SMRTR Science & EngineeringFeb 22, 2025Eli Bendersky

Making any integer with four 2s

SMRTR summary

A popular math puzzle challenges people to create any target number using only four instances of the digit 2 and various mathematical operations. The difficulty ranges from simple arithmetic for elementary students to complex operations involving exponents, factorials, and even advanced functions like Gamma for university graduates. In the 1920s, physicist Paul Dirac devised a general solution using nested square roots and logarithms that works for any number. This clever formula demonstrates how mathematical creativity can solve seemingly impossible challenges.

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