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# How do you win a NIM game in Python?

## How do you win a NIM game in Python?

In Python, XOR is denoted by ^ operator. In normal play, the winning strategy is to finish every move with a nim-sum of 0. This is always possible if the nim-sum is not zero before the move. If the nim-sum is zero, then the next player will lose if the other player does not make a mistake.

### Can you win Nim?

You can always win a Nim game if the number of stones n n n in the pile is not divisible by 4 4 4. Let us think of the small cases. It is clear that if there are only one, two, or three stones in the pile, and it is your turn, you can win the game by taking all of them.

How do you calculate Nim Sum?

If the number of 1s in a column is odd, you write a 1 underneath it; if it’s even, you write a 0 underneath it. Doing this for each column gives a new binary number, and that’s the result of the Nim addition. So the result, which is called the Nim sum, is the binary number 101.

Who can lose in a NIM game problem?

“ Given a number of piles in which each pile contains some numbers of stones/coins. 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). ”

## How do you play Nim games?

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.

### Can you win Nim If you go first?

Perhaps one of the easiest special cases of Nim occurs when there is only one pile. If there is only one pile, then clearly one wants to go first, in order to make the winning move: take the entire pile! A slightly less trivial and probably more informative case arises when there are exactly two piles.

How do you always win Fibonacci Nim?

In a winning position, it is always a winning move to remove all the coins (if this is allowed) or otherwise to remove a number of coins equal to the smallest Fibonacci number in the Zeckendorf representation.

Is Nim a zero sum game?

There are two general types of zero-sum games: those with perfect information and those without. In a game with perfect information, every player knows the results of all previous moves. Such games include chess, tic-tac-toe, and Nim.

## Is Nim solved?

Mathematical theory Nim has been mathematically solved for any number of initial heaps and objects, and there is an easily calculated way to determine which player will win and which winning moves are open to that player.

### Is chess solved?

As of 2022, work is still being done to solve 8 pieces on the board. Since there are more chess games (10^120) than the number of atoms in the observable universe (10^80), it is highly unlikely that chess engines will ever completely solve the game of chess with all 32 pieces on the board in our lifetime.

Has Connect 4 been solved?

Connect Four has since been solved with brute-force methods, beginning with John Tromp’s work in compiling an 8-ply database (February 4, 1995).