A puzzle from the 1998 Moscow Mathematical Olympiad, via Peter Winkler’s excellent Mathematical Puzzles, 2021:
An anthropologist is surrounded by a circle of natives. Each native either always lies or always tells the truth. The anthropologist asks each native whether the native to his right is a liar or a truth teller. From their answers, she’s able to deduce the fraction of the circle who are liars. What is the fraction?
|
SelectClick for Answer> |
The key is to notice that if all the liars were changed to truth-tellers and vice versa, none of the answers would change. So if the fraction x can be determined, it must have the property that x = 1 – x, and x must be 1/2.
|