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Q: How many times does the digit 1 appear in the page numbers of a 50 page book?

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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 columne.g. 50,51,52,53,54,55,56,57,58,59That 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 numbersIn 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

First 9 pages = 9 digit. That leaves 142 digits. @ 2 digit per page, that is 142/2 = 71 pages with 2-digit numbers. So, 9 pages with 1-digit numbers + 71 pages with 2-digit numbers = 80 pages.

50 times

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