Chapter 11
Making The ‘Hardest Logic Puzzle Ever’
a Bit Harder
Walter Carnielli
Abstract This paper intends to propose new forms of logic puzzles by adopting
a pluralist perspective. Not only can this expanded view lead to more challenging
puzzles, but it also helps the understanding of novel forms of reasoning. In 1996,
George Boolos published a famous puzzle, known as the ‘hardest logic puzzle ever’.
This puzzle has been modified several times, and is known not to be ‘the most difficult
of all logical puzzles’. I argue that modified versions of this famous puzzle can be
made even harder by using non-standard logics. As a study case, I introduce a version
of the puzzle based on the three-valued paraconsistent logic LFI1 and show how it
can be solved in three questions, leaving the conjecture that this three-valued puzzle
cannot be solved in fewer than three questions.
11.1 Harder and Harder Puzzles
Almost a quarter of a century ago, George Boolos published a short paper (Boolos
1996) that he qualified as ‘the most difficult of all logical puzzles’, attributed to the
logico-mathemagician Raymond Smullyan and modified by the computer scientist
John McCarthy, although related puzzles can be found throughout Smullyan’s books
since the seventies.
More than just another logical puzzle involving gods, genies, and strange tribes-
men who always tell the truth or lie, Boolos’ puzzle possesses interesting peculiarities
that make it highly non-trivial (though not to the maximum degree, as we shall see)
and philosophically relevant. Boolos’ original puzzle is as follows: Three gods A, B ,
and C are called, in some order, Verus, Falsus and Aleatorius. Their English nick-
names are True, False and Random. Verus always tells the truth, Falsus always lies,
and Aleatorius always speaks truthfully or lies in a completely random way. Your
task is to determine, in the original version of the puzzle, the identities of A, B , and
C with three questions whose answers are ‘yes or no’; each question should be posed
W. Carnielli (B )
Department of Philosophy and Centre for Logic Epistemology and the History of Science,
University of Campinas – UNICAMP, Campinas, SP, Brazil
e-mail: walter.carnielli@cle.unicamp.br
© Springer International Publishing AG 2017
M. Fitting and B. Rayman (eds.), Raymond Smullyan on Self Reference,
Outstanding Contributions to Logic 14, https://doi.org/10.1007/978-3-319-68732-2_11
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