On Wed, Sep 29, 2010 at 10:23 AM, Andy Latto <andy.latto@pobox.com> wrote:
On Wed, Sep 29, 2010 at 12:11 PM, Veit Elser <ve10@cornell.edu> wrote:
Your solution was exactly what I was looking for.
As a participant in the new math experiment in California schools in the 1960s my reaction to doing arithmetic in base-5 was similar to Tom Lehrer's. A problem such as this one, I imagine, would have stimulated my interest because the binary representation enables you to do something you wouldn't have been able to do otherwise (unlike computing sums).
How so? Can't you do the same thing with decimal representations?
a_n are the numbers with 0 in every even place in their decimal representation. b_n are the numbers with 0 in every odd place in their decimal representation.
Doesn't that work just as well, with no need for binary?
No: 5 can be written as 2+3 or 1+4. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com