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Logic Puzzle

Postby Bill » Wed Jun 14, 2017 11:53 am

You are a detective trying to locate a witness named John.

You track him down at his social club, the "One Truth" society. There are three men, one of which is John. You must determine which.

You also happen to know that the three men are - in some order - a philatelist, a numismatist, and an illeist.

Each man makes a statement, but because of their club rules, only one of the three men makes a true statement. The other two are lying.

The first man points to the second man and says "He is the philatelist."

The second man nods enthusiastically, "Yes, I am the philatelist!"

The third man says "John is the numismatist."

Which man is John?
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Re: Logic Puzzle

Postby jbenz » Thu Jun 15, 2017 4:43 am

Is it cheating if I had to look up "illeist"?

Spoiler: show
(Which I now know means "one who refers to himself in the third person".)

I think John is the second man.

There are two lies and one truth. The first two guys agree on something, which means it can't be true.

So the only truth is "John is the numismatist."

.

I spent a while going down the path of the third man...

We could guess that third man is the illeist and is named John, but if that were true, his statement would have to be "John is the illeist". Maybe he is lying, but if he was, then all three statements would be lies.

.

Then I realized it is simpler to think about it like this:

We know the second man is not the philatelist, because we established that as a lie.

We know he is not the illeist, because he speaks in the first person.

So he must be the numismatist, and we know the numismatist is named John.

.

Thus the first man is the philatelist.

The second man, John, is the numismatist.

The third man is indeed the illeist, but his name isn't John.

.

*Edit... I guess the first man or the third man could be the illeist.

It's tricky. I like the puzzle because once you know it's about people speaking in the third person, you're immediately interested in the guy who says "John is the..." But then it turns out that person isn't speaking about themselves, and that it doesn't really matter. No one speaks in the third person in the puzzle itself. The key is that the one person who does talk about themselves uses the first person.
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Re: Logic Puzzle

Postby Neel Mehta » Fri Jun 16, 2017 9:16 am

jbenz wrote:Is it cheating if I had to look up "illeist"?


Yes. You should already know that it's a brand name for golf balls.

I first read this puzzle about 10 minutes after Bill posted it, when it was very different and suspiciously easy. I decided not to reply.

This revised version is harder, but it still brings up a question I had the first time around:

Spoiler: show
If an illeist happens to use a first person pronoun, does that alone make his statement false?


Otherwise, I think I agree with most of jbenz's reasoning. We can't identify everyone, but we have just enough to identify John.
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Re: Logic Puzzle

Postby Bill » Fri Jun 16, 2017 12:55 pm

Yes, you've got it. I was playing with the idea of a simple logic puzzle that required you to know the meaning of a seemingly unimportant word to solve it.

The first version I posted looked something like this:

The first man points to the second man and says "I can tell you truthfully that he is the philatelist."

The second man nods enthusiastically, "Yes, I am the philatelist!"

The third man says "John is the illeist."


Which is funnier, because if you don't know what the word means, it seems to pull you away from the correct answer (which is now the third man). And then you look the word up and get the joke.

But after I posted it, I thought I could do better, so (incorrectly) believing nobody had seen it yet, I made the change. But the fact that Neel saw it and dismissed it makes me think I did the right thing.

In the current version, it is not possible to determine everything, but you can pick out John. I can now tell you that Jimmy was the illeist.

Neel Mehta wrote:If an illeist happens to use a first person pronoun, does that alone make his statement false?


I think we're defining an illeist as one who doesn't use first person pronouns. That may seem like a strict standard, but it is a logic puzzle after all. I mean, how would you feel if my solution to the puzzle was that the first man was John, and the second man was the illeist who refers to himself in the third person most of the time, but did happen to use a first person pronoun that one time he was making his statement to you?
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