MathDB

Suppose you are playing a game against Daniel. There are

2017

chips on a table. During your turn, if you can write the number of chips on the table as a sum of two cubes of not necessarily distinct, nonnegative integers, then you win. Otherwise, you can take some number of chips between

1

and

6

inclusive off the table. (You may not leave fewer than

0

chips on the table.) Daniel can also do the same on his turn. You make the first move, and you and Daniel always make the optimal move during turns. Who should win the game? Explain.

Problem Statement