Easy Logic - Liars and Truthtellers

[chlorella]

I'll apologize in advance if you've seen this one before:

You are a secret agent for the FBI, looking for an unknown enemy spy. After months of hard work, you end up with three possible suspects. All you know about these three is that one is the owner of a reputable charity, one is a politician, and one is the spy you are looking for. The charity owner always tells the truth, the politician always lies, and the spy can either lie or tell the truth. The problem is that all three men are identical triplets! With only days left for you to figure this out, you decide to ask each person about another:

The first brother says that the third brother is either the politician or the spy, but your bad memory prevents you from remembering which!

The second brother says that the first brother is either the charity owner, the politician, or the spy, but, again, your horrible memory prevents you from remembering which!

The third brother says that the second brother is either the charity owner, the politician, or the spy, but, once again, your chronic memory prevents you from remebering which!

Assuming that your memory is accurate enough, although not too reliable, you can use all the above statements from the three brothers to figure out which brother is the spy. So, who is the spy?

[This message has been edited by chlorella (edited 04-07-2002 12:52 AM).]

[mathgrant]

Oh, sorry, I think I may have misinterpreted. I thought he literally said, "This guy is the politician, spy, or charity worker." That's obviously true.

[This message has been edited by mathgrant (edited 04-06-2002 12:32 PM).]

[ralphmerridew]

I think you need to add it a statement that, on the basis of these statements alone, you were able to identify the spy back then.

[quercitron]

The second brother is the spy.

[cubestudent]

I figured out which one of the brothers was the spy, but my terrible memory made me forget which it was. . .

[chlorella]

ralphmerridew:
I've now added that change to the puzzle. Thanks!

quercitron:
Can you prove it?

[ralphmerridew]

It looks like that information isn't quite enough to solve it. I think this will do:

Once you had those three statements, you were able to identify the spy.
A few years ago, you thought about the problem, and were able to remember the first brother's exact statement, and from that, were able to work out who the spy was.

(It's also possible for the reader to work out what the answer is if told that remembering the second brother's exact statement enabled the speaker to identify the spy, though that case is less interesting.)

Adding this condition, the reasoning goes as follows:

There are 18 cases for what the three people said.
STT - brothers must be TSF
FTS - must be FST
FTF - could be TSF or SFT
FSS - could be STF or FST
FSS - could be STF or FST
FSF - could be TSF or STF
and so on.

Since knowing all three statements is enough to work out who the spy is, it suffices to take those cases for which the spy is unique. That leaves seven cases:
FTT, spy is 2
FTS, spy is 2
FST, spy is 2
STS, spy is 2
STF, spy is 1
SST, spy is 3
SFT, spy is 3

If the first brother said that the third is the politician, then the speaker could have worked out that the spy is the second. If the first brother said third is the spy, then it couldn't. Therefore, the second brother is the spy.

[sweetwater]

The second and third brother speak the truth, therefore the first brother is the politician. It follows that the third brother is the charity owner (not politician or spy), and the second brother is the spy.

[ralphmerridew]

You misunderstand the problem, sweetwater.

The third brother didn't say "The second brother is the politician, charity worker, or spy". Instead, maybe he said "The second brother is the politician." Maybe he said "The second brother is the charity worker". And maybe he said "The second brother is the spy." But it isn't recorded which of those three statements he said.

So it could be that #1 said "#3 is the spy", 2 said "#1 is the spy", and 3 said "#2 is the politician", and that #1 is the charity worker, #2 is the politician, and #3 is the spy.

[SaberKitty]

wouldn't the order spy=1, polotician=2, and charity owner=3 work?
edit: spelling

[This message has been edited by SaberKitty (edited 04-07-2002 12:44 PM).]

[quercitron]

my thoughts exactly, ralphmerridew

[ralphmerridew]

I was saying that that combination of quotes and roles was possible, given what we know about they said. I did not claim that if they said those things then they must have those roles.

[chlorella]

Well, there IS enough information to solve this, but I can give a clue if anyone likes.

[sweetwater]

The puzzle as presented contains ambiguity.