Deceitful Conversation

Logic Level 1

There are 5 people sitting around a table. And each of them is either those who always spoke the truth: truth-tellers, or those who always tells lies: liars.

Each of these 5 people claims that the two neighboring people sitting next to them are both liars. How many liars are there in this​ table?

0 1 2 3

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Fayssal Abdelli by Fayssal Abdelli , 35, Germany

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2 solutions

Calvin Lin Staff
May 19, 2016

Observe that

  1. We cannot have 2 truthtellers sitting next to each other.
  2. We cannot have 3 liars sitting together.

Hence, the neighbours must be of the form "LTL" or "LLT".

With 5 people, we can check that the only way to arrange them is in the form "LTLLT". This gives us 3 liars.

For 6 or more people, how many ways can we arrange for truthtellers and liars? For example, with 6 people, we can have "LLTLLT" and "LTLTLT". Are there other possibilities?

11 Helpful 0 Interesting 1 Brilliant 0 Confused

If you don't take into consideration the direction Left-Right or Right-left , you will have only TLTLTL TLLTLL else LTLTLT LLTLLT LTLLTL will be added as solutions as well :)

Fayssal Abdelli - 5 years ago

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For sitting around a table, the standard understanding is that rotations are not different arrangements, but reflections are.

Calvin Lin Staff - 5 years ago
Rex Holmes
May 13, 2016

skip count the number of people 1, 3, and 5, only 2 people can possibly be telling the truth and it is also the only solution that really makes sense.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Excellent :)

Fayssal Abdelli - 5 years, 1 month ago

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