27445998 the hardest logic puzzle ever

7/30/2019 27445998 the Hardest Logic Puzzle Ever

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Thehardest

logicpuzzle

everThe following puzzle was titled "L'indovinello pi difficile del mondo", which means"The hardest logic puzzle ever" in Italian. An American philosopher and logiciannamed George Boolos gave this Raymond Smullyan logic puzzle the name. It waspublished in an Italian newspaper called La Repubblica. Think you can solve it?

The Puzzle

Three gods A, B, and C are called, in some order, True, False, andRandom. True always speaks truly, False always speaks falsely, butwhether Random speaks truly or falsely is a completely randommatter. Your task is to determine the identities of A, B, and C byasking three yes-no questions; each question must be put to exactly

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one god. The gods understand English, but will answer all questions intheir own language, in which the words for yes and no are 'da' and 'ja',in some order. You do not know which word means which.

Clarifications

Boolos gave the following clarifications regarding this puzzle:

It could be that some god gets asked more than onequestion (and hence that some god is not asked any questionat all)

What the second question is, and to which god it is put, may

depend on the answer to the first question. (And of coursesimilarly for the third question.)

Whether Random speaks truly or not should be thought of asdepending on the flip of a coin hidden in his brain: if the coincomes down heads, he speaks truly; if tails, falsely.

Random will answer 'da' or 'ja' when asked any yes-noquestion.

P.S. from the author, but I agree with him: I'm posting this logic puzzle here for theenjoyment of puzzle lovers. I actually am actually pretty bad at logic puzzles.

The

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in heresomewher

edonteven think

aboutcheating,

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youvegiven up.

If so, hint:whats the

quad rootof 424 ?

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TheSolutionBoolos states that the first move is to find either the god True or False,

not Random.

One possible strategy is to use logical connectives in your questions:

Boolos' question was:

Does 'da' mean yes if and only if you are True if and only if B isRandom?

Or:

Are an odd number of the following statements true: you are False, 'ja'means yes, B is Random?

The puzzle's solution can be simplified by using counterfactuals. Thekey to this solution is that, for any yes/no question Q, asking eitherTrue or False the question:

* If I asked you Q, would you say 'ja'?

This results in the answer 'ja' if the truthful answer to Q is yes, and theanswer 'da' if the truthful answer to Q is no. The reason this works canbe seen by looking at the eight possible cases, explained below.

* Assume that 'ja' means yes and 'da' means no.

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(i) True is asked and responds with 'ja'. Since he is telling the truth thetruthful answer to Q is 'ja', which means yes.

(ii) True is asked and responds with 'da'. Since he is telling the truth

the truthful answer to Q is 'da', which means no.

(iii) False is asked and responds with 'ja'. Since he is lying it followsthat if you asked him Q he would instead answer 'da'. He would belying, so the truthful answer to Q is 'ja', which means yes.

(iv) False is asked and responds with 'da'. Since he is lying it followsthat if you asked him Q he would in fact answer 'ja'. He would be lying,so the truthful answer to Q is 'da', which means no.

* Assume 'ja' means no and 'da' means yes.

(v) True is asked and responds with 'ja'. Since he is telling the truththe truthful answer to Q is 'da', which means yes.

(vi) True is asked and responds with 'da'. Since he is telling the truththe truthful answer to Q is 'ja', which means no.

(vii) False is asked and responds with 'ja'. Since he is lying it followsthat if you asked him Q he would in fact answer 'ja'. He would be lying,so the truthful answer to Q 'da', which means yes.

(viii) False is asked and responds with 'da'. Since he is lying it followsthat if you asked him Q he would instead answer 'da'. He would belying, so the truthful answer to Q is 'ja', which means no.

Now that we know the eight cases, we can proceed:

Ask god B, "If I asked you 'Is A Random?', would you say'ja'?"

If B answers 'ja', then either B is Random (and is answeringrandomly), or B is not Random and the answer indicates that A isindeed Random. Either way, C is not Random. If B answers 'da', theneither B is Random (and is answering randomly), or B is not Randomand the answer indicates that A is not Random. Either way, A is notRandom.

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Go to the god who was identified as not being Random bythe previous question (either A or C), and ask him: "If I asked

you 'Are you True?', would you say 'ja'?"

Since he is not Random, an answer of 'ja' indicates that he is True andan answer of 'da' indicates that he is False.

Ask the same god the question: "If I asked you 'Is BRandom?', would you say 'ja'?"

If the answer is 'ja' then B is Random; if the answer is 'da' then the

god you have not yet spoken to is Random. The remaining god can beidentified by elimination.

There you have it - the word's hardest logic puzzle! It doesn't seem that bad, but itcan get really confusing. As for me - I can't even begin to wrap my head around it.But hopefully you've found this puzzle is be a tricky treat for your grey matter.

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Youre onthe

moon

27445998 the hardest logic puzzle ever

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