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Deterministic Games

Whether you’re just playing around or a master of games, see how mathematical and logical ideas can be combined to analyze games from tic-tac-toe to Nim.

Nim Warmup

         

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, 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.

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?

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