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        riddles >> easy >> http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB
        
(Message started by: srn347 on Sep 21st, 2007, 6:28pm)
Title: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB
Post by srn347 on Sep 21st, 2007, 6:28pm
there are 9 coins, one of which is counterfeit. the fake one weighs less. You have a scale that compares their weight. How do you find the counterfeit in one measurement? How about 2?
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by TenaliRaman on Sep 21st, 2007, 8:09pm

on 09/21/07 at 18:28:28, srn347 wrote:
How do you find the counterfeit in one measurement? How about 2?

ROFL!!!

To answer the question,
since 0/0 is anything, all numbers can be shown to be equal and hence none of the coins is fake.

-- AI
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by FiBsTeR on Sep 22nd, 2007, 9:13am
Great title.
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by srn347 on Sep 22nd, 2007, 3:38pm
thanks(assuming it wasn't sarcasm). And 0/0 isn't involved here. Creative, but irrelevant.
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by Sir Col on Sep 22nd, 2007, 4:57pm

on 09/22/07 at 15:38:35, srn347 wrote:
thanks(assuming it wasn't sarcasm).

Surely you're not serious? Have you actually seen the title you used for this thread?


Solution:
[hide]Place three coins on one side of the balance and three coins on the other. If it balances the fake is among the three coins not weighed. If it doesn't balance then you know which pile of three it's in, as the fake coin is lighter.

Take the three coins containing the fake and place two of the coins on the balance. If they balance the third is fake, it they don't balance you know which one is fake.[/hide]

srn347, as an extension... if you were allowed three separate weighings, what is the most coins that you could work with to identify the fake coin?
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by srn347 on Sep 22nd, 2007, 8:01pm
27. And the title is a link to the page I was on when I was entering the title.
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by Sir Col on Sep 23rd, 2007, 1:56am
Have you tried going to that "page"? Every URL here on the forum begins with that, but has a lot more after it.



on 09/22/07 at 20:01:09, srn347 wrote:
27.

Very good, and I assume, therefore, you've discovered the "pattern".

So what if you don't know whether the fake coin is heavier or lighter? Find the maximum number of coins for W weighings.  ;)
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by srn347 on Sep 23rd, 2007, 2:38pm
For any specific number I could find an answer, but not the specific formula for w. Sometimes using a formula is easier than knowing it. Do you know what it is? Here's one for you:if you have 0 envelopes and 0 letters to put in them, how many ways can you put no letters in the correct envelopes?
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by ThudanBlunder on Sep 23rd, 2007, 3:40pm

on 09/23/07 at 14:38:13, srn347 wrote:
Here's one for you:if you have 0 envelopes and 0 letters to put in them, how many ways can you put no letters in the correct envelopes?

00 by convention.

Here's one for you: if there are 4 letters and 4 envelopes, what is the probability that exactly 3 letters will be randomly matched with the correct envelopes?


on 09/22/07 at 20:01:09, srn347 wrote:
27. And the title is a link to the page I was on when I was entering the title.

Here's another: when are you going to change the name of this thread, now that you are on the same page as the rest of us?
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by Sir Col on Sep 23rd, 2007, 3:45pm

on 09/23/07 at 14:38:13, srn347 wrote:
Do you know what it is?

Yes, which is why I asked the question.


Quote:
Here's one for you:if you have 0 envelopes and 0 letters to put in them, how many ways can you put no letters in the correct envelopes?

If there are no letters and no envelopes then the concept of correct/wrong matching is meaningless. It's like saying, if you don't write a random number on a piece of paper and I don't think of a random number, then what is the chance of me guessing your number correctly? There are no numbers to compare. Although we both thought of "nothing", they do not match, as neither of us thought of a number, which was the substance of the comparison. Similarly, is there are no letters and no envelopes then we have eliminated the essential component which we are being asked to determine correct matchings of.
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by srn347 on Sep 23rd, 2007, 4:51pm
Actually the answer is 0, because the formula for the subfactorial(which is what I asked) is !n=n!/e rounded to the nearest integer. Now what is the answer to your question?
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by ThudanBlunder on Sep 23rd, 2007, 5:14pm

on 09/23/07 at 16:51:02, srn347 wrote:
Actually the answer is 0, because the formula for the subfactorial(which is what I asked) is !n=n!/e rounded to the nearest integer.

1) You didn't ask for a subfactorial. You asked for the answer to your question.
2) The formula you use is rounded down to the nearest integer.
3) This formula applies only for n http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/ge.gif 1
4) The answer to your question is allowed to be equal to 1, but only in order to satisfy the appropriate difference equation. As Sir Col says, your question is meaningless in the physical context in which you put it.


on 09/23/07 at 16:51:02, srn347 wrote:
Now what is the answer to your question?

5) I don't post questions in order to answer them myself. If you don't know the answer, just say so.
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by FiBsTeR on Sep 23rd, 2007, 5:23pm

on 09/23/07 at 15:40:56, ThudanBlunder wrote:
Here's one for you: if there are 4 letters and 4 envelopes, what is the probability that exactly 3 letters will be randomly matched with the correct envelopes?


I believe it is the same probability as [hide]srn answering the problem correctly, also equal to the probability of him knowing what he is talking about[/hide]?
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by ThudanBlunder on Sep 23rd, 2007, 5:45pm

on 09/23/07 at 17:23:08, FiBsTeR wrote:
I believe it is the same probability as [hide]srn answering the problem correctly, also equal to the probability of him knowing what he is talking about[/hide]?

Good job you hid that - no point in making it too easy. In fact, my question is similar to his, except that he cannot mindlessly read off the answer from whatever page the kid is on.
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by srn347 on Sep 23rd, 2007, 8:29pm
I did ask the subfactorial because that's what it is. The factorial was also only meant for integers, but half integers also work. Just because you can't apply certain functions(like 0/0), doesn't mean you can't). If this confuses you, that means you need to read it again. does anyone here know the answer to the w thing?
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by ThudanBlunder on Sep 23rd, 2007, 8:46pm

on 09/23/07 at 20:29:25, srn347 wrote:
...does anyone here know the answer to the w thing?

Yes, I do. (http://math.ucdavis.edu/~lai/22b/handouts/Wronskian.pdf)
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by srn347 on Sep 23rd, 2007, 9:01pm
Does anyone(or someone) have any solutions that are actually in english mathematics. Also, no one actually is just anyone.
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by Barukh on Sep 24th, 2007, 12:26am
Again: didn't we agree to Ignore?
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by Sir Col on Sep 24th, 2007, 12:31am
As I've not had any direct dealings with him yet, I am willing to give him the benefit of the doubt. I may come to regret it, but it gives him another chance.

srn347, there is far more to be gained by working it out for yourself rather than read someone else's solution. If you want I can give you pointers to work towards a full solution.

First of all, are you wanting to find the general solution to (i) it is known whether the fake coin is heavier or lights, or, (ii) it is not known?
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by Grimbal on Sep 24th, 2007, 12:39am

on 09/23/07 at 20:29:25, srn347 wrote:
does anyone here know the answer to the w thing?

If the number of coins is a multiple of 3, you can make 3 equal heaps and find out in a single weighing which heap has the fake coin.
So, each weighing can reduce by 3 the number of coins that could be fake.  Or seen the other way round, each additional weighing lets you find the coin among 3 times as many coins.

With 1 weighing you can find the fake among 3 coins.
With 2 weighings you can find it among 9 coins.  9 is 3 times 3.
With 3 weighings you can find it among 27 coins.  27 is 3 times 9.

The pattern that emerges is:
[hide]With W weighings you can find it among 3W coins.[/hide]
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by ThudanBlunder on Sep 24th, 2007, 2:17am

on 09/24/07 at 00:26:47, Barukh wrote:
Again: didn't we agree to Ignore?

While I believe you can take a horse to water, towr, Sir Col, and Grimbal seem to believe you can actually make it think!
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by mikedagr8 on Sep 24th, 2007, 2:43am

on 09/24/07 at 02:17:38, ThudanBlunder wrote:
While I believe you can take a horse to water, towr, Sir Col, and Grimbal seem to believe you can actually make it think!


Lol, here's one I heard today.

Quote:
Computers are never stupid. It's just the idiots using them, which make it appear so.
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by srn347 on Sep 24th, 2007, 9:49pm
Or maybe it was made by idiots. I knew it had something to do with three.
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by Sir Col on Sep 25th, 2007, 2:02am
srn347, you've received a number of positive replies to your problem in this thread, so why don't you ignore the rest and focus on them. It's within your power to rise above the past and show everyone that you really want to be part of this community.

Grimbal has taken the time to provide a well furnished solution to your original problem; a courteous response to that might go down well. And I am willing to give you some hints to help you work towards a solution to the case where you do not know if the fake coin is heavier or lighter.
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by srn347 on Sep 25th, 2007, 4:55pm
Ok. For any specific number(for weighings or coins), I can find the other one. I believe the answer to the w thing is 3w.
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by mikedagr8 on Sep 25th, 2007, 5:13pm

on 09/25/07 at 16:55:54, srn347 wrote:
Ok. For any specific number(for weighings or coins), I can find the other one. I believe the answer to the w thing is 3w.


You're kidding me right!!! Unbelievable. He can read!!! :o


on 09/24/07 at 00:39:40, Grimbal wrote:
If the number of coins is a multiple of 3, you can make 3 equal heaps and find out in a single weighing which heap has the fake coin.
So, each weighing can reduce by 3 the number of coins that could be fake.  Or seen the other way round, each additional weighing lets you find the coin among 3 times as many coins.

With 1 weighing you can find the fake among 3 coins.
With 2 weighings you can find it among 9 coins.  9 is 3 times 3.
With 3 weighings you can find it among 27 coins.  27 is 3 times 9.

The pattern that emerges is:
[hide]With W weighings you can find it among 3W coins.[/hide]
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by srn347 on Sep 25th, 2007, 5:14pm
I did that intentionally! how did you not know? HOW?!
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by ThudanBlunder on Sep 25th, 2007, 6:02pm

on 09/25/07 at 17:13:35, mikedagr8 wrote:
You're kidding me right!!! Unbelievable. He can read!!! :o

You claim to have reduced your baiting.   ::)
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by mikedagr8 on Sep 25th, 2007, 6:04pm

on 09/25/07 at 18:02:25, ThudanBlunder wrote:
You claim to have reduced your baiting.   ::)

That was not baiting. That was showing how he has improved.
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by srn347 on Sep 25th, 2007, 7:24pm
Baiting? I am not a fish!
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by Sir Col on Sep 25th, 2007, 11:44pm
srn347, now you have the general solution to the "it is known that the fake coin is heavier or lighter" version, why don't you have a crack at "it is not known" version.

May I suggest you try solving for 2 coins, 3 coins, 4 coins, and 12 coins, where one is a fake but it is not known if it is heavier or lighter than a normal coin. What can you deduce about the 2 coin case? Remember that you are looking for the minimum number of weighings required to guarantee finding the fake.
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by Grimbal on Sep 26th, 2007, 12:36am
Uh... srn, do you know what these orange blocks are?
[hide] this is an example [/hide]
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by srn347 on Sep 26th, 2007, 7:04am
Yes I know, but why would I use them?[hideb]                                                                                                                [/hideb]
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by Grimbal on Sep 26th, 2007, 8:34am
I was wondering if you could read them.  I thought that if you didn't know that there was hidden text, that would explain why sometimes you didn't see that a problem has been answered.
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by srn347 on Sep 26th, 2007, 7:20pm
I already said that was intentional! Forget it! Next riddle, one coin weighs -1, one weighs a positive number times -1, and one weighs 1. You only know the one that weighs one. How do you differentiate the other two.
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by FiBsTeR on Sep 26th, 2007, 8:12pm
Hint: [hide]Divide the negative masses by negative zero.[/hide] <--Dead giveaway.
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by srn347 on Sep 26th, 2007, 8:14pm
<press caps lock> YOU CANNOT DIVIDE BECAUSE THIS IS NOT AN EQUATION! <press caps lock>(self contradictory)
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by srn347 on Sep 26th, 2007, 8:18pm
Thanks for reminding me, it can't be one.
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by ThudanBlunder on Sep 26th, 2007, 8:19pm

on 09/26/07 at 19:20:11, srn347 wrote:
Next riddle, one coin weighs -1, one weighs a positive number times -1, and one weighs 1. You only know the one that weighs one. How do you differentiate the other two.

I don't; I just assume that the positive number is equal to 1 and take the rest of the day off.
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by srn347 on Sep 26th, 2007, 8:25pm
WELL IT ISN'T! And if you'll take the day off, try the logic gate one while you do it.
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by ThudanBlunder on Sep 26th, 2007, 8:38pm

on 09/26/07 at 20:25:29, srn347 wrote:
WELL IT ISN'T! And if you'll take the day off, try the logic gate one while you do it.

Nah, I think I'll just use the door like everybody else.
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by srn347 on Sep 26th, 2007, 8:40pm
Now I see why thunder and blunder weren't meant to mix.
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by Noke Lieu on Sep 26th, 2007, 10:00pm
srn347....

don't do it man.
You're not smart enough to take him on. Seriously.
Not at maths, not at general knowledge, not at chess.

Not at spelling, not a word games, nor at tying shoelaces.

"thudnblunder"... it's a spoonerism. It's very clever.
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by Sir Col on Sep 27th, 2007, 12:29am

on 09/26/07 at 19:20:11, srn347 wrote:
Next riddle...

Whoa! (and to use the words of Simon and Garfunkel) Slow down you move too fast. You've still not solved the alternative challenge I presented to you. Surely you don't expect other people to solve your problems if you don't solve anyone else's?!
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by mikedagr8 on Sep 27th, 2007, 1:02am
Hahaha. Since this is a real problem, nothing weighs negative. I solved it; no discussion.

Good call Col and Noke. :D :)
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by Grimbal on Sep 27th, 2007, 1:14am
You glue the 1 coin to one of the other coins (-1 coin or -n (n>1) coin).  If it flies to the ceiling, it is the -n coin, if it floats in mid-air, it is the -1 coin.
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by JiNbOtAk on Sep 27th, 2007, 1:42am

on 09/26/07 at 22:00:09, Noke Lieu wrote:
Not at spelling, not a word games, nor at tying shoelaces.


Is this considered baiting ?  :P
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by mikedagr8 on Sep 27th, 2007, 1:48am

on 09/27/07 at 01:42:51, JiNbOtAk wrote:
Is this considered baiting ?  :P

It's called honesty.
Title: Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
Post by srn347 on Sep 27th, 2007, 4:39pm
Actually it can weigh negative because since this riddle is hypothetical, I have the power of 'if'. You cannot glue them, and it might not fly, because the positive number is not neccesarily an integer.


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