This paper is used to investigate the optimal solution to the NIM game by using the knowledge of binary in elementary number theory. In other words

proving and finding the corresponding solution of the NIM game for each of the players. It is concluded that the first player must have a winning strategy when the two piles of original numbers are not equally large or when the number of digits in each pile is represented in binary and all the digits are added up to an even number; conversely

the second player have also a winning strategy. In addition

the authors verify that it is not possible to generalise from the optimal solution of a 2-count heap to the optimal solution of several count heaps.