In the 53 years since finding this problem, I have discovered only one man (a statisticain in 2004) who solved it correclty, although with only one of the standard methods of solution.

Another reason I claim this is the National prejudice that "average" means only the arithmetic mean, which represents well for large samples.

Another reason is the following.

My criterion for first class (presentatin of) mathematics is that it be computer programmable. The most eqalitarian programming I know is by JavaScript,created by Netscape. It can be easily embedded in any HTML document (such as this one) ONLINE. It is simpel to write for most types of problems.

Now, a standard method for solving this present "problem" is by the harmonic mean.

Given a arithmetic progression (such as the counting order), the reciprocals of the memberrs of this progression forms a harmonic progression. This is because Pythagoras (x-y) is suppossed to have dsicvoered that vibratin of a fixed string subdivided into halves, thirds, etc., results in the chromatic scale of Western music. That this situation has prvailed for so many years is, to me, evidence that the Nation "just doesn't understand".