Home > Riddles > The chain of lies (7 in a circle)
There are 7 people sitting in a circle. Each one says exactly:
“My neighbor on the right is a liar.”
It is known that each person is of a unique type:
Is it possible for all 7 phrases to be compatible at the same time?
Back to problem
Answer: No, it is impossible.
If a person tells the truth when stating “my right neighbor is a liar,” then his neighbor is a liar.
If a person lies in stating that, then his right neighbor is truthful.
In both cases, the right neighbor type is the opposite. Therefore, around the circle you must alternate:
$$ V,M,V,M,\dots $$
This alternation can only be closed without contradiction when the number of people is even.
With 7 (odd), returning to the beginning requires that the first person be both equal and different from themselves.
Conclusion: Impossible configuration for 7.
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