# Winning way of NIM

#### The case of two piles

Winning way is to make the number of stones the same.

#### The case of three cases

Winning way is to make the nim-sum of the numbers of stones of piles equal to 0.

#### How to calculate nim-sum.

To calculate the nim-sum of two numbers x and y is to express them in base 2 and add them without carryies.

For each n, we count the number of 1 that are contained in the column for 2

^{n}. If the number of 1 is even for each n, then the nim-sum of these three number is 0.

#### The nim-sum is very important concept for combinatorial games including chocolate games.

NIM is mathematically the same as Rectangular Chocolate Game.