What is the least number of links you can cut in a chain of 21 links to be able to give someone all...

logic/chain Added material

Problem

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?

Show solution

Two.

        OOO C OOOOO C OOOOOOOOOOO
(where Os are chained unbroken links, and the Cs are the unchained broken links)

And equivalently:

        OOO C OOOOOO C OOOOOOOOOO

Additional material

[ Editor: a reader's objection mailed to the archive in June 1995, from
the Explora Science Center <explora@Rt66.com>.  The reader reads "cuts"
as cuts dividing the chain into separate lengths, rather than links
opened so that the opened links can themselves be handed over.  The
archive maintainer's reply was not collected. ]

The logic/chain archive solution seems incorrect unless I am
misunderstanding the question.  Isn't it asking what is the least
number of cuts to a 21 link chain in order to be able to hand someone
combinations of those cut lengths summing to any length from the set of
lengths {1,2,3,4,...19,20,21}?  If so, wouldn't the minimum be 4 cuts,
an example of which is...

0-00-0000-00000000-000000