# How many times does the digit 4 occur in the page numbers of a 50 page book?

Dec 13, 2016

$15$

#### Explanation:

The digit $4$ can occur in the units or tens positions.

It occurs in the units position in the numbers:

$4 , 14 , 24 , 34 , 44$

It occurs in the tens position in the numbers:

$40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49$

So there are a total of $5 + 10 = 15$ occurrences of the digit $4$.

If the question asked in how many page numbers the digit $4$ occurs then the answer would be $14$ - avoiding counting $44$ twice. However, since it asks for the number of occurrences of the digit $4$, $44$ should be counted twice.