How many times will Tom have to paint the number 8?

Question:

Tom was asked to paint numbers outside 100 apartments, which means he will have to paint numbers 1 through 100. How many times will he have to paint the number 8?

Answer:

Tom will have to paint the number 8 a total of 20 times.

Explanation

Get ready to explore the occurrences of the number 8 in the exciting painting task. Within the range of numbers from 1 to 100, the number 8 appears in various forms: in the tens place, as a single digit, and in numbers where it appears only in the units place.

Let’s list each occurrence of the number 8:

  1. In the tens place: 18, 28, 38, 48, 58, 68, 78, 88, 98
  2. As a single digit: 8
  3. In numbers where 8 appears in the units place but not in the tens place: 80, 81, 82, 83, 84, 85, 86, 87, 89 (88 is excluded because it’s already listed above)

Now, let’s put all 20 numbers inline: 8, 18, 28, 38, 48, 58, 68, 78, 88, 98, 80, 81, 82, 83, 84, 85, 86, 87, 89

Thus, Tom will have to paint the number 8 a total of 20 times.

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