<HTML>In a message dated 1/10/02 8:48:30 AM Central Standard Time, jgunderson@monmouth.com (John Gunderson) writes: <BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">Just in case you were wondering. </BLOCKQUOTE> Here is what I read on this website: <<As a lecturer, Enrico Fermi used to challenge his classes with problems that, at first glance, seemed impossible. One such problem was that of estimating the number of piano tuners in Chicago given only the population of the city. When the class returned a blank stare at their esteemed professor, he would proceed along these lines: From the almanac, we know that Chicago has a population of about 3 million people. Now, assume that an average family contains four members so that the number of families in Chicago must be about 750,000. If one in five families owns a piano, there will be 150,000 pianos in Chicago. If the average piano tuner serviced four pianos every day of the week for five days rested on weekends, and had a two week vacation during the summer, then in one year (52 weeks) he would service 1,500 pianos. 150,000/(4 x 5 x 50) = 150, so that there must be about 150 piano tuners in Chicago. This method does not guarantee correct results; but it does establish a first estimate which might be off by no more than a factor of 2 or 3--certainly well within a factor of, say, 10. >> There seems to be a little problem with the math, here (duh).  4 x 5 x 50 = 1000, not 150, for starters.  Next, this idea that a piano "tuner" would "tune" 4 pianos a day, 5 days a week would also amount to 1,000 pianos, not 1,500.  But this supposition would amount to a rarity, not what an *average* piano technician would do. First of all, pianos need more than *just tuning*, as I'm sure we can all confirm.  I'd really question such a claim, that *anyone* really, only tuned 1,000 pianos every year, year after year.  That would inevitably amount to a *dis* service, not a good and honest way to make a living.  Please don't ask me to believe that there 150 of these guys running that kind of racket in Chicago! My off the cuff guess is there would be about 50 piano technicians in Chicago.  I'm not sure in this exercise if the 3 million figure is just Chicago or the whole metro area that includes all the suburbs or not.  The PTG directory lists a total of 110 for both the Chicago and Waukegan (a north suburb of Chicago) Chapters.  Of course there may be many people who are not PTG members. But still, that list includes people like Jack Greenfield and Virgil Smith whom I'm quite certain don't tune 20 pianos a week, 1,000 a year.  Then, there are people like Alan Vincent who run a company and do belly work and hardly ever tune and people like Kurt Saphir who probably *sells* 1,000 pianos a year and also rarely do any tuning. Wouldn't an easier and more accurate way of determining this number be to look in the phone book and count the names, then add maybe 10% for those who don't list themselves? Bill Bremmer RPT Madison, Wisconsin <A HREF="http://www.billbremmer.com/">Click here: -=w w w . b i l l b r e m m e r . c o m =-</A> </HTML>