Wednesday, June 16, 2010

leaving

Well, our last days at Woodstock have been full of packing what we need and getting rid of what we don't. The very real constraints of space and weight and their costs have made us sharpen our ideas of what is important among the piles of our papers and clothes and other junk which has become such a burden in the light of our impending move. It is refreshing and liberating, and a bit melancholy. I feel like Ma Joad sitting next to her wood stove, taking one last look and pushing into the flames those papers that need to not make the trip. Quite literally, as this process has included some actual pushing letters into the wood stove.

That is something special about traveling, is a more frequent need to let go, to evaluate. Sometimes I just want a big attic or a garage with the potential to hold on to any box of papers I simply do not want to decide about. And other times I enjoy the healthy feeling of being rid.

And the leaving is very anticlimactic as we say goodbyes and then see people a few more times, or don't say goodbye because we didn't realize we wouldn't run into somebody during these last few frantic days. C'est la vie.

Wednesday, June 9, 2010

5-star challenge: hailstone numbers

Luke asked why I stopped with the math contest questions. As he forms a strong percentage of recent commenters on this blog, I suppose I ought to humour him. The fact is, these questions are tricky to find. I don't want something that just amounts to boring computations, and I don't want something that can be artlessly mined from Google or WolframAlpha.

This is one of the recent 5* challenge problems I ran. It's tied to a set of sequences that could keep me (has kept me) busy for hours. It's not like useful math, it's more the sort that could be warmly amusing and deeply intriguing, the kind of thing I would be thankful for on a desert island.

A hailstone sequence is defined recursively by this equation:

an = { 3*(an-1)+1 if an-1 is odd; (an-1)/2 if an-1 is even}

For example, if we start with 10, the next term (because 10 is even) is 5, the next term (because 5 is odd) is 16, then 8, then 4, then 2, then 1, then 4, 2, 1, 4, 2, 1… for ever and ever. The shortest hailstone sequence starting with 10 and concluding with 1 is 10, 5, 16, 8, 4, 2, 1 and its length is seven.

Find the sum of all positive integers N such that the length of the shortest hailstone sequence starting with N and concluding with 1 is thirteen.

Thursday, June 3, 2010

brainy legos

Two Lego projects for your consideration:
A Lego printer
A Lego Rubik's Cube solver
Oh, the people on that internet. My own obsession with Legos was so much more primitive. The internet brings us all so frighteningly close to some properly obscure endeavors.