by **JC**, updated: 2013-03-05 20:44 viewed: 425 times

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Here is another challenge math problem for gifted students in their 4th grade. It is somewhat interesting as it relates more to logic/brain teaser than math.

The Problem:

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Two brothers named Arthur and Robert Zeno were on trial for espionage (spying), since it was known that one of the two was a spy. It was also known that at least one of the two never told the truth, although it was not known that the spy was a liar - perhaps his brother was, perhaps both were.

At the trial the judge, a stern man named Wittgenstein, first asked Arthur, "Are you the spy?" Arthur replied, "Yes." The judge then asked Robert: "Are you the spy?" Robert answered (with either a yes or a no), and Judge Wittgenstein then figured out which one was the spy.

Who was it?

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Before I post the answer, I'd have to ask, what's your answer to this and how you got it? Please follow with your comment.

The Problem:

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Two brothers named Arthur and Robert Zeno were on trial for espionage (spying), since it was known that one of the two was a spy. It was also known that at least one of the two never told the truth, although it was not known that the spy was a liar - perhaps his brother was, perhaps both were.

At the trial the judge, a stern man named Wittgenstein, first asked Arthur, "Are you the spy?" Arthur replied, "Yes." The judge then asked Robert: "Are you the spy?" Robert answered (with either a yes or a no), and Judge Wittgenstein then figured out which one was the spy.

Who was it?

-------------

Before I post the answer, I'd have to ask, what's your answer to this and how you got it? Please follow with your comment.

1. craig omidyar 2013-03-05 19:20

There is 2/3 propable that Robert is the spy when Robert answers Y.
2. JC 2013-03-05 20:44

@craig,Sort of, but that's not the main point I guess. One tip/trick I'd say is, read the question carefully again and see if you are missing anything that could give you the definitive answer ;-)

3. sam 2014-03-03 21:59

Does the answer has to do with "it", I am confused, what's the solution?
4. JC 2014-03-04 07:11

@sam,The hint is "Judge Wittgenstein then figured out which one was the spy". This is a condition that would limit the answers to the correct answer. So try using this hint to solve the problem.

5. JC 2014-04-22 12:45

Okey, so here is the definitive answer. Let's get started to analyze it first.The trick is, the fact that the judge figured out who is the spy, this alone could be used as a condition to help solve the problem.

So, it really comes down to listing all the possibilities and then narrow down to get the result. Here are all the combinations:

1. Arthur is the spy

1.1)

Arthur: spy, liar

Robert: liar

1.2)

Arthur: spy, liar

Robert: none

1.3)

Arthur: spy

Robert: liar

2. Robert is the spy

2.1)

Robert: spy, liar

Arthur: liar

2.2)

Robert: spy, liar

Arthur: none

2.3)

Robert: spy

Arthur: liar

Now, use the conditions mentioned in the question, we can exclude these scenarios, 1.1, 1.2, 2.2.

So we are left with these combinations:

1.3)

Arthur: spy

Robert: liar

2.1)

Robert: spy, liar

Arthur: liar

2.3)

Robert: spy

Arthur: liar

Okey, so now we need to use the last bit of info from the question. When judge asked Robert if he is a spy. Robert answered and then the judge figured out. This means that Robert must have answered "no". Then, the judge knows that Robert is the spy.

If Robert answered "yes", then it could be either 1.3 or 2.3, the judge still won't know who is the spy.

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