UPDATED: I've often used this puzzle to stump people, and this time I fell into my own trap. I tried to create even numbers for easy mental calculations, but I kept changing the numbers of volumes. In typing up the solution, I got sloppy and forgot that the central trick of the puzzle is that there are TWO FEWER BOOKS eaten than would appear to be the case. In my original solution, I only calculated one. Thanks to readers Eye of the Frog and Ethan C. for catching the error. This post has been revised to correct the mistake. (I plead exhaustion: aside from the puzzles that are directly quoted, I wrote the last two weeks worth of material from memory in a single sitting. No, Martin Gardner would not have bought that excuse either, but it's my story and I'm sticking to it.)
58 inches
Remember, if a set of books is in order on a shelf, the first volume will be the furthest book on the left. This would place the first page of that book to the right of that volume. The front cover of each book (except for the last) touches the back cover of the next book in line. The back cover of the first volumes touches nothing.
Therefore, a worm starting on the first page of the first volume will not need to eat through the first volume. It only needs to eat through the cover.
Since it's only going to the last page of the last volume, it doesn't need to eat through the front cover or text of volume 26.
24 volumes at 2 inches each = 48 inches
50 covers (front and back for volumes 2 to 25, plus the front cover of volume 1 and the back cover of volume 26) at 1/5th of an inch each = 10 inches
58 inches
Remember, if a set of books is in order on a shelf, the first volume will be the furthest book on the left. This would place the first page of that book to the right of that volume. The front cover of each book (except for the last) touches the back cover of the next book in line. The back cover of the first volumes touches nothing.
Therefore, a worm starting on the first page of the first volume will not need to eat through the first volume. It only needs to eat through the cover.
Since it's only going to the last page of the last volume, it doesn't need to eat through the front cover or text of volume 26.
24 volumes at 2 inches each = 48 inches
50 covers (front and back for volumes 2 to 25, plus the front cover of volume 1 and the back cover of volume 26) at 1/5th of an inch each = 10 inches
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ReplyDeleteWait, what? The last page of the last volume would be the first page the worm gets to in the last volume.
ReplyDelete*Deleted my first comment to edit for clarity*
Right, ending on the last-page-of-the-last nets the same advantage as starting on the first-page-of-the-first.
ReplyDeleteSo that's another 2 inches off. 58 inches total.
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ReplyDeleteDame, you're right. I did these from memory and screwed up the math on this one. There IS an extra 2" lost, bringing it down to 58".
ReplyDeleteThe post has been updated and I am duly humbled.
ReplyDelete