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Numberphile: 4 ideas worth knowing

4 ideas from Numberphile, each explained in a minute and credited to the original work. Free on Savvy.

• Watch: why switching doors wins the car two times in three

  Numberphile works through the Monty Hall problem. The trick is the host: he knows where the car is and never opens its door, so his choice hands you information.

  — Numberphile, Monty Hall Problem - Numberphile

• Watch: every four-digit number falls into 6174

  Sort the digits high to low and low to high, subtract, repeat. Numberphile shows Kaprekar's routine reaching 6174 from almost any four-digit start, in seven steps at most.

  — Numberphile, 6174 - Numberphile

• Watch: a two-rule ant wanders in chaos, then builds a highway

  Numberphile runs Langton's ant: turn right on white, left on black, flip the square. About ten thousand steps of mess later, the ant locks into a repeating diagonal road.

  — Numberphile, Langton's Ant - Numberphile

• Watch: why 1 leads about 30% of real-world numbers

  Numberphile explains Benford's law: in many real data sets — populations, prices, river lengths — numbers start with 1 far more often than 9, and auditors use it to spot faked acco…

  — Numberphile, Number 1 and Benford's Law - Numberphile

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