Question

Srinivasa Ramanujan, the great East Indian mathematician, was invited to Cambridge University in England in 1914 by the English mathematician G. H. Hardy. One day Ramanujan was ill in the hospital, and Hardy came to visit him. Hardy remarked that he had come in taxicab #1729, and said that he thought that this was an entirely uninteresting number. Ramanujan instantly replied, "Oh no! 1,729 is the smallest number that can be written as the sum of two cubes in two different ways."
The table below shows two patterns of numbers. The pattern in the top row represents the counting numbers. The pattern in the second row consists of the cubes of the counting numbers.

Which two pairs of numbers have cubes that add up to 1,729? Because there are two pairs of numbers to find, you should select a total of four numbers from the list below.



A. 8
B. 10
C. 3
D. 2
E. 5
F. 6
G. 1
H. 7
I. 9
J. 4
K. 11
L. 12

Answer 1

The two numbers are 1 and 12, and 10 and 9 (1+1728) (1000 729)