On a certain island there live only knights, who always tell the truth, and knaves, who always lie.
One day you find 10 island natives standing in a circle. Each one states: "Both people next to me are knaves!"
Of the 10 in the circle, what is the minimum possible number of knights?
if every other one is a knight, then 5 will be telling the truth, but all can say the statement above.
If four of them are Knights, it can be true (KkkKkkKkKk...)
To determine the minimum possible number of knights among the 10 island natives, let's analyze the statements they make.
Assume A represents a knight and B represents a knave. We need to find the arrangement of A's and B's that satisfies the given statements.
Let's break down the statements made by each person in the circle and analyze the possibilities:
1. If the first person in the circle is a knight (A), then both people standing next to them must be knaves (B). This would make the arrangement: ABBBABBBBB (where A represents a knight and B represents a knave).
2. If the first person is a knave (B), the second person must be a knight (A) because they claim that both people next to them are knaves. The arrangement would then be: BAABBBABBB.
Now we can observe that every knight (A) is always surrounded by knaves (B). It means that there must be at least one knight in the circle, otherwise it would contradict the statements.
Therefore, the minimum possible number of knights in the circle is one.