Oz's Question of the day #176 (18/12/09) Maths !

[OZXJR]

I am writing a book about the FZ6 forum and the number of pages is quite large.
I know that it takes 333 digits to print the page numbers in sequence.
How many numbered pages does the book have and how many times does the number 3 appear?

PM answers please.

 

[SirIsaac]

Count of pages and occurrences of the number 3 PMed.

 

[Jb40k]

Count of pages and occurrences of the number 3 PMed.

Sir Isaac in name and nature! GL dude!

 

[Less]

PM being sent.

 

[CHEMIKER]

I sent you 3 PMs.

 

[C-bus Biker]

PM on the way!

 

[teej21012]

PM Sent :rockon:

 

[OZXJR]

Answer:There are 147 pages and the number 3 appears 35 times.

Rep and casino cash winners:Sir Isaac,Chemiker and C-Bus Biker

Rep winner:Teej21012

congrats guys and thanks for playing.

 

[westgoingzax]

I didn't know where to start for this one. Can you explain a little, please?

 

[SirIsaac]

Oz said that if he put all of the page numbers together it would have 333 digits. For example if there were 9 pages, put together it would be 123456789, 9 digits long. Up through 99 pages you would add 20 digits for every 10 pages, so a 99 page book bould be 189 digits (9 times 20 plus 9). Over 100 pages, 3 digits are added for each page, so 333 minus 189 divided by three equals 48 more pages to get a 333 digit number. 99 plus 48 equals 147. The number 3 occurs as the units digit once each set of 10 numbers so that happens 15 times from 1 to 147, and it occurs 10 times in the 10 position from 30 to 39, then 130 to 139 which adds 20 more occurrences, total 35. QED.