It's a puzzle often credited to Enrico Fermi, the physicist who loved guessing big numbers from small ones. On 16 July 1945, at the first atomic test in New Mexico, he stood about ten miles away and dropped small pieces of paper from about six feet as the blast wave passed. They shifted about two and a half metres, and from that he worked out on the spot about 10,000 tons of TNT.

The trick is to break one big unknown into small guesses. About 9.5 million people live in the Chicago area. Say 2.5 to a home: 3.8 million homes. One home in 20 with a piano: 190,000 pianos, each tuned once a year. A tuner manages about four a day, roughly 1,000 a year. That makes about 190 tuners.

Each guess could be off by double or half, and if all five leaned the same way you would be 32 times off. But errors rarely line up. We ran 1,000 chains in which every step was off by a random amount up to double either way: 537 landed within a factor of two of the truth, 860 within four, and the worst was 23 times off.

The nearest real number: the U.S. Bureau of Labor Statistics counts about 350 musical instrument repairers and tuners on payrolls in the Chicago area (May 2023). That covers every kind of instrument and leaves out the self-employed, so it is a ballpark, not an answer. Our 190 is inside a factor of two of it.

And Fermi's paper? The Department of Energy's figure for the test is 21,000 tons, roughly twice his guess; a 2021 Los Alamos reassessment puts it at 24,800. Physicists call this kind of reasoning a Fermi estimate.

So, what was your guess?

Sources: Enrico Fermi, "My Observations During the Explosion at Trinity on July 16, 1945"; Selby et al., Los Alamos National Laboratory, "A New Assessment Statement for the Trinity Nuclear Test, 75 Years Later", 2021; U.S. Bureau of Labor Statistics, Occupational Employment and Wage Statistics, May 2023; our own chain and simulation.
Sounds: our own, made in code (earshot, CC0).