Sunday, November 23, 2008

The Hardest Logic Puzzle on Earth

Well first of you may have noticed (if you use I.E.) that the layout has changed drastically and is almost completely free of bugs. I have also lost all respect for Microsoft and am considering to create a website just to combat them. I am just so sick of them...

On a happier note I was being bored again and surfing through the net I found this: It's a very interesting website and I advise you to read through it if you haven't finished a course on Psychology and Critical Thinking yet. The website states that George Boolos states that this is the most difficult logical puzzle on earth:

Three gods A , B , and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. 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 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.
I thought I might give it a try.

First of I Organised My Data:
  • 3 Gods: A,B,C
  • True Names of 3 Gods: True, False, Random
  • I can ask 3 true and false questions.
  • The response is either da/ja which means either yes/no.

After that I used one of my favorite computer algorithms; Brute Force =)
I calculated all of the possible answers to the puzzle:

So once I knew the 6 different answers I couldn't do anything more on that part of the puzzle but wonder if it was even something useful I had done.

I moved on to another part of the puzzle: The Questions.
I would have to ask 3 true and false questions to find out which of the 6 answers was the correct one. Not only would I have to consider the questions I would ask but also to which God I would ask them to.

Lets look closer at "True and False Questions". The question would have to be answered by yes or no (da/ja). The types of "True and False Questions" I could think of are listed below:
  1. Asks weather dogs are animals (true)
  2. Asks weather dogs are stones (false)
Upon further thinking I also thought of these more personal questions:
  1. Asks: Are you True/False/Random
  2. Asks opposite of 1-3
  3. Asks: Are you "Insert a Double Combination of Questions 1-3"
  4. Asks opposite of 5
I wasn't really sure if the first pair of questions or the latter bunch of questions would help me more so I just wrote both down. I would probably have to ask a correct combination of the above questions to find out what da/ja meant. Once I know what da/ja means I probably could find out with ease which god lied and which one didn't, I'm not sure about the Random god yet.

Lets apply the Brute Force Method Again:
  • The different Questions I could ask is: 2+3+3+3+3=14
  • The amount of Questions I could ask is: 3 (given)
  • The number of Responses I could get is: 2 (da/ja)
The Total Different Routes I Could Take or be Chosen to Take: 14*3*2=84
I'm pretty much stuck there. I will analyse the routes more carefully in the Next Post and I hope I'll get a result.

No comments: