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How many times will the 5 digit be used in numbering the pages of a 145-page book?

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βˆ™ 2007-07-13 12:20:49

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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 once,
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
e.g. 50,51,52,53,54,55,56,57,58,59
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 5.

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 chances.

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 units-place only.

The hundreds place cannot be filled with any other number except 1.

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: www.icoachmath.com


2007-07-13 12:20:49
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