Question

How many of the first one hundred positive integers contain the digit 7?

Short answer

20 of first one hundred positive integers contain the digit 7.

Step-by-step solution

Step-1 – Count the number of 7 from 1 to 10

The objective is to count the digit 7 in first one hundred positive integers.

7 appears only once when counted from 1 to 10.

Step-2 – Count the number of 7 from 1 to 11 to 69

7 appears only once when counted from 11 to 20.

7 appears only once when counted from 21 to 30.

7 appears only once when counted from 31 to 40.

7 appears only once when counted from 41 to 50.

7 appears only once when counted from 51 to 60.

7 appears only once when counted from 61 to 69.

Till now, the count of digit 7 is 7.

Step-3 – Count the number of 7 from 1 to 70 to 80

The numbers are 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80.

7 appears 11 times when counted from 70 to 80.

Till now, the count of digit 7 is 11 plus 7 which is 18.

Step-4 – Count the number of 7 from 1 to 81 to 100

7 appears only once when counted from 81 to 90.

7 appears only once when counted from 91 to 100.

Therefore, the count of digit 7 is 18 plus 2 which is 20.

Thus, 20 of first one hundred positive integers contain the digit 7.