TED-Ed: Can you solve the cheating royal riddle? | Dan Katz

In a competition devised by an eccentric King to choose his successor, contestants roll two dice 20 times to achieve the highest score. The advisor must disqualify any contestant suspected of cheating. Bertram's score of 840 is impossible, Cassandra's 700 is highly improbable, and Draco's 423 is mathematically impossible due to number theory. Alexa's score of 385 is valid, making her the new heir.

What is the probability of Cassandra rolling the highest number 40 times?

Explain why Draco's score of 423 is impossible.

Who is declared the worthiest successor and why?