An improvement on Braegh's answer.

1. Ask everyone what Y₁'s identity is. Majority is correct. If Y₁ is a villager or a knave, proceed to step two. Otherwise, proceed to step three.

2. Choose one of the people in the majority; they are a knight. Proceed to step three.

3. Use the knight to determine everyone else's identity.

An improvement on Braegh's answer.

1. Ask everyone what Y₁'s identity is. Majority is correct. If Y₁ is a villager or a knave, repeat this step. Otherwise, proceed to step two.

2. Use the knight to determine everyone else's identity.