knights and scoundrels
Source: ItaMO 2003, P4
February 13, 2012
number theory proposednumber theory
Problem Statement
There are two sorts of people on an island: knights, who always talk truth, and scoundrels, who always lie. One day, the people establish a council consisting of members. They sit around a round table, and during the council each member said: "Both my neighbors are scoundrels". In a later day, the council meets again, but one member could not come due to illness, so only members were present. They sit around the round table, and everybody said: "Both my neighbors belong to the sort different from mine". Is the absent member a knight or a scoundrel?