Fermi's
Piano Tuner Problem
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 1,000 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. We know, for example, that we should
not expect 15 piano tuners, or 1,500 piano tuners. (A factor of 10 error,
by the way, is referred to as being 'to within cosmological accuracy.'
Cosmologists are a somewhat different breed from physicists, evidently!!!)