A bookworm can chew through a millimiter (mm) of paper or cardboard in half an hour. One day it encounters a particularly tasty treat: a two-volume edition of a large book standing on a shelf as shown.

The volumes are identical in size, each has a front and a back cover that is a millimeter thick on each side, and the pages of each are a 10mm thick stack of paper from the first page to the last.

If a bookworm starts its meal on the first page of the first volume (already inside the front cover), how long will it take to eat his way through to the last page of the second volume (inside the second volume’s back cover)?

We really do not have enough informtion to provide a definitive answer....

The "trick" to the puzzle is that with the books stacked upright as shown in the given figure -- volume 1 on the left and volume 2 on the right -- the first page is usually on the right-side and last page on the left-side of each volume, with 2mm between the first page of volume 1 and the last page of volume 2. Yet, we are not given these facts definitively AND we given that the bookworm STARTS its meal on the FIRST PAGE of the FIRST VOLUME. 

Some of the information lacking is not being given the thickness of the each page or the turn-around time (how much chewing time required to turn around) and in what manner are the pages ordered, as some books (such as written in Hebrew) have their first page on the left-side and last page on the right-side. Also we are not given whether the last page of volume 2 is inclusively eaten.

Here are a few possibilites, with assuptions:

[1] Assuming the books are both written in a language like Hebrew or in the manner of, with pages left-to-right, and the last page is inclusively eaten:
10mm (volume 1's pages) + 1mm (back cover volume 1) + 1mm (front cover volume 2) + 10mm (volume 2's pages) => 22mm * 1/2 mm/hr = 11 hrs. 

[2] Assuming the books are both written in a language like English or in the manner of, with pages right-to-left, and assuming 1mm = 10 pages with the bookworm required to eat through the first page twice to make a turn-around, and the last page of volume 2 is inclusively eaten:
2*(1/10 mm) (first page volume 1, turning around) + 1mm (front cover volume 1) + 1mm (back cover volume 1) + 1/10 mm (last page of volume 2) => 23/10 mm * 1/2 mm/hr = 23/20 hrs = 1 hr 9 minutes.

[3] Assuming the books are both written in a language like English or in the manner of, with pages right-to-left, and the bookworm immediately abandons eating the first page of volume 1 to eat toward the last page of volume 2 (i.e., the last page is excluded in the diet of the bookworm for this puzzle): 2*1 mm * 1/2 mm/hr = 1 hr.

[4] Assuming volume 1 is written in a language like English or in the manner of, with pages right-to-left, and volume 2 is written in a language like Hebrew or in the manner of, with pages left-to-right, and the bookworm immediately abandons eating the first page of volume 1 to eat toward the last page of volume 2 (with the last page included in the bookworm's diet): 2*1mm + 10mm => 12 mm * 1/2 mm/hr = 6 hrs.

[5] Assuming volume 1 is written in a language like Hebrew or in the manner of, with pages left-to-right, and volume 2 is written in a language like English or in the manner of, with pages right-to-left, and the bookworm eats to the last page (with the last page of volume 2 excluded in the bookworm's diet): 10mm + 2*1mm => 12mm * 1/2mm/hr = 6 hrs.

Posted by Dej Mar on 2008-06-27 12:21:24