Taxicab Numbers

November 9, 2012

We haven’t done a coding interview question for a while. Here’s one that is supposedly asked at Google:

The mathematician G. H. Hardy was on his way to visit his collaborator Srinivasa Ramanujan who was in the hospital. Hardy remarked to Ramanujan that he traveled in a taxi cab with license plate 1729, which seemed a dull number. To this, Ramanujan replied that 1729 was a very interesting number — it was the smallest number expressible as the sum of cubes of two numbers in two different ways. Indeed, 103 + 93 = 123 + 13 = 1729.

Given an arbitrary positive integer, how would you determine if it can be expressed as a sum of two cubes?

Your task is to write a function that returns all the ways a number can be written as the sum of two non-negative cubes; use it to verify the truth of Ramanujan’s statement. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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