The royal court of Prince Lemon had dukes, earls, and barons. At the beginning of the Prince's reign, there were 2020 members of the court and each day, one of them killed another one in a duel. Dukes only killed earls, earls only killed barons, and barons only killed dukes. No person won a duel twice. In the end, the only member of the court left alive was Baron Orange. What was the title of the first court member who was killed?

Question

Mathematics

Aspen Gates

2 November, 11:00

The royal court of Prince Lemon had dukes, earls, and barons. At the beginning of the Prince's reign, there were 2020 members of the court and each day, one of them killed another one in a duel. Dukes only killed earls, earls only killed barons, and barons only killed dukes. No person won a duel twice. In the end, the only member of the court left alive was Baron Orange. What was the title of the first court member who was killed?

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Adyson Rich · Answer 1

The tile of the first member of the court who was killed is an Earl

Step-by-step explanation:

The parameters given are;

Number of members in the court = 2020

Members of the court = Dukes = D, Earls = E and Barons = B

D only killed E, E only killed B and B only killed D

Therefore, the possible duels (combinations) are;

3! = 6 = DD, DE, DB, EB, EE, BB

Given that no one won a duel twice, we have that then DD, BB, and EE could not have occurred as it would result in one winning twice because D only killed E, E only killed B and B only killed D;

The relevant combinations are;

DE, DB, EB

The last person alive was a, baron, B, therefore, he killed a Duke, D, who killed an Earl, E

Given that there were 2020 members, there can be only 2020 - 1 duels = 2019 duels

Following the sequence, BD→DE→EB we have, 2019/3 = 673 complete repiting cycles

So, from the start, we have, a Baron killed an Earl, the Earl killed a Duke, and the Duke killed a Baron, making the tile of the first member of the court to be killed to be an Earl.