This weeks Riddler Express is deceptively difficult. I say that I fell for the simple solution and did not catch it until it was too late.
The problem starts with an encyclopedia with 20 volumes. Each volume is 2 cm thick, and has a cover that is 2 mm thick. A bookworm wiggles to page one of volume one. The worm then eats through each volume to the last page of volume 20. The problem is to find how far the worm travels.
The solution is below.
The worm travels 43.6 cm.
The obvious part of the solution is that the worm will eat through the entirety of volumes 2 through 19. Each volume is 2.4 cm thick, 2 cm for the pages and 0.4 cm for the front and back cover. This is a total of 43.2 cm.
The devilishly difficult part is the distance the worm travels through volumes 1 and 20. When the books are arranged on a shelf, the first page of volume 1 is to the right. That means the worm only eats through the front cover to get to volume 2. The last page of volume 20 is on the left. The worm only eats through the back cover from volume 19. This adds an additional 0.4 cm to the total.
In my haste to finish, I submitted an answer of 47.6 cm. This has the worm eating through all of the pages of volumes 1 and 20. Without thinking of the arrangement of the books on the shelf, this is an easy mistake to make. I did not catch this mistake until after I submitted my answer.
A very similar problem was written by Marin Gardner in his 1969 book Perplexing Puzzles and Tantalizing Teasers. I vaguely recalled the problem when I read this week’s version. I knew there was a twist, but I did not remember it until after I submitted my answer.