MathDB
Person on the chair n says that the n on their left are liars

Source: 2022 3rd OMpD L3 P3 - Brazil - Olimpíada Matemáticos por Diversão

July 8, 2023
combinatorics

Problem Statement

Let n≥3n \geq 3 be a positive integer. In an election debate, we have nn seats arranged in a circle and these seats are numbered from 11 to nn, clockwise. In each of these chairs sits a politician, who can be a liar or an honest one. Lying politicians always tell lies, and honest politicians always tell the truth.
At one heated moment in the debate, they accused each other of being liars, with the politician in chair 11 saying that the politician immediately to his left is a liar, the politician in chair 22 saying that all the 22 politicians immediately to his left are liars, the politician in the char 33 saying that all the 33 politicians immediately to his left are liars, and so on. Note that the politician in chair nn accuses all nn politicians (including himself) of being liars.
For what values of nn is this situation possible to happen?
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