Question

What is the smallest two-digit prime that is the sum of three (not necessarily distinct) positive perfect cubes?

Answer 1

17

Explanation:

We begin by listing the smallest positive perfect cubes with two digits or fewer:

1, 8, 27, 64.

And now we sum them. 1+1+1 is too small; 1+1+8=10 which is not prime; but 1+8+8=17, which is indeed a prime. Hence the answer is 17

Answer 2

`17`

Explanation:

`1+8+8=17\\1^3+2^3+2^3=17`