Problem

Source: 42nd International Tournament of Towns, Junior A-Level P4, Spring 2021

Tags: knights and knaves, combinatorics, Tournament of Towns



A traveler arrived to an island where 50 natives lived. All the natives stood in a circle and each announced firstly the age of his left neighbour, then the age of his right neighbour. Each native is either a knight who told both numbers correctly or a knave who increased one of the numbers by 1 and decreased the other by 1 (on his choice). Is it always possible after that to establish which of the natives are knights and which are knaves? Alexandr Gribalko