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Problem 1: Gamov, 1953

The paper "Extended Universe and creation of Galactics" by G.A. Gamov was published in 1953.
In that paper Gamov took two numbers - the age of the world and average density of matter in the Universe - and basing on them he determined the third number: the temperature of the relic radiation (cosmic microwave background). Try to repeat this scientific feat of Gamov.