the smallest five-digit number (10,000) from the largest (99,999) and add 1.