Nthe “folklore” of mathematics, g. h. hardy, a twentieth-century mathematician, remarked to a colleague that the number 1,729 was “rather a dull number.” his colleague responded, “no, hardy! it is a very interesting number. it is the smallest number expressible as the sum of 2 cubes in 2 different ways.” which of the following are those 2 ways?

i. 1^3 + 12^3
ii. 2^3 + 11^3
iii. 4^3 + 8^3
iv. 9^3 + 10^3

select your answer.

i and ii

i and iii

i and iv

ii and iii

iii and iv