Riddles Round 2

[Firemeboy]

you would argue it and lose quite badly

 Does everything need to be an argument?

It's a curious mathematical phenomenon.  One that you can 'prove' mathematically, but of course is silly.  But still, fun to think about.

[Firemeboy]

0.9 repeating may be as close to 1 as to make no difference in any real world calculation, but it is *not* actually 1.

Yes, it is.  

Do the math.
1/3 + 1/3 + 1/3 = 1

Therefore .33333(etc) + .33333(etc) + .33333(etc) = 1 or .9999999999

[Firemeboy]

http://mathforum.org/dr.math/faq/faq.0.9999.html

[The Holy Saint, Grand High Poobah, Master of Monkeys, Ehlers]

no, but YOU called it an argument first

[The Holy Saint, Grand High Poobah, Master of Monkeys, Ehlers]

and you also can't ever make any progress, because every time you move half the distance to something, you still have half the distance left.

this is called a "paradox." It's also an inaccurate way of looking at things. The simply fact that you can produce a number that does not contain a 3 in it shows that it is untrue that 100% of numbers do not have a 3 in them. The math, used then, is a problem. Because it can "prove" something that is patently false.

Again, it's small enough that there's no reason to calculate it differently, but there is an infinitessimally small difference.

[The Holy Saint, Grand High Poobah, Master of Monkeys, Ehlers]

look at it this way (also from the Dr. Math site you posted a link to, showing that there is disagreement on the answer -- people proving your point tend to say "if you are going to assign a value to it the only sensible value is 1" and so forth, not very exacting language). 1/3 != 0.3 repeating. .3 repeating is just the closest you can get to it using the decimal system. 1/3 + 1/3 + 1/3 = 1, but .3 repating + .3 repeating + .3 repeating = .9 repeating. Not one. It's the closest decimals can approach the fraction system, which is why we have ratios in the first place. because 22/7 is not the same as the decimal expression commonly substituted for pi. Infinitely close, but not quite there. 1/3 is actually 1 divided by three. multiplying it by 3 makes 3 divided by three. which is one.

It's infinitely close, no point in picking the nit if you're doing a calculation because the difference will be indiscernable. However, when it comes to proving that every real number contains the digit "3" in it, it becomes a vitally important nit to pick.

[Eric James Stone]

e, I'm glad to see someone who looks at it the same way I do.  I've been arguing for years that .9 repeating is not quite equal to 1 -- it's just the largest number less than one.

Anyway, I guess it's my turn to post a riddle.

OK, back to the Island of Truthtellers, Lietellers, and Outcasts.

The rules this time:

Truthtellers always tell the truth.
Lietellers always lie by telling the exact opposite of the truth, when possible.
Outcasts alternate between telling the truth like Truthtellers and and lying like Lietellers.  Natives of the island know instinctively whether an outcast will next tell a lie or tell the truth, but an outsider like you lacks the necessary instinct.

You come upon a fork in the road.  A sign indicates that one path leads to the Fountain of Youth and that the other leads to the Pit of Despair.  Unfortunately, the sign doesn't have any arrows designating which is which.  But it does say that there will always be exactly one Truthteller and one Lieteller standing at the fork.  You may ask a total of two questions of any natives you find standing there -- either two questions to the same person, or one question to one person and one question to another.

Unfortunately, there aren't just two natives standing at the fork: there are ten.  One is a Truthteller and one is a Lieteller, and the rest are outcasts.  Unfortunately, there is no way for you to determine which group any of them belong to, other than by asking questions.

So, explain what two questions you would ask, of whom, in order to determine the way to the Fountain of Youth.

[Legion]

DO they have to be yes or no questions?

[Eric James Stone]

Not this time.  You can ask any question you want.

[Eric James Stone]

Also, you must use the verbal answers to the questions to make your determination.  So you can't ask something like, "Did you hear they're giving away free hot dogs and ice cream at the Fountain of Youth?" and then watch to see which way the natives go.

[Peter Ahlstrom]

Do they alternate strictly or randomly?

[Firemeboy]

Sorry, I was in class all afternoon.  

As far as the .999 goes, I felt the same way.  But after many debates on several boards, and hearing discussion from freaks who knew math much better than me, I started to lean toward the idea that .999~ = 1.  What finally sold me was Cecil Adams.

http://www.straightdope.com/columns/030711.html

If you don't read that column, I highly recomend it.  He is a guy with a great writing style, and his topics are usually quite interesting, and the guys is a freaking genius.

[Firemeboy]

I would pick one person at random and ask him to identify each of the 10 people.  If he was the liar, he would tell me that 8 of the people were village members, that he was the truth teller, and that the truth teller was the liar.  

If he was the truth teller, he would tell me that 8 of the people were outcasts, and that he was the truth teller, and that the liar was the liar.

If I picked one of the outcasts, and they were lying, he would tell me that he was a village member, point out 7 other village members, and then identify the truth teller as a liar, and the liar as the truth teller.

If I picked one of the outcasts, and they were telling the truth, he would identify himself as an outcast, point out the other 7 outcasts, and identify the truth teller and the liar as their respective selves.

Any way I know exactly who the truth teller is, and would ask him or her for directions.

Unless, of course, you could each act of 'identifying' as alternating between lying and being honest.  But as long as they do it in once sentence, I say it's all one event.  I'd just ask him to talk in a single sentence.  

[Eric James Stone]

> Do they alternate strictly or randomly?

Strictly.




Firemeboy, your explanation works.

[Firemeboy]

Did you have another solution?  I'd like to hear it.

There are two iron rods- one is blue, the other one red. Other than their colors, the only difference between them is that one is a magnet. Everything else, their weight, size, and feel are identical.

There are a few other things on the table:

   * A glass of water
   * A 5 1/4" floppy disk
   * A spool of thread

Assuming that you only have the above items to work with, what is the easiest method to determine which rod is the magnet?