Conceptual problems

<div class='quotetop'>QUOTE(eagle33199 @ May 1 2007, 09:32 AM) [snapback]433163[/snapback]</div>

Here's the order:

1. Man 1 & Man 2 cross. (Time: 2 Minutes)
2. Man 1 back across. (Time: 1 Minute)
3. Man 3 & Man 4 cross. (Time: 10 Minutes)
4. Man 2 back across. (Time: 2 Minutes)
5. Man 1 & Man 2 cross. (Time: 2 Minutes)

Total time: 17 Minutes

What do I win?

 

<div class='quotetop'>QUOTE(eagle33199 @ May 1 2007, 09:17 AM) [snapback]433188[/snapback]</div>

Is the number you are thinking of => 2?

 

Do you have to cut a whole pie to separate it into one fewer pieces than your number?

 

<div class='quotetop'>QUOTE(jeneric @ May 1 2007, 02:17 PM) [snapback]433487[/snapback]</div>

Wouldn't the answer to this be "no" for numbers of both 1 and 2?

 

<div class='quotetop'>QUOTE(eagle33199 @ May 1 2007, 07:17 AM) [snapback]433188[/snapback]</div>

That hint is what makes the puzzle possible at all, else it's irresolvable - you can't get 3 outcomes from a binary input. So the question must be framed such that a yes-no response is impossible for one of the numbers. Something along the lines of "This is a False statement" must be incorporated. The best I can do so far is something like:

If you are not thinking of 2, you will say Yes if I ask are you thinking of 3.

Now, that's a statement, not a question, but you either affirm it, deny it, or can neither confirm nor deny it, so I hope it qualifies.

If you're thinking of 1, the first clause is true, and you won't say yes to 3, so you say NO.

If you're thinking of 3, the first clause is still true, and you'll be truthful about 3, so you say YES.

If you're thinking of 2, the first clause is false, rendering the rest of the statement moot, so it can't be confirmed or denied, and you'll say you can't answer.

I'm not 100% convinced I've framed the question absolutely correctly, but that's the gist.

Mark Baird
Alameda CA

 

<div class='quotetop'>QUOTE(San_Carlos_Jeff @ May 1 2007, 02:42 PM) [snapback]433506[/snapback]</div>

I don't think so; to me that would mean you can separate it into 0 pieces without cutting it.

 

How about: "Is it a prime number greater than two?"
If yes, then it's 3.
If no, then it's 2.
(Assuming 1's not prime, not being divisible by one AND itself.)

 

<div class='quotetop'>QUOTE(efusco @ May 1 2007, 06:59 PM) [snapback]433568[/snapback]</div>

I'm not so sure. A prime number, by definition, has exactly two factors. The number 1 has only one.

 

<div class='quotetop'>QUOTE(hyo silver @ May 1 2007, 04:10 PM) [snapback]433579[/snapback]</div>

Interesting, but 1 is not greater than 2 anyway, so the answer would still be no. It's not a prime number greater than 2, whether it's really prime or not.

 

OK, I'm wrong. Never mind.

 

<div class='quotetop'>QUOTE(eagle33199 @ May 1 2007, 07:17 AM) [snapback]433188[/snapback]</div>

If you subtract one from the number you picked, then divide your number by that one less number, is the product an even number?

1 - 1 = 0. You can't divide a number by zero. The person would have to say they cannot answer.

2 - 1 = 1 so 2 / 1 = 2 (an even number) The person would answer yes.

3 - 1 = 2 so 3 / 2 = 1.5 (an odd number) The persons would answer no.

Three answers from one yes/no question.

 

<div class='quotetop'>QUOTE(hyo silver @ May 1 2007, 04:10 PM) [snapback]433579[/snapback]</div>

I've always heard primes described as a number "divisible by itself or 1."
Now, if that counts as "two" factors, then 1 has both those factors: "itself" and "1".
1 is most definitely a prime number, even if it isn't so hot as, say, a weekly salary in Manhattan.

MB

 

<div class='quotetop'>QUOTE(airportkid @ May 1 2007, 04:50 PM) [snapback]433593[/snapback]</div>

WRONG.

One is not prime. A prime number is evenly divisibly by exactly two numbers. "1" and "1" only counts as one number, so one is not prime. Sheesh.

 

OK, so I messed up the question. But 1 is not prime. Would you believe wikipedia? http://simple.wikipedia.org/wiki/Prime_number

 

<div class='quotetop'>QUOTE(priusenvy @ May 1 2007, 05:49 PM) [snapback]433617[/snapback]</div>

I checked with Google. You guys are right, one isn't prime. It's its own category. My bad.

MB

 

<div class='quotetop'>QUOTE(airportkid @ May 1 2007, 02:46 PM) [snapback]433511[/snapback]</div>

That's basically it, you have to ask a question that can only be answered yes/no/don't know.

The most common answer is something like: "I'm thinking of either 1.5 or 2.5. Is your number greater than mine?" But it's really only limited by your imagination. The divide by zero mentioned a couple posts above is another question that works. You can even get really odd answers, like my answer the first time I heard it:

"I have two helium balloons, each of 1.5 cubic meters in volume (about 1.5kg of lifting power). I tie 2kg of lead to one balloon. I tie (your number) kg of lead to the other, and throw them both off a five story building on a windless day. Does my balloon with 2kg of lead tied to it land before yours?" Yes - number is 1, no - number is 3, don't know - number is 2.

Since this depends on aero drag, this only works if there is an atmosphere around your building, it wouldn't work on the moon.