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TOT 2014 Spring O J5, Ali Baba and 40 thieves, one boat can carry 2 or 3

Source:

September 11, 2020
combinatorics

Problem Statement

Ali Baba and the 4040 thieves want to cross Bosporus strait. They made a line so that any two people standing next to each other are friends. Ali Baba is the first, he is also a friend with the thief next to his neighbour. There is a single boat that can carry 22 or 33 people and these people must be friends. Can Ali Baba and the 4040 thieves always cross the strait if a single person cannot sail?
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