This article is from the Puzzles FAQ, by Chris Cole firstname.lastname@example.org and Matthew Daly email@example.com with numerous contributions by others.
What is the least number of links you can cut in a chain of 21 links to be able
to give someone all possible number of links up to 21?
OOO C OOOOO C OOOOOOOOOOO
(where Os are chained unbroken links, and the Cs are the unchained broken links)
OOO C OOOOOO C OOOOOOOOOO