|
|
dimis
Responsible
Supreme Hero
Digitally signed by FoG
|
posted February 25, 2009 09:00 AM |
|
Edited by dimis at 09:03, 25 Feb 2009.
|
I didn't know about Project Euler.
It's interesting though that already some people had computational approaches to some problems. I was hoping on some interesting problems here (Introduction to Programming with C) but I guess my definitions overkilled the fun that was about to come. Perhaps a better idea is a separate thread aiming on problems that require the use of some programming language and anyone will be allowed to write in his/her own favorite programming language; for example solve the N-queens problem for an arbitrary NxN chessboard, give a knight tour on an NxN chessboard, create a sudoku solver, tic-tac-toe player (may be in 3D to make it more interesting), and so on ...
The point is that all these things require by the user the knowledge of at least one programming language and that's one (probably the main) reason that I started Introduction to Programming ( with C ). Anyway, if others feel confident in programming (e.g. TheDeath is one guy), we can create a thread that tries to tackle computational problems. As a side-effect it would help on the distinction between Math and CS ... but this can be just plain day-dreaming once again ... 
____________
The empty set
|
|
Ecoris
Promising
Supreme Hero
|
|
posted February 25, 2009 12:24 PM |
|
|
Quote:
Question: Is there a "way of eating" (i.e. a path) such that the mouse eats the "inner-most" small cube last ?
No  .
____________
|
|
dimis
Responsible
Supreme Hero
Digitally signed by FoG
|
|
posted February 25, 2009 06:29 PM |
|
Edited by dimis at 18:30, 25 Feb 2009.
|
Quote:
No .
Right. Anybody else willing to prove this?
It's kind of funny that once you hear about a new technique, you might also encounter similar problems soon afterwards (I am referring to this problem which is related to other problems previously encountered in thread).
The guy who told me about the problem also told me that Laszlo Babai calls these kind of problems as "a-ha problems" due to their simple and intuitive solution. It's a funny name and from now on I'll definitely call them this way.
As a footnote, that guy heard about this "mouse" problem by Babai.
____________
The empty set
|
|
dimis
Responsible
Supreme Hero
Digitally signed by FoG
|
posted March 13, 2009 07:52 PM |
|
Edited by dimis at 19:55, 13 Mar 2009.
|
Which card(s) should I turn?
Initially I wanted to make a poll on this, but it turns out that the "10-options" restriction is just not good enough to support it.
Anyway, here is a problem:
_______________________________________________________________________
Suppose we are given a rule:
Rule: If a card has a vowel on one side, then there is an even number on the other side of the card.
And now suppose that someone presents you the following four cards:
A, K, 4, 7
The question is:
Question: Which cards should I turn to verify the rule above?
_______________________________________________________________________
So, which one(s) would you "flip"?
Please do not say why at the moment (although I encourage you when you make your final decision to write something down for future reference). Also try to answer before reading further from this point. I think it will be interesting to see how people interpret this kind of question (at least some percentages on right/wrong answers ...).
If you are not feeling comfortable posting your choice, you can send me an IM (or not at all!). From what I know, most people don't get it right, so I guess the odds are that we don't get it either. This is just a warning in case you don't feel comfortable about that.
____________
The empty set
|
|
DagothGares
Responsible
Undefeatable Hero
No gods or kings
|
|
posted March 13, 2009 07:55 PM |
|
|
I would flip 'A'... Only A. the other ones wouldn't prove anything.
____________
If you have any more questions, go to Dagoth Cares.
|
|
TheDeath
Responsible
Undefeatable Hero
with serious business
|
|
posted March 13, 2009 08:12 PM |
|
|
Unless this is some puzzle, and we are allowed to flip more cards? All of them and check the result? 
I know, maybe I missed something, is it a puzzle regarding AK-47 or word play or something?
____________
The above post is subject to SIRIOUSness.
No jokes were harmed during the making of this signature.
|
|
DagothGares
Responsible
Undefeatable Hero
No gods or kings
|
|
posted March 13, 2009 08:16 PM |
|
|
You're allowed to flip all of them, but I'd say they're obsolete. Not posting my reasons yet... Though, it shouldn't be hard... Unless I'm totally missing something...
I also hope that the AK 47 is a coincidence.
____________
If you have any more questions, go to Dagoth Cares.
|
|
Asheera
Honorable
Undefeatable Hero
Elite Assassin
|
|
posted March 13, 2009 08:46 PM |
|
|
Flip 4 to get a vowel.
But really I'm totally clueless about this, I'm not sure what we're supposed to do
____________
|
|
DagothGares
Responsible
Undefeatable Hero
No gods or kings
|
|
posted March 13, 2009 08:51 PM |
|
|
There is this rule. How do you prove this theory to be true? You are allowed to flip the cards and make a smart point after ya did.
____________
If you have any more questions, go to Dagoth Cares.
|
|
Asheera
Honorable
Undefeatable Hero
Elite Assassin
|
|
posted March 13, 2009 08:56 PM |
|
|
Dunno, flip all and see if they follow the rule? I don't get it.
____________
|
|
dimis
Responsible
Supreme Hero
Digitally signed by FoG
|
|
posted March 13, 2009 08:56 PM |
|
|
Well, the question is clear and on a separate line from all other stuff. So, try to answer to the question. That's all I am saying. And please don't post your thoughts on inference, because this guides or misleads others.
Thank you all for having participated so far.
____________
The empty set
|
|
Cepheus
Honorable
Legendary Hero
Far-flung Keeper
|
|
posted March 13, 2009 08:58 PM |
|
|
Quote:
Flip 4 to get a vowel.
Without giving too much away... not necessarily!
|
|
Asheera
Honorable
Undefeatable Hero
Elite Assassin
|
|
posted March 13, 2009 09:01 PM |
|
|
Right 
Then flip A, the others could give you anything. A seems to be the only 'special' one since it has to give you an even number, so I guess that's the answer.
____________
|
|
friendofgunnar
Honorable
Legendary Hero
able to speed up time
|
|
posted March 13, 2009 09:21 PM |
|
|
haha! are you reading "The Math Gene" too, Dimis? 
|
|
dimis
Responsible
Supreme Hero
Digitally signed by FoG
|
|
posted March 13, 2009 09:27 PM |
|
|
Nope!
But I suspect it is a good suggestion for a book if you can find that problem there.
I heard about this problem today on a talk in AI / reasoning.
____________
The empty set
|
|
Binabik
Responsible
Legendary Hero
|
|
posted March 13, 2009 10:45 PM |
|
Edited by Binabik at 02:16, 14 Mar 2009.
|
Quote:
Suppose we are given a rule:
Rule: If a card has a vowel on one side, then there is an even number on the other side of the card.
And now suppose that someone presents you the following four cards:
A, K, 4, 7
The question is:
Question: Which cards should I turn to verify the rule above?
I think it kind of depends on what you mean by "verify". And we must assume the 4 cards are all of the cards.
The way I interpret it, you must flip the A and the 7 to verify the rule. The reverse of the A MUST be an even number AND the reverse of the 7 must NOT be a vowel. If either of these is not true then the rule is proven to be false.
The reverse of the K can be even or odd, neither of which violates or validates the rule.
The reverse of the 4 can be a vowel or consonant, neither of which violates or validates the rule.
edit: I have to put a condition on the above answer. The assumption was made that all cards have a number on one side and a letter on the other. If that's not true then all four cards must be flipped.
|
|
Stratos
Hired Hero
|
|
posted March 13, 2009 11:59 PM |
|
|
The answer is A and 4.
You flip the A card to reveal the even number.Vice Versa. Flip the 4 over to reveal the vowel.
____________
|
|
Binabik
Responsible
Legendary Hero
|
|
posted March 14, 2009 02:11 AM |
|
|
It doesn't matter what's on the other side of the 4.
If vowel, then even
does not imply
If even, then vowel
The other side of the 4 could be a vowel, consonant, completely blank or a picture of a duck, and it would have no bearing on the validity of the rule.
One way of looking at it, is that the rule is an "IF" statement. The rule only applies when the IF condition is met.
Let's say for example that the 4 card has a consonant on the reverse side. The "IF" condition has not been met, therefore it doesn't matter what's on the other side.
____________
|
|
Stratos
Hired Hero
|
|
posted March 14, 2009 02:26 AM |
|
|
You defantely taught me a lesson Binabik.
____________
|
|
Ecoris
Promising
Supreme Hero
|
|
posted March 15, 2009 09:52 PM |
|
Edited by Ecoris at 21:55, 15 Mar 2009.
|
Quote:
One way of looking at it, is that the rule is an "IF" statement. The rule only applies when the IF condition is met.
I can't see any other way of looking at it:
Quote:
Rule: If a card has a vowel on one side, then there is an even number on the other side of the card.
The sentence is of the form "if A, then B" and it is posted in a mathematics thread. As you said, only the cards with A and 7 can violate the claim. Therefore, one needs only turn these two cards and must do so.
Interesting question. I had expected people to miss 7, but not to suggest 4.
____________
|
|
|
|
This thread is pages long: 
