Ten Problems

This problem is almost exactly the same as a previous one I posted about the gates to heaven and hell.

Simply ask one of the tribesman, “To what tribe would the other man say he belonged to?” Regardless of whether the first man is the liar or truth-tell, the answer will be opposite from the truth.

Finally, if you also saw one of the tribesman, you can determine is tribe by asking him “If I asked you if you were a Liari, would you say yes?”. If he is a liar, he would of course say no; but if he were the truth-teller, he would also say yes.

To make this explanation just a little less confusing, I’m going to refer to the Truthwi man as Mr. Truth (he always tells the truth), the Liari man as Mr. Liar (he always lies), and the Randwi man as Mr. Maybe (he tells the truth and lies at random).

A good place to start with this problem is to realize that Mr. Maybe’s answers are completely irrelevant. Therefore, the first 2 questions need to be directed at different people because you can’t afford to “waste” two questions on someone who may turn out to be Mr. Maybe. Next, as you would like to avoid asking questions to Mr. Maybe (since his answers are irrelevant), you would like to find a way to use the first question to either identify Mr. Maybe, or at least identify who Mr. Maybe is not. In the latter case, you will be able to direct the second question to the non-Mr. Maybe.

At this point, let’s number the three men 1-3, and make a chart displaying their possible arrangements:

Truth Maybe Liar
Liar Truth Maybe
Liar Maybe Truth
Maybe Truth Liar
Maybe Liar Truth

Let’s ask our first question to man number one. What are our requirements of this first question?

1. If the first man is Mr. Maybe (an unavoidable possibility), the first question will be irrelevant.
2. If the first man is not Mr. Maybe, the first question needs to determine which of men 2 and 3 is not Mr. Maybe (so that question 2 can be directed at this man). Therefore, question 1 must reveal information about Mr. Maybe’s identity, yet also prompt the same answer regardless of whether it is asked of Mr. Truth or Mr. Liar.

After a bit of thought, it might become apparent that the easiest way to accomplish this not so easy task is to ask man #1, “If I asked you if man #2 is Mr. Maybe, would you say yes?” If man #1 is Mr. Truth, and man #2 is Mr. Maybe, then the answer will of course be “yes”. However, careful study of the question’s wording reveals that if man #1 is Mr. Liar and man #2 is Mr. Maybe, the answer will still be “yes”. The same logic follows if this question is answered with a no.

We can see that if the first question is answered “yes”, then man #3 is not Mr. Maybe. If answered “no”, then man #2 is not Mr. Maybe. Whoever you determine is not Mr. Maybe should be asked the second question. Now what should the second question be? Since the previous question was helpful, let’s just repeat it. Whichever man is asked, make the question “If I asked you if man #1 is Mr. Maybe, would you say yes?” Through the same logic as the first question, this will deduce that a second invidiual is not Mr. Maybe. Thus, by process of elimination, Mr. Maybe is positively identified.

At this point, we have 2 men left - one Mr. Truth and one Mr. Liar - and only 1 question. This time, we don’t want to ask a question that will result in the same answer if asked to either Mr. Truth or Mr. Liar. A little more thought might lead us to this final question: Ask one of the two unidentified men “Would the other unidentified man answer yes if asked if he were Mr. Truth?” If the answer is “yes”, then the final question was asked to Mr. Truth. If the answer is “no”, then the final question was asked to Mr. Liar

This is what’s called a Simpson’s Paradox, although it’s not much of a paradox at all. The rabbit, being an overachiever, took 10 tests in the first month and averaged 60 (i.e. 60, 60, 60, 60, 60, 60, 60, 60, 60, 60,) while the tortoise only took two tests and averaged 50 (i.e. 50,50).

In the second month, the hare and tortoise both took the rest of their tests. The hare took two tests and averaged 90 (i.e. 90, 90), but the tortoise took eight tests and averaged 80.

Thus, the average comes out 65 for the hare and 75 for the tortoise!

Each man spent five dollars. They were son, father, and grandfather! (And thus two sons and two fathers)

Only one! After that the bag isn’t empty anymore!

Clever Young Al crossed his arm, then picked up the ends of the string and unfolded his arms!

The lions! Dead lions really can’t do much, can they?

They weren’t playing each other!

Three, because there are three letters in the word TEN.