Three Puzzles Inspired by Ramanujan

Srinivasa Ramanujan’s story is part of mathematical folklore, one of the most romantic in the history of mathematics. He started as a poor self-taught clerk in India. Working alone, he discovered highly original and unknown mathematical results that were far ahead of his time. In 1913, he sent a letter filled with strange-looking mathematical theorems to G. H. Hardy, a mathematician at the University of Cambridge. Hardy, one of the world’s leading experts on number theory, later said that “some of [Ramanujan’s theorems] defeated me completely; I had never seen anything in the least like them before.” He was referring to results like the one below.