Modified Ver. of Hardest Logic Puzzle Ever

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Baz
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Joined: Thu Jul 05, 2012 10:41 am

Modified Ver. of Hardest Logic Puzzle Ever

Postby Baz » Thu Jul 05, 2012 12:48 pm

Hi all,

Here is a version of Boolos' "Hardest Logic Puzzle Ever."

Give it a go if you have a couple of minutes to spare!

I have provided a solution to the problem at the end.
Would any skeptics be willing to check my solution and its validity?


PUZZLE BEG

Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but Random speaks in a completely random manner.

Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god.
The gods understand English, but will answer all questions in their 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:

a. It could be that some god gets asked more than one question (and hence that some god is not asked any question at all).

b. What the second question is, and to which god it is put, may depend on the answer to the first question. (And of course similarly for the third question.)

PUZZLE END

What follows is my solution to the problem. (NOTE: this problem, in its modified and original version, may be solved quite easily by using biconditionals. I avoid using these, as I believe the simplest way of solving a problem is usually the best... provided, of course, that I have actually solved the problem.)


SOLUTION BEG

Question 1
ASK GOD {A} - Is god {B} False?

Question 2
ASK GOD {B} - Is god {C} True?

Question 3
ASK GOD {A} - Are you True?

SOLUTION END

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Gulliver
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Joined: Wed Jun 27, 2012 10:40 pm
Location: Michigan

Re: Modified Ver. of Hardest Logic Puzzle Ever

Postby Gulliver » Sun Jul 08, 2012 3:14 pm

SOLUTION BEG

Question 1
ASK GOD {A} - Is god {B} False?

Question 2
ASK GOD {B} - Is god {C} True?

Question 3
ASK GOD {A} - Are you True?

SOLUTION END


If you get AT,BF,CR: A will answer one way, B will answer the same, and C will be either.
If you get AT,BR,CF: A will answer one way, B will answer either, and C will answer the opposite of A.
If you get AF,BT,CR: A will answer one way, B will answer the opposite, and C will answer either.

But already we have a problem since the third scenario may not necessarily be distinguished from the second. If A answers ja and B answers da and C answers da, then each is satisfied, which means neither is a better answer.

I don't think the provided solution works.


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