Three Gods - God of Truth, Lies and Chaos

Problem:

You are stranded on an Island and on that island are 3 all knowing all powerful gods. One god is the god of truth, who always tells the truth and can never lie. The second god is the god of lies, he always lies and never tells the truth. The 3rd god is the god of chaos, he tells both lies and truths, however, completely randomly. The gods appear as identical twins, they all look the same. The gods also speak a language that you do not understand, except that you know that "uga" and "booga" are the responses yes and no (you however do not know which word is yes and which is no). You can only ask 3 yes or no questions to the gods in order to figure out which god is which. What 3 questions do you ask? 

 Solution

 We have to take advantage of the fact, that even the all-knowing god of truth doesn't know what God of chaos will answer to any question. Once, we find of god of truth, we can easily find of god of chaos or god of lies.

Lets denote god of truth by T, lies by F and god of chaos by C.

If we ask one of the 3 gods, about answer what C will answer, and he remains silient, its god of Truth, T.

Example

Lets order gods by 1,2, 3

Question # 1
Ask god 1 and 2 : “if I ask 3rd god of chaos 'you are one god of truth, who always tells the truth, right?' what would 3rd God
say?"
Case 1
God 1 : reply = Yes or No
God 2 : reply = Yes or No

Case 2
God 1 : silent
God 2 : yes or no

If its case 1, we know that both are answering and hence god 3 is T. In case 2, god 1 is silent so he is T, and god 3 may or may not be C.


Question #2
After case 1 of Question 1, ask god 3 : "f I ask 3rd god of chaos 'you are one god of truth, who always tells the truth, right?' what would 3rd God say?"

Case 11 : God 3 : = Can't reply.He is god of truth T.

After case 2 of Question 1, ask god 1 "if I ask 3rd god of chaos 'you are one god of truth, who always tells the truth, right?' what would 3rd God say?"
God 1 - Cant reply, god 3 is C

if god 1 replies, 2nd god is C.

Now we know who is  which god, but still don't know what is Uga and Booga.

Question #3
Ask God 3 : " is god 2 god of lies,who always lies ? "

God 3 : = Yes.(or whatever answer he tells, that means he is Uga or Booga is equal to yes)


hence, god 1 = god of chaos
god 2 = god of lies
god 3 = god of truths

Please let me know if you have some other solution.