Plep's Puzzles

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Monday, January 03, 2005

Bookworm Puzzle

A bookworm eats from the first page of an encyclopaedia to the last page. The bookworm eats in a straight line.

The encyclopaedia consists of ten 1000-page volumes and is sitting on a bookshelf in the usual order. Not counting covers, title pages, etc., how many pages does the bookworm eat through?

(I found/stole this one from rec.puzzles some time ago - look it up if you like, but it's better to try and figure it out!)

Anonymous said...

Aahm ... 9001 or something like that? Because the first page (p.1) of the first book is 999 away from the left side of the shelf?? So only 9 vol. are following ...

- robert -

January 3, 2005 at 11:56 AM
guantanamo chicken said...

the answer's a thousand. i feel so special...

January 3, 2005 at 12:39 PM
Anonymous said...

You're both wrong... but Robert has the right idea... - Steven

January 5, 2005 at 12:33 AM
Anonymous said...

Aah ... now I see the problem with my suggestion, but not the solution. If he really starts with page 1, then he will come out of page 2. Means: he is moving from the right side of the first volume to the left. But doing so and (as given in the puzzle)only eating "in a straight line" he will never be able to reach the last page of the whole encyclopaedia.
Mmh ... no I'm really puzzled :o(
- robert -

January 6, 2005 at 6:40 AM
Anonymous said...

Ha, now I've got it (in German I would say "Ich hatte ein Brett vor dem Kopf) ... if page 1 of vol. 1 is 999 from the left, then of course page 1000 of vol. 10 is 999 pages from the right end of the shelf.
So the bookworm eats 1 on the left, 1 on the right and 800 in between (= 802)
Ha!!! ;o)

- robert -

January 7, 2005 at 2:20 AM
Anonymous said...

Gggrrr ... not 802 but 8002

January 7, 2005 at 2:22 AM
Anonymous said...

Is it 20000 because the pages are double sided?

January 8, 2005 at 8:03 AM
cbeck said...

a thousand page volume, assuming we are talking about numbered pages, would only consist of 500 actual pages. 1 & 2 being a front and back page etc. Starting with the first page, ten volumes "the encyclopedia" would consist of 5000 pages and that would be the number of pages he must eat through. if he does not eat the first and last page, then it would be 4998 pages...

February 8, 2005 at 2:40 PM
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October 6, 2005 at 2:43 PM
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November 8, 2005 at 9:07 AM
Anonymous said...

4000. If he starts on p1 Vol 1, then he doesn't eat any pages in Vol 1. When he reached p1000 of vol 10, he would not have eaten any pages in vol-10. Hence the bookworm will have eaten through the pages of vols2-9, ie 8 volumes. Assuming 500 pages per vol, so it eats 8x500 = 4,000 pages (assuming 1,000p book consists of 500 actual pages since one page has a front & back etc)

December 6, 2006 at 12:06 PM
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