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Finding an Impostor
There are three people of a certain profession (say, medical doctors)
in a room, but one of them may be an impostor. Each person asks the other two a question that can determine whether the person is real.
The six yes (real) / no (impostor) opinions are presented to a judge
who must decide whether an impostor is present and, if so, who it is.
How would the judge go about deciding?
Somewhat similar to the fake coin puzzle
A real person always arrives at the correct judgment about another one,
but an imposter may render an incorrect judgment
1 2 3
-- N Y
N -- N
Y N --
Person assessed 1 2 3 A s s e s s o r
Assessment matrix A
Assessment matrix B
-- N Y
Y -- N
Y N --
Person assessed 1 2 3 A s s e s s o r
Impostors at a Dinner Table
At a round dinner table, n people of a certain profession (say, computer
engineers) try to determine if there are impostors among them. Each asks the person to his or her right a question and renders a judgment.
Assumptions are identical to the previous puzzle.
How many impostors can be correctly identified?
Repeat the puzzle above, but this time assume that each person asks
a question of his/her neighbor on both sides
A Related Puzzle: Blue-Eyed Islanders
Inhabitants of an island are blue-eyed or brown-eyed, but none of them knows the color of his/her own eyes, and must commit ritual suicide the next day at noon if s/he ever finds out.
[Okay, this is silly, but don’t argue with the premises, such as there not being any mirrors, etc.; just view it as an exercise in logical reasoning.]
The islanders are quite proficient in logical reasoning and won’t miss a chance to deduce their eye color, should there be enough info to do so.
Unaware of the islanders’ traditions, which make discussing eye colors a taboo, a visitor giving a speech on the island begins his speech thus: “It’s so good to see someone else with blue eyes on this island.”
What are the consequences of this faux-pas?
Hint: Begin by thinking about what would happen if there were just one blue-eyed islander and build up to larger numbers of blue-eyed people.
