The Magic Café
Username:
Password:
[ Lost Password ]
  [ Forgot Username ]
The Magic Cafe Forum Index » » Puzzle me this... » » Bookshelf puzzle (0 Likes) Printer Friendly Version

Rennie
View Profile
Inner circle
I think I have about
1876 Posts

Profile of Rennie
I never had anyone figure this out, after I told them it was obvious. You have to imagine 10 books on a bookshelf, each book contains 100 pages exactly, including the cover and back. A bookworm starts eating on the first page of the first book and eats through to and including the last page of the last book.

How many pages did the bookworm eat through?

Rennie
The effect is the important thing, how you achieve it is not.......
Jonathan Townsend
View Profile
Eternal Order
Ossining, NY
27097 Posts

Profile of Jonathan Townsend
Gosh I'm confused.

Is the cover a page?
Can a bookworm eat through a cover?
By page do you mean side of a printed sheet?
...to all the coins I've dropped here
pxs
View Profile
Loyal user
London
284 Posts

Profile of pxs
My guess: 901
0pus
View Profile
Inner circle
New Jersey
1739 Posts

Profile of 0pus
Are you sure that shouldn't be "A bookworm starts eating on the first page of the last book and eats through to and including the last page of the first book" instead?
pxs
View Profile
Loyal user
London
284 Posts

Profile of pxs
I think that's the nub of the puzzle, Opus
Mushu
View Profile
Loyal user
253 Posts

Profile of Mushu
When the bookworm eats through a single sheet of paper, it's actually fishished off two "pages". The front and back covers are considered "pages" in this puzzle, and presumably the inside of the covers are also considered a "page" as well.

So if the bookworm starts on the first page of the first book, I'm assuming that it's the outside cover of the first book which faces the inside of the row, which means he leaves the first book untouched.

Similarly, he stops after comsuming the front cover of the second last book, and leaves the last book untouched, as the last page of the last book faces the row.

Then we'd also have to assume that the first and last books are put in the shelf right-side up, and are not Chinese (which open from the other side).

In the end, it depends on the definition of a "page", and being consistent in that definition.
0pus
View Profile
Inner circle
New Jersey
1739 Posts

Profile of 0pus
Well, given the way the problem was originally presented, the answer is 1,000, if both the first and last books are rightside up; 901, if one of the first book is rightside up and the last book is upside down (or vice versa); and 902 if both the first and last books are upside down.
Rennie
View Profile
Inner circle
I think I have about
1876 Posts

Profile of Rennie
Yes, the cover is considered a page and it is being counted as page #1 in the question, and the last page of the last book is the back cover. Sorry for any confusion.

Again, the bookworm starts on the first page (cover) of the first book and eats through to and including the last page of the last book. Each book is considered 100 pages each (counting front and back cover).

Rennie
P.S. Opus is on the right track.
The effect is the important thing, how you achieve it is not.......
pxs
View Profile
Loyal user
London
284 Posts

Profile of pxs
The worm only eats one page of book one (as the first page is on the right)
The worm eats every page of books two to nine
The worm only eats one page of book 10 (as the last page is on the left)

So my revised answer is 802
Mushu
View Profile
Loyal user
253 Posts

Profile of Mushu
First book—two "pages" (assuming that first page of the first book is inclusive) since he can't just eat through half a sheet, both the front cover and inside cover must be eaten, and by definition counts as two pages.

Second through Ninth—100 "pages" each.

Last book—another two "pages", as per explanation for first book, same goes for the back cover of the last book.

Thereby, 2 + (8*100) + 2 = 804

But if this industrious little bookworm can just eat halfway through a sheet and does so on the covers of the first and last books, then I'll go along with pxs and say 802.
landmark
View Profile
Inner circle
within a triangle
4919 Posts

Profile of landmark
The problem is more elegant in this form:

Two volumes of a two-volume dictionary are on a bookshelf next to each other. Each volume is one inch thick plus an additional quarter inch for each cover. If a bookworm bores through from the first page of the first volume to the last page of the last volume, how far has it traveled?

Answer: one-half inch.

Ever helpful,
Jack Shalom
Rennie
View Profile
Inner circle
I think I have about
1876 Posts

Profile of Rennie
PXS,

That is the correct answer. For some reason when I present this puzzle no one can imagine the books sitting as they would on a bookshelf. It just shows me that people into magic have a high I.Q. (I knew it all along) can not convince my wife of that though...

Mushu, you are correct except I should have stated the cover counts as a page and we do not count page numbers, just the number of pages.

Good job everyone..
Rennie
The effect is the important thing, how you achieve it is not.......
0pus
View Profile
Inner circle
New Jersey
1739 Posts

Profile of 0pus
Rennie,

I think there is a discrepancy here. The problem as stated by you is: "A bookworm starts eating on the first page of the first book and eats through to and including the last page of the last book."

That is ALL of the pages on the bookshelf if the books are all oriented rightside up, isn't it?

If the problem was: "What is the least number of pages..." then mxs would be correct.

Or, if the problem was: "A bookworm starts eating on the first page of the last book and eats through to and including the last page of the first book," then mxs would again be correct.

Are you sure the problem is stated properly?

0pus
Rennie
View Profile
Inner circle
I think I have about
1876 Posts

Profile of Rennie
Opus,

The problem you stated is the reason no one gets it right. If you look at a book on a shelf, the first page is actually the last page on the right side of the book. Hence the bookworm starts on the first page (last page on the right side of the first book) eats through to and including the last page of the last book (the first page on the left of the last book). Remember, you have to look at the books like they would be on a shelf.

By the way, where are you from in Jersey, as that is where I am originally from?

Rennie
The effect is the important thing, how you achieve it is not.......
0pus
View Profile
Inner circle
New Jersey
1739 Posts

Profile of 0pus
As Homer Simpson would say, "Doh!"

I live in Berkeley Heights, near Summit.

0pus
Granite Golem
View Profile
New user
St.-Petersburg, Russia
3 Posts

Profile of Granite Golem
Let me guess, the bookworm will eat through 998 pages. The last two pages it will simply eat, not through because it will set against bookshelf's wall.

P.S. "Don't make people think—they won't forgive you for it." Smile
The Magic Cafe Forum Index » » Puzzle me this... » » Bookshelf puzzle (0 Likes)
[ Top of Page ]
All content & postings Copyright © 2001-2020 Steve Brooks. All Rights Reserved.
This page was created in 0.12 seconds requiring 5 database queries.
The views and comments expressed on The Magic Café
are not necessarily those of The Magic Café, Steve Brooks, or Steve Brooks Magic.
> Privacy Statement <

ROTFL Billions and billions served! ROTFL