JuJu and the tribes

Logic Level 4

On the Tito Island, there are two tribes, TiTi and ToTo living separately in two villages, TiLavi and ToLavi. TiTi tribesmen are truth tellers while ToTo people are pathological liars. You just landed alone on the island as an anthropologist to conduct research on the tribes. As an outsider, you know you have to meet the JuJu, the high priest(ess) / ritual specialist / medium (both spiritual and between the tribes) to get your approval stamp from him / her before nightfall. The JuJu lives alone outside of both TiLavi and ToLavi, so you cannot just tail anyone to reach his / her place. You saw three male islanders on the beach and decided to ask for their assistance in heading to the JuJu's hut, but you need to know if you can trust them first by asking a question (you have already learnt the basics of the tribes' mutual language before making the research plan).

You : How many of you are TiTi tribesmen?
Islander 1 : Three
Islander 2 : Three
Islander 3 : Three

Assumptions :
1) They have the same number of people in each tribe (for a total of 2x+1 islanders).
2) Even as liars, the ToTo tribespeople are smart. When they lie, they do it convincingly and LOGICALLY. Their lies might be contradictory to each other as they don't coconspire the lying plots together, all that matter is that they
a) are lying, and
b) don't get busted with their own lies (I mean, you might suspect that some of them is / are definitely lying, but that's fine by them if you can't point fingers to any one of them conclusively).

Now that you know everything that you needed to know, how likely is that you're talking to a group of 3 ToTo tribesmen, based on the conversation above? Give your answer as percentage (%).


The answer is 3.57142857.

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1 solution

Omek K
Feb 13, 2021
  • I am not sure if this is the correct but this how I did it
  • One trivial case is talking to 3 Titi tribesmen
  • now if there were 1 or 2 number of Titi tribesmen, then all the three statements won't be 3, so those three are toto tribesmen but each of the toto tribesmen can say three statements
  • That is 1 or 2 or 3 , so total 27 possibilities out of which the 3,3,3 is one case
  • Therefore the answer is 1 28 \frac{1}{28} ×100 = 3.57142%
  • Correct me if i am wrong

Based on the conversation above, you are either talking to 3 TiTi or you are talking to 3 ToTo, and the percentage is 50%

Another attempt for domestication in the footsteps of Brilliant.. in addition, the person raising the problem is accustomed to write for himself/herself as if others are living in his/her mind.. finally, unnecessary details, extensions & annotations

argi nargi - 1 week, 5 days ago

This is wrong, you have to calculate conditional probability not the probability of theses three statements out of all possible ones

j h - 4 days, 15 hours ago

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