
In heaps of real-world data (invoices, censuses, river lengths, prices) the digit 1 shows up as the first figure around 30% of the time, and the 9 barely 4.6%. When someone makes numbers up, that invisible pattern breaks.
It's called Benford's law, and its discovery is a small gem: in 1881, the astronomer Simon Newcomb noticed that the first pages of the logarithm tables in his library (the ones for numbers starting with 1) were far more worn than the last. In 1938, the physicist Frank Benford confirmed the phenomenon across thousands of datasets.
Today forensic auditors use it as an accounting lie detector: whoever falsifies the books tends to spread the leading digits out evenly, and that evenness, paradoxically, is what gives them away.
Source: American Mathematical Society