Brussels Sprouts Game and Euler's Characteristic

The video introduces the game 'Brussels Sprouts', explaining its rules and demonstrating gameplay. It reveals the mathematical trick behind the game, showing that the number of moves is predetermined. The Euler characteristic is used to analyze the game, demonstrating that the player who makes the last legal move wins. The video concludes with strategic tips for winning the game.

What is the main objective of the game Brussels Sprouts?

• To finish the game with the fewest moves

• To create the most number of vertices

• To be the last player to make a legal move

• To connect all free ends without crossing lines

In the game demonstration, why does the narrator claim the game is not a fair fight?

• Because the narrator starts with more crosses

• Because the narrator has a secret strategy

• Because the narrator is more experienced at the game

• Because the narrator is using a different set of rules

What is a planar graph in the context of the game?

• A graph where edges can cross each other

• A graph with only one face

• A graph with no vertices

• A graph where edges do not cross each other

According to Euler's characteristic, what is the formula for a connected planar graph?

• Vertices - Edges + Faces = 2

• Vertices + Edges - Faces = 2

• Vertices + Edges + Faces = 2

• Vertices - Edges - Faces = 2

How many vertices are there at the start of the game with two crosses?

• Eight

• Six

• Four

• Two

What happens to the number of free ends after each move in the game?

• It doubles

• It remains the same

• It decreases by two

• It increases by two

How many moves does the game end with if it starts with two crosses?

• Ten

• Eight

• Six

• Twelve

What is the outcome if the game starts with an odd number of crosses?

• Player 2 wins

• The game is a draw

• Player 1 wins

• The game never ends

How many moves does the game end with if it starts with three crosses?

• Seventeen

• Fifteen

• Thirteen

• Eleven

What is the formula for the number of moves if the game starts with n crosses?

• 5n - 2

• 4n - 2

• 6n - 2

• 7n - 2