How many times will the 5 digit be used in numbering the pages of a 145-page book?
Assume that the pages are numbered 1-145 in order and we don't
have any other page numbering system.
In every ten pages the digit 5 will appear in the units column
e.g. 5, 15, 25, 35, 45 etc.
That makes 15 fives.
In the 50's the digit 5 will also appear in the tens column
That makes another 10 fives.
Don't worry about page 55, remember we counted the unit's digit 5
first then the ten's digit 5.
The book is too short to have digit 5 in the hundreds column.
So the digit 5 appears 25 times in the numbering of a 145-page
book. == Answer
== From 1 to 145, we have 9 one-digit numbers and 100 two-digit
numbers and 46 three-digit numbers
In one-digit numbers we have only one chance to have
In two-digit numbers we can have 5 in the units place, in the tens
place or the both.
If we have 5 in the units place, then we can fill up the tens place
by the numbers from 1 to 9. So, we get 9 chances.
If we have 5 in the hundreds place, then we can fill up the units
place by the numbers from 0 to 9. So, we get 10
In three digit numbers, we can’t have 5 in hundreds place and tens
place because we have 145 pages in all. So, we can have 5 in
The hundreds place cannot be filled with any other number except
So, we can fill the tens place by the numbers from 0 to 4 only. So,
we get 5 chances.
In total, 25 times we come across 5. Source: