Question

Isaac wrote the integers from 1 through 104, inclusive. How many digits did he write?

Answer 1

We know that Isaac wrote the integers from 1 to 104, and we need to determine how many digits did he write

Let's look at single digit, double digit and triple digit numbers separately:

Single Digit Numbers' Range: 1-9

Total Single Digit Numbers = Ending Number - Beginning Number + 1

⇒ Total Single Digit Numbers = 9 - 1 + 1 = 9

Number of digits written in single digit numbers = 9 × 1 = 9 ......... (i)

Double Digit Numbers' Range: 10-99

Total Double Digit Numbers = Ending Number - Beginning Number + 1

⇒ Total Double Digit Numbers = 99 - 10 + 1 = 90

Number of digits written in double digit numbers = 90 × 2 = 180 ....... (ii)

Triple Digit Numbers' Range: 100-104

Total Triple Digit Numbers = Ending Number - Beginning Number + 1

⇒ Total Triple Digit Numbers = 104 - 100 + 1 = 5

Number of digits written in triple digit numbers = 5 × 3 = 15 .......... (iii)

Adding (i), (ii) and (iii)

Total number of digits written from 1-104 = 9 + 180 + 15

⇒ Total number of digits written from 1-104 = 204

Hence, while writing the integers from 1-104, we use 204 digits.