Ebook: Mathematical Quickies: 270 Stimulating Problems with Solutions (Dover Books on Mathematical and Word Recreations)

Many of these problems are indeed quite elegant, but way too many (generally the geometric ones) require the use of theorems that even many math majors may not know -- this is more for the "contest math" genius in high school more than necesasrily a math major, and even they may not know the theorems required.

And not all of these problems are necessarily "quickies". For instance, one asks multiplcation of a very large number by 125 -- the quickie solution is to multiply by 1000 and divide by 8, but this is not even so "quick".