Logic
# Deterministic Games

You are playing a game of Nim with an opponent by drawing stones from a single pile. On each turn a player can draw either 1 or 2 stones.

The person who takes the last stone wins.

It's your turn and the pile currently has 5 stones. How many stones should you take to win the game?

You are playing a game of Nim with an opponent by drawing blocks from the pile above. (The picture is a side view; gravity applies.) On each turn a player can take a block and any blocks that it supports. For example taking block C would also take D and E.

The person who takes the last block -- block A -- **loses**.

It's your turn. Which block should you take if you want to win? (**Remember, the one to take the last block loses.**)

You are playing a game of Nim with an opponent by drawing coins from two piles.

On each turn a player can draw as many coins as they like from one particular pile (but not both piles at once).

The person who takes the last coin **wins**.

It's your turn and the first pile and second piles both have 3 coins each. Assuming your opponent plays optimally (and is also trying to win), are you able to win the game?

You are playing a game with a single opponent where you are taking pieces from a 2x3 bar of chocolate. At each turn you can take a rectangle of chocolate along the lines. The main chocolate bar is required to be a single piece of chocolate at all times.

The 1x1 square in the upper left corner is poisoned chocolate, so the last person who takes it **loses**.

Given it's your move, which of these moves will guarantee you a win?

You are playing a game of Nim with an opponent by drawing stones from a single pile. On each turn a player can draw either **1, 2 or 3** stones.

The person who takes the last stone **wins**.

It's your turn and the pile currently has 6 stones. How many stones should you take to win the game?