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riddles >> hard >> Stuck: How can you guess that?
(Message started by: TruthlessHero on Sep 28th, 2006, 1:32pm)

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Title: Stuck: How can you guess that?
Post by TruthlessHero on Sep 28th, 2006, 1:32pm
I am stuck on a riddle from Steven Miller's Page (http://www.math.brown.edu/~sjmiller/riddles/riddles.htm)
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.

Title: Re: Stuck: How can you guess that?
Post by Icarus on Sep 28th, 2006, 3:56pm
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.

Title: Re: Stuck: How can you guess that?
Post by TruthlessHero on Sep 28th, 2006, 4:25pm
Still lost. Do you know what the question would be?

Title: Re: Stuck: How can you guess that?
Post by SWF on Sep 28th, 2006, 7:04pm
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) )

Title: Re: Stuck: How can you guess that?
Post by towr on Sep 29th, 2006, 1:35am

on 09/28/06 at 19:04:50, SWF wrote:
 (Edited to add another suggestion):    "Is iN-1 greater than zero?"   (where i=sqrt(-1) )
Very nice.

Title: Re: Stuck: How can you guess that?
Post by TruthlessHero on Sep 29th, 2006, 3:33am
Umm sqrt(-1) is radical....I'm not sure how/why you're using it...

Title: Re: Stuck: How can you guess that?
Post by towr on Sep 29th, 2006, 3:50am

on 09/29/06 at 03:33:07, 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

Title: Re: Stuck: How can you guess that?
Post by Grimbal on Sep 29th, 2006, 4:49am

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).

Title: Re: Stuck: How can you guess that?
Post by TruthlessHero on Sep 29th, 2006, 12:47pm
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? ???

Title: Re: Stuck: How can you guess that?
Post by honkyboy on Sep 29th, 2006, 1:08pm
Is that the exact sqrt of 2?

*edit -  or must it be is 1/(3-n) odd?

Title: Re: Stuck: How can you guess that?
Post by TruthlessHero on Sep 29th, 2006, 1:34pm
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?

Title: Re: Stuck: How can you guess that?
Post by honkyboy on Sep 29th, 2006, 1:53pm
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.

Title: Re: Stuck: How can you guess that?
Post by Icarus on Sep 29th, 2006, 4:03pm
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.

Title: Re: Stuck: How can you guess that?
Post by honkyboy on Sep 29th, 2006, 5:31pm
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?

Title: Re: Stuck: How can you guess that?
Post by Paul Hammond on Sep 30th, 2006, 4:47am
How about "I am thinking of either 1.5 or 2.5 - is your number greater than mine?"

Title: Re: Stuck: How can you guess that?
Post by Icarus on Sep 30th, 2006, 7:14am
Nice, and good to hear from you again, Paul!

Title: Re: Stuck: How can you guess that?
Post by Barukh on Sep 30th, 2006, 9:42am
IMHO Paul's solution has the same drawbacks as Grimbal's.  ::)

Title: Re: Stuck: How can you guess that?
Post by towr on Sep 30th, 2006, 10:41am

on 09/30/06 at 09:42:01, 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.

Title: Re: Stuck: How can you guess that?
Post by TruthlessHero on Sep 30th, 2006, 3:13pm
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

Title: Re: Stuck: How can you guess that?
Post by Icarus on Sep 30th, 2006, 3:23pm
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".

Title: Re: Stuck: How can you guess that?
Post by Bamaboys on Oct 4th, 2006, 8:00pm
I know it's very unlikely, but how about [hideb]   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. [/hideb]

Title: Re: Stuck: How can you guess that?
Post by TruthlessHero on Oct 4th, 2006, 8:02pm
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.

Title: Re: Stuck: How can you guess that?
Post by towr on Oct 5th, 2006, 12:54am

on 10/04/06 at 20:02:21, 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).

Title: Re: Stuck: How can you guess that?
Post by TruthlessHero on Oct 5th, 2006, 3:58am
I suppose, but it would be a better answer if you knew what the number was regardless.

Title: Re: Stuck: How can you guess that?
Post by jollytall on Oct 5th, 2006, 12:28pm
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

Title: Re: Stuck: How can you guess that?
Post by TruthlessHero on Oct 5th, 2006, 12:50pm
Do you mean 100 digits or 100 thousand digits? Becaue I know people have memorized more than 100 digits of pi. Also, I believe it was my idea for the sqrt not honkeyboy's. I still stick to that answer even though Icarus doesn't think it's right.

Title: Re: Stuck: How can you guess that?
Post by jollytall on Oct 6th, 2006, 12:42am
Sorry TruthlessHero, I missed it up. Of course credit should go, where it is due.

I meant 100 thousand digits obviously (decimal and thousand separators are different in different languages/local practices and by mistake I used the Hungarian thousand separator rather than the English). Still I hope you did not read 100.000 digits but 100,000 digits, since the number of digits is always integer, hence there would be no meaning of decimals.

Furthermore 100 digits even I could remember if invested some time, but the 100,000 number I found astonishing.

Title: Re: Stuck: How can you guess that?
Post by TruthlessHero on Oct 6th, 2006, 3:44am
True, 100k is most impressive.

Title: Re: Stuck: How can you guess that?
Post by grungy on Dec 17th, 2006, 2:38am
Yeah, but doesn't Pi start to repeat after a few hundred digits?  That, admittedly, would make it easier.  Although, 100K still is freaky... wouldn't he at some point screw up?

Title: Re: Stuck: How can you guess that?
Post by towr on Dec 17th, 2006, 3:06am

on 12/17/06 at 02:38:36, grungy wrote:
 Yeah, but doesn't Pi start to repeat after a few hundred digits?
That would mean it was rational. It actually never repeats.

Title: Re: Stuck: How can you guess that?
Post by Icarus on Dec 17th, 2006, 8:25pm
The several billion digits of pi that have been calculated have been studied several times for any hint of a pattern - even a subtle one. None has ever been found. And as towr indicates, we can prove that it never repeats.

Title: Re: Stuck: How can you guess that?
Post by Gollelio on Dec 27th, 2006, 7:03pm
Hello and Merry Xmas!
I saw this forum while searching for some riddles to solve and i can say that i like the whole concept.

Now to the riddle. I think a question could be "If n is the number you are thinking of, is 1/(n-2) positive?"

So

If n=1, 1/(1-2) negative, so No.
If n=2, 1/(2-2) indefinite, so Don't know if it's positive.
If n=3, 1/(3-2) positive, so Yes.

The hint in the original post was very helpfull though, so i was searching for a form of indefinability.

As i quickly scanned through the answers later i saw a correct answer, the one with the complex numbers and another that tried to use the 1/0 but since the question had = and not > the 1/0 would count as no.

Edit: I saw the answer with the kidneys too. Very good answer!

Title: Re: Stuck: How can you guess that?
Post by Icarus on Dec 27th, 2006, 10:57pm
Sorry - that doesn't work. Because 1/(2-2) is undefined, it is not positive (it is not negative either, or any thing else that requires it to exist), so your answers are
n=1: "No"
n=2: "No"
n=3: "Yes"

The answer with complex numbers suffers the same problem. i is not > 0, so the answer for 2 there is also "no", not "I don't know".

One question would be: Do any non-real zeros of the Reimann zeta function have real part less than (n-1)/2?

Until someone proves or disproves the Reimann hypothesis, the answers have to be:
1: no
2: I don't know
3: yes

Title: Re: Stuck: How can you guess that?
Post by BNC on Jan 1st, 2007, 3:54am

on 12/27/06 at 22:57:27, Icarus wrote:
 One question would be: Do any non-real zeros of the Reimann zeta function have real part less than (n-1)/2?Until someone proves or disproves the Reimann hypothesis, the answers have to be:1: no2: I don't know3: yes

Being honest and truthful, I would answer:
1: I don't know
2: I don't know
3: I don't know

...

Title: Re: Stuck: How can you guess that?
Post by Icarus on Jan 1st, 2007, 8:36am
You could include a short description of the Riemann hypothesis (my apologies to Riemann for mispelling his name in my earlier post) in the question, but then it boils down to the same thing as Paul Hammond's suggestion.

Of all the approaches so far, I like Paul Hammond's best: "I'm thinking of either 1.5 or 2.5 - is your number greater than mine?"

It is a variant of the Unsolved problem method, but in this case, you can be sure that the other person doesn't secretly have a solution to the problem, and is aware of what the problem is.

And I can't agree with Barukh about it suffering from the "is that really one question" shortcoming.

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

Just for the record: The Riemann zeta function is defined for real s > 1 (using s as the variable is traditional) by
http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/zeta.gif(s) = 1-s + 2-s + 3-s + ...
It can be extended analytically to the entire complex plane except s=1. It is fairly easy to show that http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/zeta.gif(s) = 0 if s is a negative integer, and http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/zeta.gif(s) is non-zero for all other real s. It has also been shown that the non-real zeros of http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/zeta.gif(s) must have 0 < Re(s) < 1, where Re(s) is the real part of s.

The Riemann Hypothesis says that for all non-real zeros of http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/zeta.gif(s), Re(s) = 1/2.

This is important because of a relationship that Euler discovered:

1/http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/zeta.gif(s) = (1-2-s) (1-3-s) (1-5-s) (1-7-s) (1-11-s)...,

where the product is for all primes in the base. Riemann used this relation to prove an early version of the Prime number theorem (whose full version he also conjectured), which gives the overall density of primes. If we could be sure that all non-real zeros of http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/zeta.gif lie on the line Re(s) = 1/2, a large number of stronger results will follow. It is quite common in Analytic Number Theory to see a theorem begin with "If the Riemann Hypothesis is true, then ...".

Title: Re: Stuck: How can you guess that?
Post by BNC on Jan 2nd, 2007, 1:30am
Thanks for the explaination, Icarus  :D

Title: Re: Stuck: How can you guess that?
Post by Locke64 on Jan 5th, 2007, 5:25pm
I don't see how there can possibly be any better question than
"Is your number greater than a number that is randomly selected between 1.5 and 2.5?".  There may be more that accomplish the same thing, but I don't know how they could possibly be better, as this gets the job done.  I think I'm being a bit redundant... :(

Title: Re: Stuck: How can you guess that?
Post by Three Hands on Jan 9th, 2007, 1:15am
Well, if he randomly selects a number between 1.5 and 2.5, then he can provide a "yes" or "no" answer for if he is thinking of "2", thus creating some problems...

I think you could do better if you say "I have randomly selected a number between 1.5 and 2.5. Is the number you are thinking of greater than the number I have selected?", although I suspect someone will come up with a suitably devious way around this...

Title: Re: Stuck: How can you guess that?
Post by JiNbOtAk on Jan 30th, 2007, 5:52pm
If 3 is not the number that you have in mind, is the number odd ?

Yes : 1
No  : 2

Now, what is wrong with that approach ?   :P

Title: Re: Stuck: How can you guess that?
Post by Padfoot on Jan 30th, 2007, 6:42pm

on 01/30/07 at 17:52:32, JiNbOtAk wrote:
 If 3 is not the number that you have in mind, is the number odd ?

Well if they have 3 in mind than they would say "No".  Or am I misreading this?

Title: Re: Stuck: How can you guess that?
Post by Icarus on Jan 30th, 2007, 7:42pm
Actually, my interpretation is that if 3 is the number, they are free to answer in any way they like.

An if-then statement is true when the if clause is false, regardless of the truth value of the predicate.

Answering your question "Yes" is equivalent to saying "If my number is not 3, then it is odd" - true for 1 or 3.
Answering "no" is equivalent to saying "If my number is not 3, then it is not odd" - true for 2 or 3.

Title: Re: Stuck: How can you guess that?
Post by CowsRUs on Feb 8th, 2007, 5:19pm
Is it Three?

Title: Re: Stuck: How can you guess that?
Post by maxmin on Feb 9th, 2007, 4:25am
Is F(n) possitive if
F(x) < 0 if x < 1.5
F(x) > 0 if x > 2.5 ?

Title: Re: Stuck: How can you guess that?
Post by Icarus on Feb 9th, 2007, 8:04pm

on 02/09/07 at 04:25:22, maxmin wrote:
 Is F(n) possitive if F(x) < 0 if x < 1.5F(x) > 0 if x > 2.5 ?

n=1: "No"
n=2: "No"
n=3: "Yes"

To be positive F has to be defined, since F is not defined for 2, it is not positive there.

Title: Re: Stuck: How can you guess that?
Post by CowsRUs on Feb 11th, 2007, 1:28pm
Of course you can always ask if:
Is the number prime? ;D

Title: Re: Stuck: How can you guess that?
Post by TruthlessHero on Feb 11th, 2007, 1:35pm

on 02/11/07 at 13:28:47, CowsRUs wrote:
 Of course you can always ask if:Is the number prime? ;D

Not really:

1:
2: Yes
3: Yes

I'm not sure what 1 is technically considered, but since 2 and 3 are both prime, it doesn't matter.

Title: Re: Stuck: How can you guess that?
Post by CowsRUs on Feb 11th, 2007, 2:14pm
forgot prime And odd or a lot of And combinations

Title: Re: Stuck: How can you guess that?
Post by Icarus on Feb 11th, 2007, 8:27pm

on 02/11/07 at 13:35:21, TruthlessHero wrote:
 I'm not sure what 1 is technically considered, but since 2 and 3 are both prime, it doesn't matter.

1 is considered a "unit", not a prime. For the natural numbers, this is a trivial distinction, but the concept of primes and factorization can arise in more general settings, called "Unique Factorization Domains", or UFDs (the set of natural numbers is not a UFD itself, but the full set of integers is). In UFDs the various "numbers" fall into three types: units, primes, composites. Units are "numbers" that have an inverse. You can always "factor" them out of any number by multiplying by the inverse. Factorization is only "unique" up to multiplication of the factors by units. Primes are numbers x such that if x = y*z, then either y or z is a unit. Composites are everything else.

After the integers, the next example of a UFD is the Gaussian integers: complex numbers of the form a+bhttp://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/imath.gif, with a and b integers. The units of the Gaussian integers are 1, -1, http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/imath.gif, -http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/imath.gif. The primes turn out to be the natural prime numbers of the form 4k+3 (and their opposites and multiples by http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/imath.gif and -http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/imath.gif), and all numbers of the form a+bhttp://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/imath.gif, where a2 + b2 is a natural prime of the form 4k+1.

Other well known examples:
The set of all polynomials in one variable with complex coefficients. The units consist of the complex numbers (which are polynomials of degree 0). The primes are all the linear polynomials (those of the form ax + b).

The set of all real polynomials in one variable. Units are all real numbers. Primes are linear polynomials, and quadratic polynomials with non-real roots.

The set of all polynomials in one variable with integer coefficients. The units are 1 and -1. And just like the natural numbers, identifying exactly which are prime is not an easy task.

Title: Re: Stuck: How can you guess that?
Post by TruthlessHero on Feb 11th, 2007, 8:36pm

on 02/11/07 at 20:27:25, Icarus wrote:
 1 is considered a "unit", not a prime. For the natural numbers, this is a trivial distinction, but the concept of primes and factorization can arise in more general settings, called "Unique Factorization Domains", or UFDs (the set of natural numbers is not a UFD itself, but the full set of integers is). In UFDs the various "numbers" fall into three types: units, primes, composites. Units are "numbers" that have an inverse. You can always "factor" them out of any number by multiplying by the inverse. Factorization is only "unique" up to multiplication of the factors by units. Primes are numbers x such that if x = y*z, then either y or z is a unit. Composites are everything else.After the integers, the next example of a UFD is the Gaussian integers: complex numbers of the form a+bhttp://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/imath.gif, with a and b integers. The units of the Gaussian integers are 1, -1, http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/imath.gif, -http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/imath.gif. The primes turn out to be the natural prime numbers of the form 4k+3 (and their opposites and multiples by http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/imath.gif and -http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/imath.gif), and all numbers of the form a+bhttp://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/imath.gif, where a2 + b2 is a natural prime of the form 4k+1.Other well known examples:The set of all polynomials in one variable with complex coefficients. The units consist of the complex numbers (which are polynomials of degree 0). The primes are all the linear polynomials (those of the form ax + b).The set of all real polynomials in one variable. Units are all real numbers. Primes are linear polynomials, and quadratic polynomials with non-real roots.The set of all polynomials in one variable with integer coefficients. The units are 1 and -1. And just like the natural numbers, identifying exactly which are prime is not an easy task.

Interesting. Might I inquire as to what math degrees you have, if any?

Title: Re: Stuck: How can you guess that?
Post by Whiskey Tango Foxtrot on Feb 11th, 2007, 9:52pm
Be careful, Hero.  I don't think you meant to sound pretentious, but it came out that way.  There's been a rash of Icarus-doubters recently and I know I would be past the point of mere annoyance.

Title: Re: Stuck: How can you guess that?
Post by TruthlessHero on Feb 11th, 2007, 10:01pm
Oh, no, no, no, not in the least. I respect him greatly.

I honestly would like to know if you are just an avid mathematician or if you have degrees and such.

Title: Re: Stuck: How can you guess that?
Post by Whiskey Tango Foxtrot on Feb 11th, 2007, 10:14pm
Yeah he's a pretty smart guy.  I think I could take him, though.  ;)

I suggest you check out the Who's Who? (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_general;action=display;num=1033780880;start=0) topic.  There is plenty of information about most of the major contributors on this site.  Many of the minor contributors also left some details about themselves so feel free to let everyone know who you are.  Speaking of which, I should probably head over there soon.

Title: Re: Stuck: How can you guess that?
Post by TruthlessHero on Feb 11th, 2007, 10:17pm

I think everyone that posted in this thread put together could take him  ;D

Title: Re: Stuck: How can you guess that?
Post by Icarus on Feb 13th, 2007, 5:50am
Actually, there are a number of people who post here who run circles around me mathematically, though I have a doctorate in the subject and some of them do not. Michael_Dagg is also a PhD, and a professional mathematician, while I make my living as an engineer. Eigenray regularly produces answers to questions that have stumped me. Ecoist has also produced many posts on subjects that escaped me, as has Pietro K.C. I could continue the list, but I doubtlessly would miss names that should be included (SWF, James Fingas, Nick H., etc).

As for my quoted comments, you can learn about those subjects in an undergraduate Abstract Algebra course. UFDs in particular are a subject that the great female mathematician Emmy Noether studied in detail.

Title: Re: Stuck: How can you guess that?
Post by TruthlessHero on Feb 13th, 2007, 6:01am
Good to know. It's probably a longshot, but is "Eignenray" perhaps the author of a program called Eigenmath (http://en.wikipedia.org/wiki/Eigenmath)?

Title: Re: Stuck: How can you guess that?
Post by Eigenray on Feb 13th, 2007, 1:44pm

on 02/13/07 at 06:01:35, TruthlessHero wrote:
 Good to know. It's probably a longshot, but is "Eignenray" perhaps the author of a program called Eigenmath (http://en.wikipedia.org/wiki/Eigenmath)?

Any other eigen*s out there probably have nothing to do with me.  It's a standard prefix in math terminology.

Title: Re: Stuck: How can you guess that?
Post by naveenreddyp on Feb 14th, 2007, 10:15pm
the question is ...

" say yes if u think - 1
say no if u think - 2
"

Title: Re: Stuck: How can you guess that?
Post by BNC on Feb 15th, 2007, 1:27am

on 02/14/07 at 22:15:19, naveenreddyp wrote:
 the question is ..." say yes if u think - 1   say no if u think - 2 "answer : if answer is yes - 1               if answer is no -2               if answer is " cannot answer" its 3 !!!!

I thought "3". You didn't tell me what to say, so I chose to say "yes".

Title: Re: Stuck: How can you guess that?
Post by beatsamurai on Feb 22nd, 2007, 9:45am

Of course this is language dependent, but hey.

Title: Re: Stuck: How can you guess that?
Post by Whiskey Tango Foxtrot on Feb 22nd, 2007, 10:24am
Beatsamurai, I could respond yes or no to your question and you would have no idea what number I was thinking of.

For example, if I respond "no" I could either be thinking of one and answering no or thinking of two and answering no.

If I respond "yes" the opposite would be true.

Title: Re: Stuck: How can you guess that?
Post by beatsamurai on Feb 22nd, 2007, 6:19pm
Hrm.  I think I jumped the gun on that one.

For one thing I think I may have not phrased it very well.  And on top of that I'm realizing that it wouldn't work anyway heh.

My thought was to force the person to compare his number [N] to the number of letters in his yes/no answer.  With the question, "Are you thinking of the number of letters in your answer?", I pictured 3 scenarios:
N=2.  Can't answer 'yes' or 'no' truthfully.

Unfortunately I forgot that one could truthfully answer 'no' when N=3.  Ah well.

Title: Re: Stuck: How can you guess that?
Post by jollytall on Feb 22nd, 2007, 11:49pm
I still like the solution. All other solutions are also based on the logic that we have one yes, one no and the third is either I don't know, or Cannot be answered or alike. So N=2 is OK. The problem is the answer no that might work for both N=1 and N=3.
But if we improve your question a bit and say also that if both yes and no can be a true answer then you must choose yes, it might work. N=2 still remains: Cannot be answereed truthfully, while N=1 is No, N=3 is Yes.

Title: Re: Stuck: How can you guess that?
Post by webdreamer on Oct 2nd, 2007, 2:46pm
I know nobody is writing about this thread anymore, but if it's possible to get some answer is it possible to twist the definition of a yes-no question?

If you have a odd number say yes and if the number you're thinking of it's 3, say no.
Then if he was thinking of 3, he would have to say no and yes at the same, don't know or cannot answer, or something.

By the way, how does this site works? I understand it has a riddle archive besides a forum, are we suppose to post new riddles and answer the old ones in the forum?

After post: I noticed someone wrote a similar answer, but still I think this should work better...

Title: Re: Stuck: How can you guess that?
Post by FiBsTeR on Oct 2nd, 2007, 2:49pm
As the old questions have been mutilated beyond recognition, people regularly post "new" ones on the forum, although others will tell you that most of them are just old ones in disguise.

Welcome to the forum!

Title: Re: Stuck: How can you guess that?
Post by srn347 on Oct 2nd, 2007, 8:44pm
Ask, if in logic gates 1 meant truth, 2 meant lie, and 3 was contradiction(truth and lie at the same time), and I asked you to say if pi was irrational in the logic gate of your number, would your answer be truthful? If someone already said this, which I doubt, It's because there are 3 pages.

Title: Re: Stuck: How can you guess that?
Post by towr on Oct 2nd, 2007, 11:40pm
Your conception of logic gates is baffling. It doesn't seem to make sense in the slightest.
Logic gates work on on/off (1/0) signals, not real numbers.

Title: Re: Stuck: How can you guess that?
Post by mikedagr8 on Oct 3rd, 2007, 2:30am

on 10/02/07 at 23:40:54, towr wrote:
 Logic gates work on on/off (1/0) signals, not real numbers.

It depends who you are...

Title: Re: Stuck: How can you guess that?
Post by einstein7th on Oct 12th, 2007, 4:05pm
Gotten from a friend:

if 3...  1/(3-2) ==> yes.
if 1...  1/(1-2) ==> no.
if 2...  1/(2-2) ==> I don't know, 1/0 = both positive infinity and negative infinity.

Title: Re: Stuck: How can you guess that?
Post by Hippo on Oct 13th, 2007, 2:32am
[spam] Sorry for spamming :) ... all the solutions are based on a trick with answers yes, no, I cannot decide.
The beauty of the solution depends on how it achieves the third answer.
1) The undefined value is not nice as in that case the answer "no" fits well. Answering "No because this is not defined ... shortened to "This is not defined" is an answer with nonrequested additional information.
2) The I cannot decide as the question is too complex that nobody knows the answered yet is better but risky. What about the new progress in computing ... ?
Suppose the queried person have a time limit to consider all three computations so the number cannot be guessed according to reply time.
3) The I cannot decide and I know I will never be able to decide is the solution you cannot beat.
This is why I vote for variants of "I have roled x on the usual 6 sided dice. Is your number bigger than (7+2x)/7?"
(As was post by Paul Hammond (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1159475568;start=0;#14) ... who preferes coin flips to dice rolls)
Refolmulated as a single question ... Is your number minus 1 alltogether multiplied by 3.5 greater than random roll on a standard dice?
(As was post by towr (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1159475568;start=0;#17) ... who preferes even more powerfull random generators).
The constant 3.5 can be changed to 4 if you prefere nice numbers to symmetry ...

4) The questions which are not well defined (following post) ... Suppose he can ask you to explain your question ... and answers according to your chosen definition ... I still vote for 3)
[/edit]
[/spam]

Title: Re: Stuck: How can you guess that?
Post by FiBsTeR on Oct 13th, 2007, 7:07am
The dice solution is nice, but how about something simpler:

"Is one less than your number an even natural number?"

1: "It depends/I don't know", since zero is even, but sometimes included in the set of naturals (http://mathworld.wolfram.com/NaturalNumber.html).
2: "No", since 1 is natural but odd.
3: "Yes", since 2 is natural and even.

Title: Re: Stuck: How can you guess that?
Post by TruthlessHero on Oct 13th, 2007, 7:14am
Just because we know that it's sometimes included, doesn't mean that the person answering will...But I like yours the best so far.

Title: Re: Stuck: How can you guess that?
Post by FiBsTeR on Oct 13th, 2007, 7:52am

on 10/13/07 at 07:14:56, TruthlessHero wrote:
 Just because we know that it's sometimes included, doesn't mean that the person answering will

Well whenever I see problems involving asking questions to other people, I assume the other person is omniscient, or at least close enough to it to suit the needs of the problem. By that logic, our person might not know how to add/subtract/multiply/divide, but we assume he does.

Title: Re: Stuck: How can you guess that?
Post by towr on Oct 14th, 2007, 7:06am

on 10/13/07 at 07:52:10, FiBsTeR wrote:
 Well whenever I see problems involving asking questions to other people, I assume the other person is omniscient
Then he'd know what concept of "natural number" you subscribe to, and could reply either yes or no :P

Title: Re: Stuck: How can you guess that?
Post by FiBsTeR on Oct 14th, 2007, 5:07pm

on 10/12/07 at 16:05:44, einstein7th wrote:
 "Is 1 divided by your number minus 2 positive?"if 3...  1/(3-2) ==> yes.if 1...  1/(1-2) ==> no.if 2...  1/(2-2) ==> I don't know, 1/0 = both positive infinity and negative infinity.

Does this work? 1/0 is not defined, so it is not positive, so the answer for this would be "No".

EDIT:

on 10/14/07 at 07:06:54, towr wrote:
 Then he'd know what concept of "natural number" you subscribe to, and could reply either yes or no :P

Well suppose I didn't consider zero to be a natural number: does that mean zero isn't a natural number? If I asked an omniscient mind whether a movie was "good", and I thought the movie was good, does that mean he/she would answer "yes"?

Title: Re: Stuck: How can you guess that?
Post by towr on Oct 14th, 2007, 11:37pm

on 10/14/07 at 17:07:12, FiBsTeR wrote:
 Well suppose I didn't consider zero to be a natural number: does that mean zero isn't a natural number?
In your mathematical system, it wouldn't be. The question doesn't have an objective answer; you won't find the answer 'in the world'. Mathematics is a system of axioms and definitions, and so it depends on what system you work in. Of course, the same holds for every mathematical concept (addition and subtraction included).
An omniscient being has the luxury to answer a question as you mean it, rather than merely its own interpretation thereof; it unambiguously knows what you mean. It wouldn't be answering truthfully if it answered to a different meaning. Otherwise it could answer any question with "well, I don't know, depends on your definition of ..."

Quote:
 If I asked an omniscient mind whether a movie was "good", and I thought the movie was good, does that mean he/she would answer "yes"?
Whether a movie is good or bad is typically an opinion, it doesn't follow from axioms or definitions.

Title: Re: Stuck: How can you guess that?
Post by Grimbal on Jul 19th, 2017, 4:07am
I stumbled here by chance.

I have seen better answers to this question before.  Maybe a duplicate or another forum.  Here they are.

1. "I am thinking of the numbe 1 or 2.  Is your number strictly larger than mine?"
yes -> 3, no -> 1, don't know -> 2.
(actually a variation of Paul Hammond's answer)

2. "Answer by "yes" or "no".  Answer with a word that has that many letters".
yes -> 3, no -> 2, er... -> 1.

Title: Re: Stuck: How can you guess that?
Post by riddler358 on Apr 7th, 2019, 9:49am
Is the number you are thinking of greater than number of legs i will be standing on for a moment after you answer me?

Title: Re: Stuck: How can you guess that?
Post by rmsgrey on Apr 12th, 2019, 9:54am

on 04/07/19 at 09:49:59, riddler358 wrote:
 Is the number you are thinking of greater than number of legs i will be standing on for a moment after you answer me?

That fails when you do a handstand...