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I got Charlie's number


Best Answer plasmid, 21 April 2013 - 05:21 AM

I don't know about everyone else, but I'm stuck.

If the "I" in this problem has information that we (the problem solvers) are not privy to by virtue of the OP, then I could come up with a solution.

If the "I" in this puzzle definitely does NOT have any more information than what's presented, then I am Stuck with a capital S.

Spoiler for
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10 replies to this topic

#1 bonanova

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Posted 13 April 2013 - 06:47 AM

They wear numbers in the land of Truthtellers and Liars, and it was a great help. I had to find Bob, and I knew only that he was across the room talking with two of his friends. I decided on a direct approach. I asked the group, "Which of you is Bob?" The person wearing 576 replied, "I am." The person on his left, wearing 238, disagreed: "Not at all. It is I who am Bob." Since number 382 remained silent I prodded him: "You're not helping all that much by your silence. Might I trouble you for at least a clue?" He smiled slyly and ventured, "We're a strange group, we are, I would not expect to receive all that much help: only one of us will ever tell you the truth." "Thanks," I said. Next, I fixed my attention on Bob and told him: "I really need to find Charlie." I knew he was in the room elsewhere, and it held only two other small groups: 3117 was talking with 1137, and 4741 was standing next to 2305. Bob helpfully(?) motioned to one of the groups. Hmmm... should I believe him? Not only did I want to meet Charlie, I also wanted to know whether he would tell me the truth. I decided on the second pair, and blurted out my question "Does Charlie tell the truth?" Number 2305 replied (with a yes or no;) and with that I was able to deduce Charlie's number. But ... could I trust him?

What do we know about Bob's number and type, and about Charlie's number and type?

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#2 plasmid

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Posted 13 April 2013 - 06:04 PM

I'm coming up with an answer that makes me think my analysis is just a little off.

Spoiler for Identity of Bob

Spoiler for Charlie's identity

Spoiler for A little extra

Spoiler for But...

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#3 bonanova

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Posted 13 April 2013 - 06:10 PM

The group 382 mentioned was his group of three friends.
I meant that to be a given, but you also correctly deduced it.


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#4 bonanova

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Posted 16 April 2013 - 11:26 PM

This is partially solved, but there are four questions to answer.

What can be known about Bob's and Charlie's number and type?


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#5 plasmid

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Posted 21 April 2013 - 05:21 AM   Best Answer

I don't know about everyone else, but I'm stuck.

If the "I" in this problem has information that we (the problem solvers) are not privy to by virtue of the OP, then I could come up with a solution.

If the "I" in this puzzle definitely does NOT have any more information than what's presented, then I am Stuck with a capital S.
Spoiler for

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#6 bonanova

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Posted 21 April 2013 - 07:12 AM

You are on the right track. The logic can be tightened up,

but you basically have the correct information.

 

Spoiler for Solution


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#7 bonanova

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Posted 22 April 2013 - 03:43 AM

Giving the solution to plasmid.

See previous post for the reasoning.


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- Bertrand Russell

#8 plasmid

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Posted 22 April 2013 - 05:20 AM

I see what tripped me up. I interpreted 382's statement as "exactly one of us tells the truth", and not "no more than one of us tells the truth". That would allow 382 to be a liar if all three of the initial group were liars.
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#9 bonanova

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Posted 22 April 2013 - 07:45 AM

It's not as precisely written as it might be.

 

I intended his statement to be "... (one and) only one of us will ever tell you the truth."

I think the words in red are normally taken as implied; but making things explicit is always a good thing.

 

The intended implication is that exactly one of the three tells the truth.

Which is needed to identify him as a truth-teller -- which is needed to proceed with the second part.

That is, you need to know that they can't all three be liars.

 

The first statement in the Solution leaves the one and only one condition unstated, as well.

But the solution needs the one and only one condition.


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- Bertrand Russell

#10 plasmid

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Posted 23 April 2013 - 03:15 PM

Doesn't the "one and only one of us will ever tell you the truth" interpretation mean that it's possible for all three of the people in the first group to be liars?


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