Here is a nice round birthday cake with 2 layers. How can you cut it into eight equal pieces with only THREE cuts of the knife? (The first cut is shown.)
Cake Cutting
Set 08
Bagpipers
At the Ohio Scottish Games, a large number of beginning bagpipers are standing with their class in a circle on the grass. The class members count off. You are standing right behind the girl who calls out #16, and you observe that the boy directly across the circle from her is #47. How many members are in the class?
Nasty Book Page Fold
A nasty, horrid procedure to mark your place in the book you’re reading is to fold down the corner of the page. Fortunately, it doesn’t work very well because the folded-down corner is somewhat hard to spot. It is with considerable trepidation that I report to you that it is possible to fold a book’s page so that it protrudes from the rest of the book, thus being easy to spot. This wreaks even greater havoc on the book, but for the sake of scientific inquiry, see if you can figure out how to do it. Practice on, say, last year’s telephone book.