They should be renamed MRSA --- this fiendish contrivance represents a hazard at least to sanity, if not to life and limb. WFL On 11/28/11, Victor Miller <victorsmiller@gmail.com> wrote:

In the lastest issue of Emissary (the newsletter from MSRI) there's the following challenging puzzle:

For every positive integer n, write it in binary, and allow the following possible set of transformations:

You can insert "+" signs at arbitrary points within the binary expansion, and interpret that as a sum of binary numbers. For example

110101_2 --> 11_2+01_2+01_2 = 3 + 1 + 1 = 5 = 101_2.

Show that there is an absolute constant C such that for any positive integer n there is a sequence of at most C such transformations that results in 1.

Note: The minimal value of C is a real shocker

This made me wonder about the obvious generalization to other bases, where now we ask for a sequence of such transformation that results in a single digit base b number.

Victor _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun