Question

1. On a certain island, the inhabitants are three kinds of people: knights who always tell the truth, knaves who always lie, and spies who can either lie or tell the truth. You encounter three people, A, B, and C. You know one of these people is a knight, one is a knave, and one is a spy. Each of the three people knows the type of person each of other two is. If A says "C is the knave," B says, "A is the knight," and C says "I am the spy," determine whether there is a unique solution and determine who the knave, knight, and spy are. When there is no unique solution, list all possible solutions or state that there are no solutions.

Answer 1

A is Knight, B is Knave , and C is Spy is the solution.

Knights lways tell the truth knaver . Always lie. Spier - who can either lies or tell the truth We haved encountered 3 peopler A, B, C cone of each A says cis knare type) B says A is knight says I am the spy. To we can consider three cases as follows case 0 A is knight A tells truth A-Šknight c is knare (e always lies is not tona spy) -B is spy. one solution is a knight B- spy c-knare case B is knight → B tells douth Calwars) Buf B say. A is knight which is true A is knight and B is lenight. Hot possible. case @ cis knight ic always tell the truth c says I am the spy which is south - ( is knight & cis spy which is not possible . Problem har only one solution A-knight B- knare C-spy.