How do you always win the game of Nim?

To win at Nim-game, always make a move, whenever possible, that leaves a configuration with a ZERO “Nim sum”, that is with ZERO unpaired multiple(s) of 4, 2 or 1. Otherwise, your opponent has the advantage, and you have to depend on his/her committing an error in order to win.

What are the rules of Nim?

Nim is a combinatorial game, where two players alternately take turns in taking objects from several heaps. The only rule is that each player must take at least one object on their turn, but they may take more than one object in a single turn, as long as they all come from the same heap.

What is XOR method?

(eXclusive OR) A Boolean logic operation that is widely used in cryptography as well as in generating parity bits for error checking and fault tolerance. XOR compares two input bits and generates one output bit. The logic is simple. If the bits are the same, the result is 0. If the bits are different, the result is 1.

Who can lose in a NIM game problem?

In each turn, a player can choose only one pile and remove any number of stones (at least one) from that pile. The player who cannot move is considered to lose the game (i.e., one who take the last stone is the winner). ”

Can you win in NIM if you go first?

You may have noticed that if the first player takes a single matchstick from any of the three starting piles, he will always be leaving his opponent staring at a losing pattern. This means that the first player can always force a win!

How do you set up a NIM game?

To play Nim, one player sets up a number of piles of blocks, and the opponent chooses whether to go first or second. The players take turns removing blocks — each player may remove any number of blocks (at least one) from any one pile, and it is fine to take a whole pile — whichever player takes the last block wins.

How do you express XOR?

The logic symbols ⊕, Jpq, and ⊻ can be used to denote an XOR operation in algebraic expressions. C-like languages use the caret symbol ^ to denote bitwise XOR. (Note that the caret does not denote logical conjunction (AND) in these languages, despite the similarity of symbol.)

How do you solve the game two rocks?

Two Rocks Game. There are two piles of ten rocks. In each turn, you and your opponent may either take one rock from a single pile, or one rock from both piles. Your opponent moves first and the player that takes the last rock wins the game.

Who invented Nim?

Nim (programming language)