Answer:
The answer to the question depends on the definition of piano tuner. If you assume the question refers to professional piano tuners only, and includes those professional piano tuners who are not exclusively piano tuners, the number could be approximated as follows:
Number of piano tuners in the world = (number of pianos that are periodically tuned in the world / average number of years between tunes for a periodically tuned piano) / average number of pianos tuned per year by piano tuners.
Now:
The number of pianos in the world = (the population of the world / number of people per household) * the number of pianos per household.
The number of periodically tuned pianos in the world = the number of pianos in the world * the percentage of pianos that are periodically tuned.
Where:
The population of the world = 7,000,000,000
Number of people per household = 5.5
Number of pianos per household = 0.02
Percentage of pianos that are periodically tuned = 40%
Average number of years between tunes for a periodically tuned piano = 5
Average number of pianos tuned per year by piano tuners = 100
Number of piano tuners in the world = (7,000,000,000 / 5.5 * 0.02 * 40%) / 5 / 100 = 20,364
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