Puzzles

Guess which digit starts most of the world's numbers

Gather a huge pile of real-world numbers — river lengths, stock prices, populations, electricity bills, anything — and look only at the very first digit of each one. You'd expect the digits 1 through 9 to show up roughly equally often as the leading digit. They don't, and the imbalance shows up again and again across totally unrelated sets of numbers.

Reveal the answer

The digit 1 leads about 30% of the time, each successive digit shows up less often than the last, and 9 leads barely 5% of the time — because numbers that grow by multiplying (populations, prices, compound interest) spend more of their range with a leading 1 before rolling over to a leading 2, and so on down the line. Astronomer Simon Newcomb first noticed the pattern in 1881 from which pages of logarithm tables were most worn; physicist Frank Benford rediscovered and popularized it in 1938, and it's now used to help flag fraud in accounting, tax, and election data.

Frank Benford, The Law of Anomalous Numbers — Proceedings of the American Philosophical Society, 1938

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