Sources mentioned in my presentation at Lexington ISBN Toastmasters on February 23:
The Online Encyclopedia of Integer Sequences which allows you to search for previously studied sequences by simply entering the first several numbers of the sequence: http://oeis.org. This is an indispensable resource for mathematicians and math students. You can find out a lot about Alcuin's sequence here.
The paper I used to prepare my presentation was by Donald J Bindner and Martin Erickson. It appeared in the February
2012 American Mathematical Monthly, which can be obtained at JSTOR:
Cost is $12 unless you have a JSTOR subscription for this journal, and you can read the abstract and first page for free. It is very much worth reading for those wanting an in-depth treatment of Alcuin's Sequence.
I am using a puzzle problem to illustrate the way in which I teach math to adult students who may not have much experience in the subject, which is the purpose of my company, Math for the Rest of Us.
I will introduce the puzzle and some problems related to it in this blog, and then will talk about its solution during the meeting of Lexington (MA) Toastmasters at 12 noon on February 23. (The source of my presentation and information relating to the solution will be listed on the blog after February 23.)
A rich merchant died and left an inheritance to his three sons. The inheritance consisted of 30 identical silver boxes, of which 10 were full of gold, 10 were exactly half-full of gold, and 10 were empty. He instructed that the inheritance be divided equally, so that each of the three sons received the same amount of silver and the same amount of gold. For the purpose of the division, it is impossible to remove any gold from any box. How can the treasure be divided equally?
This puzzle goes back to the early middle ages. Before following the link, try your hand at solving the puzzle. It can be solved by a little trial and error, and some elementary algebra may be helpful.