Game Theory and Score Evaluation

The king's competition to choose an heir involves rolling two dice 20 times. Contestants report their scores, but only Alexa's score is valid. Bertram's score exceeds the maximum possible, Cassandra's is statistically improbable, and Draco's score is mathematically impossible. Alexa, with a valid score, becomes the heir.

What qualities does the king desire in his heir?

• Strength, wisdom, and honesty

• Arithmetic skills, luck, and honesty

• Bravery, intelligence, and charm

• Leadership, courage, and honesty

What is the role of the advisor in the competition?

• To ensure the scores are honest and accurate

• To roll the dice for the contestants

• To train the contestants in arithmetic

• To declare the winner based on personal preference

What is the maximum possible score a contestant can achieve?

• 385

• 840

• 423

• 700

Why is Bertram's score of 840 considered impossible?

• He reported his score incorrectly

• He rolled more than 20 times

• The maximum score is 700

• He used a different set of dice

What makes Cassandra's score of 700 suspicious?

• It is the exact maximum possible score

• It is highly improbable to achieve

• She rolled the dice incorrectly

• She reported her score late

Why is Draco's score of 423 impossible?

• He reported his score incorrectly

• He used a different set of dice

• It is not a multiple of 5

• He rolled more than 20 times

What mathematical concept helps determine the impossibility of Draco's score?

• Probability theory

• Geometry

• Number theory

• Algebra

What is the significance of the dice numbers being multiples of 5?

• It makes certain scores impossible

• It allows for easier calculation

• It increases the difficulty of the game

• It ensures fairness in the game

What is the most likely score a contestant could achieve?

• 700

• 423

• 400

• 385

Why is Alexa considered the worthiest successor?

• She is the king's favorite

• She was the first to report her score

• Her score is possible and within range

• Her score is the highest