**by Sasha kirillov**

If one makes a list of population of all the towns on Earth, it turns out that there are a lot more towns with population between 100,000-200,000 than 200,000 - 300,000. In fact, if we look at the first digit of the population number, than digit one is more common than 2, and 2 is more common than 3. And the same phenomenon happens for many other quantiites, from river lengths to electric bills amounts to physical constants. And if some numbers do not follow that rule, it may be an evidence that these numbers are fake - this was used to detect fraud in tax returns and election results.

In this lcture we show why this rule (called Benford's law) works and discuss its applications. This is intended for older students; some familiarity with logarithms is expected.