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TruthlessHero
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 Stuck: How can you guess that?   « on: Sep 28th, 2006, 1:32pm » Quote Modify

I am stuck on a riddle from Steven Miller's Page
It says:
I am an honest person, and am thinking of one of three numbers: 1, 2 or 3. You may ask me EXACTLY one yes-no question, I will answer truthfully, and if you chose the right question,  you will know which number I'm thinking of! (HINT: if I cannot answer your question, I will say I cannot answer it).

It's probably not that hard for most of you, but I am totally stuck. Thanks in advance.
 « Last Edit: Sep 28th, 2006, 1:34pm by TruthlessHero » IP Logged
Icarus
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 Re: Stuck: How can you guess that?   « Reply #1 on: Sep 28th, 2006, 3:56pm » Quote Modify

It's no wonder you are stuck! The problem, as stated, is unsolvable. I can only think that Mr. Miller is putting a different interpretation on what is a "yes-no question" than I do. My interpretation it that you are allowed to ask a question that may be definitely answered "yes" or "no" - any other sort of question is not allowed.

But a single "Yes" or "No" response is not enough to choose between 3 possibilities: If it were, then each response would have to completely specify a number. So "Yes" would mean the number was (for example) 1, while "No" would mean the number was 2. But then what happens when the number is 3?

So I suspect Mr Miller is allowing a more general type of question - one with an effective third response: a question for which neither "yes" or "no" is a true answer if the number in question is (for example) 3. In this case, if you pose the question and the responder answers "yes", the number is 1, if the answer is "no", the number is 2, and if the responder does not give an answer, the number is 3.

Now you just have to figure out a question that has these properties. The third condition is obtained by making it equivalent to "this statement is false" when the number is 3.
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TruthlessHero
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 Re: Stuck: How can you guess that?   « Reply #2 on: Sep 28th, 2006, 4:25pm » Quote Modify

Still lost. Do you know what the question would be?
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SWF
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 Re: Stuck: How can you guess that?   « Reply #3 on: Sep 28th, 2006, 7:04pm » Quote Modify

You can tie the question to an unsolved problem.

If we call your number N, and S(N) is some statement about N that is unknown when N=3, but is false when N=1 or 2. Then the question could be: "Is (N equals 1) or S(N) true?" A "yes" means N=1, "no" means N=2, and "I don't know" means N=3.

Something like S(N)="Every even integer greater than N-1 can be expressed as the sum of two primes" would almost work if I was sure you didn't secretly have a proof of the Goldbach Conjecture.

(Edited to add another suggestion):    "Is iN-1 greater than zero?"   (where i=sqrt(-1) )
 « Last Edit: Sep 28th, 2006, 7:54pm by SWF » IP Logged
towr
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 Re: Stuck: How can you guess that?   « Reply #4 on: Sep 29th, 2006, 1:35am » Quote Modify

on Sep 28th, 2006, 7:04pm, SWF wrote:
 (Edited to add another suggestion):    "Is iN-1 greater than zero?"   (where i=sqrt(-1) )
Very nice.
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TruthlessHero
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 Re: Stuck: How can you guess that?   « Reply #5 on: Sep 29th, 2006, 3:33am » Quote Modify

Umm sqrt(-1) is radical....I'm not sure how/why you're using it...
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towr
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 Re: Stuck: How can you guess that?   « Reply #6 on: Sep 29th, 2006, 3:50am » Quote Modify

on Sep 29th, 2006, 3:33am, TruthlessHero wrote:
 Umm sqrt(-1) is radical....I'm not sure how/why you're using it...
It's complex.
i0 = 1, which is greater than zero
i1 = i, which is neither greater than, smaller  than or equal to zero
i2 = -1, which is smaller than 0

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Grimbal
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 Re: Stuck: How can you guess that?   « Reply #7 on: Sep 29th, 2006, 4:49am » Quote Modify

Is the number 1 or (is the number not 2 and will you answer no) ?

or: Is it true that the number is 1 or (it is not 2 and you will answer no) ?

(btw if you are a ghost, knock once for yes, twice for no, or three times if you cannot answer).
 « Last Edit: Oct 5th, 2006, 5:39am by Grimbal » IP Logged
TruthlessHero
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 Re: Stuck: How can you guess that?   « Reply #8 on: Sep 29th, 2006, 12:47pm » Quote Modify

I'm not quite sure what you're saying towr. But I think the question is: Is the sqrt(n) greater than 1.4142135623730950488016887242097?

If yes that means the number is three
If no that means the number is one
If "I cannot answer that question" that means it is two

Anyone see anything wrong with it?
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honkyboy
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 Re: Stuck: How can you guess that?   « Reply #9 on: Sep 29th, 2006, 1:08pm » Quote Modify

Is that the exact sqrt of 2?

*edit -  or must it be is 1/(3-n) odd?
 « Last Edit: Sep 29th, 2006, 1:43pm by honkyboy » IP Logged
TruthlessHero
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 Re: Stuck: How can you guess that?   « Reply #10 on: Sep 29th, 2006, 1:34pm » Quote Modify

sqrt of any prime is non terminating and non repeating, so no it is not...

If 1/(3-n)=1 and n= 1 then it would be 1/3 and if n=2 then it would be 1/1 and if n=3 it would be 1/0

Besides the fact that it is not decisive since if the answer to that question is not one then it would be 1/3 or 1/0; you can't divide a number by 0, so you're stuck, I think.

Not sure what 1/(3-1) means. I don't think fractions can be odd and/or even since they are not whole numbers, but that is an interesting question, can fractions be considered odd/even if they are <1?
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honkyboy
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 Re: Stuck: How can you guess that?   « Reply #11 on: Sep 29th, 2006, 1:53pm » Quote Modify

oops I meant (3-n), careless. fixed it.

Is the sqrt(n) greater than 1.4142135623730950488016887242097?

n=1 -- no
n=2 -- no
n=3 -- yes

As Icarus pointed out, for one number the answer must give a non yes or no.  That's why I was trying to devide by zero.

 « Last Edit: Sep 29th, 2006, 2:01pm by honkyboy » IP Logged
Icarus
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 Re: Stuck: How can you guess that?   « Reply #12 on: Sep 29th, 2006, 4:03pm » Quote Modify

But that still does not work: 1/0 is not defined and thus is not equal to 1, so the answers would be:
1 --> "Yes"
2 --> "No"
3 --> "No"

SWF's undefined relation solution has the same problem: i is not greater than 0, so the answers are
1 --> "Yes"
2 --> "No"
3 --> "No"

The unsolved problem approach will work, though.

Grimbal has my general approach, but I am not too sure on whether this counts as a single question.
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honkyboy
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 Re: Stuck: How can you guess that?   « Reply #13 on: Sep 29th, 2006, 5:31pm » Quote Modify

Would I be able to live if I had a kidney removed n times?  (I have the usual two kidneys)

1 -- yes
2 -- no
3 -- couldn't happen?
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Paul Hammond
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 Re: Stuck: How can you guess that?   « Reply #14 on: Sep 30th, 2006, 4:47am » Quote Modify

How about "I am thinking of either 1.5 or 2.5 - is your number greater than mine?"
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Icarus
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 Re: Stuck: How can you guess that?   « Reply #15 on: Sep 30th, 2006, 7:14am » Quote Modify

Nice, and good to hear from you again, Paul!
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Barukh
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 Re: Stuck: How can you guess that?   « Reply #16 on: Sep 30th, 2006, 9:42am » Quote Modify

IMHO Paul's solution has the same drawbacks as Grimbal's.
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towr
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 Re: Stuck: How can you guess that?   « Reply #17 on: Sep 30th, 2006, 10:41am » Quote Modify

on Sep 30th, 2006, 9:42am, Barukh wrote:
 IMHO Paul's solution has the same drawbacks as Grimbal's.
You mean it's too much like two questions put together?

How about "Is your number greater than a random variable picked uniformly from the range 1.5-2.5?" It has basicly the same semantic content, but makes a more singular sentence.
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TruthlessHero
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 Re: Stuck: How can you guess that?   « Reply #18 on: Sep 30th, 2006, 3:13pm » Quote Modify

What's wrong with is sqrt(n) greater than sqrt(2)?

1=no
2=I cannot answer (Since it is neither greater or less than)
3=yes

Thanks for all the feedback though
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Icarus
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 Re: Stuck: How can you guess that?   « Reply #19 on: Sep 30th, 2006, 3:23pm » Quote Modify

what's the point of the square roots? This is exactly the same as asking "Is your number greater than 2?", and the answers are:
1 --> "No"
2 --> "No"
3 --> "Yes"

2 is not greater than 2, (and sqrt(2) is not greater than sqrt(2)). That is all that is required to answer "No" to the question when n=2. The fact that 2 is also not less than 2 does not come into it. Your question says nothing about "less than".
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Bamaboys
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 Re: Stuck: How can you guess that?   « Reply #20 on: Oct 4th, 2006, 8:00pm » Quote Modify

I know it's very unlikely, but how about
 hidden: Is   ( insert number ) the number you are thinking of? You simply choose a number to ask, and if it's right, the question was the right one.
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TruthlessHero
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 Re: Stuck: How can you guess that?   « Reply #21 on: Oct 4th, 2006, 8:02pm » Quote Modify

Yeah but if you say:
Is 2 the number you're thinking of?
If the number is 2 - Yes
If it's 3 - No
If it's 1 - No

You need to be sure that no matter what the answer you can tell what the number is.
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towr
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 Re: Stuck: How can you guess that?   « Reply #22 on: Oct 5th, 2006, 12:54am » Quote Modify

on Oct 4th, 2006, 8:02pm, TruthlessHero wrote:
 You need to be sure that no matter what the answer you can tell what the number is.
Actually, the puzzle as it's stated doesn't require that. It just says that if you ask the right question, you'll know what the answer is.
And if you ask the right question from:
- Are you thinking of 1?
- Are you thinking of 2?
- Are you thinking of 3?
Then you will indeed know the answer. Of course if you pick the wrong question from these three, then you won't.

It may not be the intended answer, but it's a clever interpretation imo. It also easily extends to greater sets of numbers (were there is no one yes-no-errr-question that can give you an answer with certainty in all cases).
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TruthlessHero
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 Re: Stuck: How can you guess that?   « Reply #23 on: Oct 5th, 2006, 3:58am » Quote Modify

I suppose, but it would be a better answer if you knew what the number was regardless.
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jollytall
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 Re: Stuck: How can you guess that?   « Reply #24 on: Oct 5th, 2006, 12:28pm » Quote Modify

Going back to honkeyboy's original idea, i.e. whether sqrt(n) is greater than 1.4.. using a lot of decimals, might be a good solution if the one who asked the question cannot use computers, books, etc.
It is not a really mathematical solution, but we saw it in case of many other riddles.

The longest rounding memorised (although for pi, not sqrt(2)) I have ever heard, was in the news today, where someone in Japan memorised  100.000 decimals of pi. So if you ask the question with enough decimals and the last few digits you choose random (and even say so in advance), then:
1 no
2 I don't know
3 yes
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