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kastellorizo

Post subject: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Wed Oct 06, 2010 7:17 am 

Joined: Fri Nov 04, 2005 12:31 am Location: Greece, Australia, Thailand, India, Singapore.

Well, there have been many interesting enigmas for thousands of years. The oldest one and most known is Sphinx's Enigma. (In fact, in ancient Greece, even oracles and mathematical requests were made in a form of an enigma, to stimulate creative thinking!) Here are two recent logical ones posted here in the past two days: viewtopic.php?p=231642#p231642viewtopic.php?f=7&t=19093&start=0As for paradoxes, there are aplenty too, and there is even one mechanical, also known as Ferguson's Paradox. I also have a "puzzle device" of it: Attachment:
Ferguson.jpg [ 71.79 KiB  Viewed 6393 times ]
So, give here your best shot of an enigma, riddle or paradox! Oh yes, and did I tell you that I AM A LIAR? Pantazis
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Jared

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Wed Oct 06, 2010 3:21 pm 

Joined: Mon Aug 18, 2008 10:16 pm Location: Somewhere Else

kastellorizo wrote: Oh yes, and did I tell you that I AM A LIAR? Well, since you didn't specify that you are a pathological liar who always lies 100% of the time, there's no paradox.


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Jorbs3210

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Wed Oct 06, 2010 4:50 pm 

Joined: Thu Jun 03, 2010 2:25 pm Location: Farmington, NM

How many grains of sand does it take to make a heap of sand?
Also, the gear paradox thingy looks amazing! Where could I get one to fool my science teacher with?
_________________ Autism Speaks can go away. I have Autism. I can speak for myself.
"You say tomater, I zader matermorts."  Coach Z


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PuzzlerDazzler

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Wed Oct 06, 2010 5:49 pm 

Joined: Sun Jun 20, 2010 3:48 pm

Here's a VERY simple one: A khalifa dies and leaves his 11 camels to his 3 sons, for the oldest one half the camels, for the second a quarter of the camels, and for the youngest one sixth of the camels, since the idea wasn't exactly cutting camels they had a big problem. A very wise old man came by on his camel and told them, "if your father would've left 12 camels it would be easy for you to divide them, here, take mine, do the division and I won't lose anything" On what does the old man base his assumption? And 10 more: http://listverse.com/2007/09/21/top10brainteasers/


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cubeguy314

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Wed Oct 06, 2010 6:09 pm 

Joined: Sat Jun 26, 2010 12:06 pm

Even simpler one: Opposite Day If it's Opposite Day then that means it's not Opposite Day. But if it's not Opposite Day then it's Opposite Day. But if it's Opposite Day then it's not Opposite Day. But if it's not Opposite Day then it's Opposite Day. But if it's Opposite Day then it's not Opposite Day. But if it's not Opposite Day then it's Opposite Day. But if it's Opposite Day then it's not Opposite Day. But if it's not Opposite Day then it's Opposite Day. But if it's Opposite Day then it's not Opposite Day. (More nonsensical babbling)
_________________ ~cubeguy314~


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ndiamond

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Wed Oct 06, 2010 10:44 pm 

Joined: Fri Jul 17, 2009 5:32 pm Location: Tokyo

kastellorizo wrote: I also have a "puzzle device" of it: Ferguson.jpg Now waiting to see an Oskar / Houlis / Ferguson Gear Cube. kastellorizo wrote: Oh yes, and did I tell you that I AM A LIAR? Well if this reply is true then you didn't even ask that question.
_________________ May the force not be with you.


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katsmom

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Wed Oct 06, 2010 11:03 pm 

Joined: Sun Apr 16, 2000 3:17 pm Location: Hong Kong

I love the Ferguson device! It's a great one for party tricks. "Hey, the gears aren't turning together" Not overly expensive (for those of us that weren't there) well worth the money if you can get one.
_________________ Rox's Rambling Blog Katsmom's Puzzling Videos


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Jared

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Thu Oct 07, 2010 3:43 pm 

Joined: Mon Aug 18, 2008 10:16 pm Location: Somewhere Else

Panda, have you got a video of the Ferguson thingie in action?


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mortsemious

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Thu Oct 07, 2010 3:58 pm 

Joined: Mon Feb 15, 2010 5:18 pm

the below post is telling the truth


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mortsemious

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Thu Oct 07, 2010 3:59 pm 

Joined: Mon Feb 15, 2010 5:18 pm


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SHomer9

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Thu Oct 07, 2010 4:10 pm 

Joined: Mon Jan 04, 2010 12:53 am Location: Louisiana

I love riddles, so here's one: A lady is reading a book at her house. When she gets tired she turns off all the lights and goes to sleep. The next day she reads in the newspaper that a boat crashed killing 400 people, and she then comminted suicide. Why?
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bhearn

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Thu Oct 07, 2010 4:24 pm 

Joined: Tue Aug 11, 2009 2:44 pm

Turns out, Pantazis, I know of one problem that all of us but you can reason about correctly. Consider: "Pantazis cannot consistently believe this sentence." If he believes it, then he is being inconsistent, in believing that he can't believe it. Therefore it is true. By this logic, all the rest of us can see that it is true, and believe it, but not poor Pantazis.


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bhearn

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Thu Oct 07, 2010 4:28 pm 

Joined: Tue Aug 11, 2009 2:44 pm

Here are some famous related paradoxes.
Berry's Paradox: What is the smallest positive integer not nameable in fewer than twelve words? (Hint: "the smallest positive integer not nameable in fewer than twelve words" contains eleven words.)
Russell's Paradox: Does the set of all sets that don't contain themselves contain itself?


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mortsemious

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Thu Oct 07, 2010 4:42 pm 

Joined: Mon Feb 15, 2010 5:18 pm

SHomer9 wrote: I love riddles, so here's one: A lady is reading a book at her house. When she gets tired she turns off all the lights and goes to sleep. The next day she reads in the newspaper that a boat crashed killing 400 people, and she then comminted suicide. Why? spoiler (highlight): she lives in a lighthouse


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Brandon Enright

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Thu Oct 07, 2010 5:43 pm 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

bhearn wrote: Turns out, Pantazis, I know of one problem that all of us but you can reason about correctly. Consider: "Pantazis cannot consistently believe this sentence." If he believes it, then he is being inconsistent, in believing that he can't believe it. Therefore it is true. By this logic, all the rest of us can see that it is true, and believe it, but not poor Pantazis. Thank you GĂ¶del . I love selfreferential logic  but not as much as selfreferential sentences .
_________________ Prior to using my real name I posted under the account named bmenrigh.


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Iranon

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Thu Oct 07, 2010 6:44 pm 

Joined: Wed Apr 01, 2009 2:59 pm

Since Russell's paradox has been thrown out there, I feel like I should add the BanachTarski paradox into the mix, for fans of mathematics here on TP. Of course, neither of these are really paradoxes, Russell's paradox is only a paradox to philosophers who don't really understand how axiomatic set theory works, and the BanachTarski paradox is just a true statement which intuitively seems false if you've never been exposed to measure theory. Anyway, the BanachTarski paradox:
Consider the unit sphere in 3 dimensional space. It is possible to divide the sphere up into finitely many pieces (you can get away with only 5 pieces, in fact), and reassemble the pieces ("reassemble" here essentially means what it should mean  only rigid motions, i.e. rotating and sliding) into TWO copies of the unit sphere. Of course, if that's not weird enough for you, you can iterate this process as many times as you want and, say, turn a sphere the size of a golf ball into a sphere the size of Jupiter by cutting it into finitely many pieces and rearranging them finitely many times.


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VeryWetPaint

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Thu Oct 07, 2010 7:11 pm 

Joined: Sun Mar 11, 2007 3:11 am Location: Oregon, USA

Write this down and ask someone to answer both trueorfalse questions. Most people start confidently, then begin having trouble when they recheck their answers! Code: 1. You exist. True or false? 2. Only one of these sentences is true. True or false? They can't both be true because if the second sentence was true then the other could not be. But if the second sentence is false then the first sentence must also be false, because otherwise the second sentence would be true. The paradox is seemingly resolved if the first sentence is false and the second is true...but most people dislike that option!


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bhearn

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Thu Oct 07, 2010 7:45 pm 

Joined: Tue Aug 11, 2009 2:44 pm

Iranon wrote: Since Russell's paradox has been thrown out there, I feel like I should add the BanachTarski paradox into the mix, for fans of mathematics here on TP. Of course, neither of these are really paradoxes, Russell's paradox is only a paradox to philosophers who don't really understand how axiomatic set theory works, and the BanachTarski paradox is just a true statement which intuitively seems false if you've never been exposed to measure theory. Well, Russell's Paradox was certainly a mathematical paradox at the time it was discovered; that's one reason there is axiomatic set theory! And the BanachTarski Paradox (which is truly wonderful) is only a true statement if you use the axiom of choice. Some mathematicians use this fact as an argument against the axiom of choice!


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Iranon

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Thu Oct 07, 2010 9:18 pm 

Joined: Wed Apr 01, 2009 2:59 pm

bhearn wrote: Iranon wrote: Since Russell's paradox has been thrown out there, I feel like I should add the BanachTarski paradox into the mix, for fans of mathematics here on TP. Of course, neither of these are really paradoxes, Russell's paradox is only a paradox to philosophers who don't really understand how axiomatic set theory works, and the BanachTarski paradox is just a true statement which intuitively seems false if you've never been exposed to measure theory. Well, Russell's Paradox was certainly a mathematical paradox at the time it was discovered; that's one reason there is axiomatic set theory! And the BanachTarski Paradox is only a true statement if you use the axiom of choice. Right, of course. Thank goodness for modern set theory. I guess pretty much both of these are best understood as tidbits of mathematical history than anything else. Nowadays, who doesn't use AC? ZF without choice has some pretty strange models. While we're at it, if people know what models are, how about the Skolem paradox  by the LĂ¶wenheimâ€“Skolem theorem, ZFC has a countable model, which is a countable set that satisfies all the theorems of ZFC, such as, say, "there are uncountably many real numbers"... Also not a paradox, per se, but it's fun to grapple with when you're still getting used to working with models.


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Brandon Enright

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Thu Oct 07, 2010 10:01 pm 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

My favorite paradox is Zeno's "Achilles and the Tortoise" paradox. Text from Wikipedia: In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 meters. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 meters, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 meters. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise.I've never been happy with any of the resolutions that either prevent time from being infinitely divided or don't allow an instantaneous snapshot of time.
_________________ Prior to using my real name I posted under the account named bmenrigh.


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kastellorizo

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Thu Oct 07, 2010 11:18 pm 

Joined: Fri Nov 04, 2005 12:31 am Location: Greece, Australia, Thailand, India, Singapore.

LOL I was hoping someone would mention set theory. For those who are into comics, the " Logicomix" is something I would recommend them to read. It features Russell and his paradox, while it goes through all of the trouble until... (ok, I won't spoil it for you!) Some sort of preview here: http://www.youtube.com/watch?v=XebglmXrgEcTo find it, just search amazon or ebay, there are many translations in different languages! Oh, and by the way, people who think that they are absolutely sure about something are silly. (I am 100% sure about this!) Pantazis
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theVDude

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Thu Oct 07, 2010 11:36 pm 

Joined: Fri Feb 06, 2009 2:57 pm Location: Pittsburgh

bmenrigh wrote: My favorite paradox is Zeno's "Achilles and the Tortoise" paradox. Text from Wikipedia: In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 meters. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 meters, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 meters. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise.I've never been happy with any of the resolutions that either prevent time from being infinitely divided or don't allow an instantaneous snapshot of time. This one is easy, and has always upset me. He's not racing to where the tortoise was, he's racing to the finish line. Just like you can't ever touch something because you have to go half the distance to it, then half that distance, then half that distance. Solution? Go PAST the object you want to touch. All of a sudden half the distance between where you're going and where you are is what you really wanted in the first place.
_________________ 3x3x3 PB: 00:48.10 "Study gravitation, it's a field with a lot of potential."


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kastellorizo

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Thu Oct 07, 2010 11:57 pm 

Joined: Fri Nov 04, 2005 12:31 am Location: Greece, Australia, Thailand, India, Singapore.

Jared wrote: kastellorizo wrote: Oh yes, and did I tell you that I AM A LIAR? Well, since you didn't specify that you are a pathological liar who always lies 100% of the time, there's no paradox. Well, if I am lying 100% all of the time, how come this time, in the sentence above, I am actually telling the truth about me? Jared wrote: Panda, have you got a video of the Ferguson thingie in action? I think I have a video of it somewhere, but I have not publicised it yet. It is not really anything spectacular, and many gifs can show a better demo of the paradox (which was not really a paradox, but it was just a trick to confuse some watchmakers LOL). Pantazis
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Last edited by kastellorizo on Fri Oct 08, 2010 2:05 am, edited 1 time in total.


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bhearn

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Fri Oct 08, 2010 12:32 am 

Joined: Tue Aug 11, 2009 2:44 pm

theVDude wrote: bmenrigh wrote: .... Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise. This one is easy, and has always upset me. He's not racing to where the tortoise was, he's racing to the finish line. Just like you can't ever touch something because you have to go half the distance to it, then half that distance, then half that distance. Solution? Go PAST the object you want to touch. All of a sudden half the distance between where you're going and where you are is what you really wanted in the first place. I think that's sort of punting on the real problem, by saying "if you look at it this way instead, it works fine". True enough, but what's wrong with the original line of reasoning that seems paradoxical? The problem is that the paradox assumes that it will take forever to reach the infinite number of points Achilles must reach to catch the tortoise. But that's simply not true; that series (100 + 10 + 1 + .1 + ...) converges when you sum it (at 111 1/9). You don't have to prevent time from being infinitely divided or disallow an instantaneous snapshot of time. You just need more powerful mathematics than the Greeks had available. They assumed, implicitly, that no infinite sum of finite numbers could be finite. Which turns out to be false.


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GuiltyBystander

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Fri Oct 08, 2010 10:49 am 

Joined: Wed May 13, 2009 4:58 pm Location: Vancouver, Washington

Here's one I enjoy.
A genie offers to sell you a magic lamp at a price you choose. If you buy the lamp, you get 3 wishes for anything (except to break the second rule). After you get your 3 wishes, you must sell the lamp to someone else cheaper than what you bought it for. So if you bought it for $5.00, you would have to sell it for $4.99 or cheaper. If you can't sell it, your soul will be damn and you be tortured for all eternity. The person you sell the lamp to has the same rules apply to them.
Now here's the paradox: Obviously, nobody would ever buy the lamp for 1 cent because there no smaller amount of money you could sell it for, and your soul would be damned. Again, obviously, nobody would buy the lamp for 2 cents because nobody would buy it from them for 1 cent, and your soul would be damned. Again, obviously, nobody would buy the lamp for 3 cents because nobody would buy it from them for 2 cent, and your soul would be damned. etc, etc... By induction, you should never buy the lamp.
But people will almost always chose to buy the lamp because they assume that they can find someone else to buy it.
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katsmom

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Fri Oct 08, 2010 10:56 am 

Joined: Sun Apr 16, 2000 3:17 pm Location: Hong Kong


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KelvinS

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Fri Oct 08, 2010 11:05 am 

Joined: Mon Mar 30, 2009 5:13 pm

@GuiltyBystander: that's an easy one, because there's no time limit to sell it, so you can buy it for 1 cent and keep it until after you die, by which time you don't care about being tortured. katsmom wrote: That's also an easy one: we actually say what we mean.
_________________ If you want something youâ€™ve never had, youâ€™ve got to do something youâ€™ve never done  Thomas Jefferson


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bhearn

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Fri Oct 08, 2010 12:04 pm 

Joined: Tue Aug 11, 2009 2:44 pm

GuiltyBystander wrote: ... By induction, you should never buy the lamp.
But people will almost always chose to buy the lamp because they assume that they can find someone else to buy it. Very nice. Here is a similar example of irrational human behavior, that can be quite entertaining. What you do is, auction off a dollar to the highest bidder. But there's a catch: not only does the highest bidder pay his bid, but the second highest bidder also pays his bid, even though he gets nothing. So, what happens? People will generally start bidding around a nickel. Hey, why not, if you might get a dollar for a nickel? But as the price inches higher, a new dynamic takes over: the secondplace bidder doesn't want to lose his bid. So if he's bid 60 cents and it's at 65 cents, he will likely bid 70 cents (hoping to net 30 cents vs. losing 60). It becomes a game of chicken. If you think it's irrational to bid higher, then you can reason that your bidding opponent will not outbid you, which justifies your bidding higher! But here's where it gets crazy. This same dynamic keeps going, well past a dollar! I know of cases where a dollar has been auctioned this way for over $20. Which means $40 profit for the auctioneer. People have to be pretty stubborn for it to reach this level, but if you have enough people together, you can almost always sell a dollar for more than a dollar.


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KelvinS

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Fri Oct 08, 2010 12:55 pm 

Joined: Mon Mar 30, 2009 5:13 pm

bhearn wrote: ...
But here's where it gets crazy. This same dynamic keeps going, well past a dollar! I know of cases where a dollar has been auctioned this way for over $20. Which means $40 profit for the auctioneer. People have to be pretty stubborn for it to reach this level, but if you have enough people together, you can almost always sell a dollar for more than a dollar. This is a wellknown effect of auctions called "winner's curse".
_________________ If you want something youâ€™ve never had, youâ€™ve got to do something youâ€™ve never done  Thomas Jefferson


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kastellorizo

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Fri Oct 08, 2010 1:09 pm 

Joined: Fri Nov 04, 2005 12:31 am Location: Greece, Australia, Thailand, India, Singapore.

Kelvin Stott wrote: bhearn wrote: ...
But here's where it gets crazy. This same dynamic keeps going, well past a dollar! I know of cases where a dollar has been auctioned this way for over $20. Which means $40 profit for the auctioneer. People have to be pretty stubborn for it to reach this level, but if you have enough people together, you can almost always sell a dollar for more than a dollar. This is a wellknown effect of auctions called "winner's curse". "Pyrrhic victory" also sounds appropriate. Pantazis
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GuiltyBystander

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Fri Oct 08, 2010 1:22 pm 

Joined: Wed May 13, 2009 4:58 pm Location: Vancouver, Washington

bhearn wrote: But here's where it gets crazy. This same dynamic keeps going, well past a dollar! I know of cases where a dollar has been auctioned this way for over $20. Which means $40 profit for the auctioneer. People have to be pretty stubborn for it to reach this level, but if you have enough people together, you can almost always sell a dollar for more than a dollar. Lol. I'd love to see that.
_________________ Real name: Landon Kryger


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Jorbs3210

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Sun Oct 10, 2010 9:58 am 

Joined: Thu Jun 03, 2010 2:25 pm Location: Farmington, NM

Would you believe that this amazing sentence contains ninety two letters, one comma and a single question mark?
This computergenerated pangram contains six A's, one B, three C's, three D's, thirtyseven E's, six F's, three G's, nine H's, twelve I's, one J, one K, two L's, three M's, twentytwo N's, thirteen O's, three P's, one Q, fourteen R's, twentynine S's, twentyfour T's, five U's, six V's, seven W's, four X's, five Y's, and one Z.
_________________ Autism Speaks can go away. I have Autism. I can speak for myself.
"You say tomater, I zader matermorts."  Coach Z


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kastellorizo

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Sun Oct 10, 2010 10:44 am 

Joined: Fri Nov 04, 2005 12:31 am Location: Greece, Australia, Thailand, India, Singapore.

Jorbs3210 wrote: Would you believe that this amazing sentence contains ninety two letters, one comma and a single question mark?
This computergenerated pangram contains six A's, one B, three C's, three D's, thirtyseven E's, six F's, three G's, nine H's, twelve I's, one J, one K, two L's, three M's, twentytwo N's, thirteen O's, three P's, one Q, fourteen R's, twentynine S's, twentyfour T's, five U's, six V's, seven W's, four X's, five Y's, and one Z. LOL nice! Allow me to expand to another form of sentences (palindromes) which involves symmetric letters and photos of a sympathetic animal which usually poses beside the puzzles made by many builders of this forum: WAS IT A CAT I SAW? Pantazis PS. Of course, palindromes may be made in other ways, which involve words instead of letters etc etc etc
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APJ

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Sun Oct 10, 2010 10:49 am 

Joined: Sat Jul 11, 2009 1:09 pm Location: My House

Alex
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kastellorizo

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Sun Oct 10, 2010 11:00 am 

Joined: Fri Nov 04, 2005 12:31 am Location: Greece, Australia, Thailand, India, Singapore.


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Chagi

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Sun Oct 10, 2010 11:06 am 

Joined: Sun Apr 13, 2008 11:48 am

Is the answer to this question "no"?


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RubixFreakGreg

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Sun Oct 10, 2010 11:52 am 

Joined: Sat Jan 16, 2010 11:48 am Location: In Front Of My Teraminx (saying WTF?)


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Jorbs3210

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Sun Oct 10, 2010 6:07 pm 

Joined: Thu Jun 03, 2010 2:25 pm Location: Farmington, NM

kastellorizo wrote: Jorbs3210 wrote: Would you believe that this amazing sentence contains ninety two letters, one comma and a single question mark?
This computergenerated pangram contains six A's, one B, three C's, three D's, thirtyseven E's, six F's, three G's, nine H's, twelve I's, one J, one K, two L's, three M's, twentytwo N's, thirteen O's, three P's, one Q, fourteen R's, twentynine S's, twentyfour T's, five U's, six V's, seven W's, four X's, five Y's, and one Z. LOL nice! Allow me to expand to another form of sentences (palindromes) which involves symmetric letters and photos of a sympathetic animal which usually poses beside the puzzles made by many builders of this forum: WAS IT A CAT I SAW? Pantazis PS. Of course, palindromes may be made in other ways, which involve words instead of letters etc etc etc World's longest palindrome (so far): http://norvig.com/pal17txt.html
_________________ Autism Speaks can go away. I have Autism. I can speak for myself.
"You say tomater, I zader matermorts."  Coach Z


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theVDude

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Mon Oct 11, 2010 10:24 am 

Joined: Fri Feb 06, 2009 2:57 pm Location: Pittsburgh

Jorbs3210 wrote: World's longest palindrome (so far): http://norvig.com/pal17txt.htmlBut... it doesn't make any sense. "Dammit I'm Mad" Dammit Iâ€™m mad. Evil is a deed as I live. God, am I reviled? I rise, my bed on a sun, I melt. To be not one man emanating is sad. I piss. Alas, it is so late. Who stops to help? Man, it is hot. Iâ€™m in it. I tell. I am not a devil. I level â€śMad Dogâ€ť. Ah, say burning is, as a deified gulp, In my halo of a mired rum tin. I erase many men. Oh, to be man, a sin. Is evil in a clam? In a trap? No. It is open. On it I was stuck. Rats peed on hope. Elsewhere dips a web. Be still if I fill its ebb. Ew, a spiderâ€¦ eh? We sleep. Oh no! Deep, stark cuts saw it in one position. Part animal, can I live? Sin is a name. Both, oneâ€¦ my names are in it. Murder? Iâ€™m a fool. A hymn I plug, deified as a sign in ruby ash, A Goddam level I lived at. On mail let it in. Iâ€™m it. Oh, sit in ample hot spots. Oh wet! A loss it is alas (sip). Iâ€™d assign it a name. Name not one bottle minus an ode by me: â€śSir, I deliver. Iâ€™m a dogâ€ť Evil is a deed as I live. Dammit Iâ€™m mad. Demetri Martin wrote this 224 word palindrome poem.
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bhearn

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Mon Oct 11, 2010 2:14 pm 

Joined: Tue Aug 11, 2009 2:44 pm

Jorbs3210 wrote: This computergenerated pangram contains six A's, one B, three C's, three D's, thirtyseven E's, six F's, three G's, nine H's, twelve I's, one J, one K, two L's, three M's, twentytwo N's, thirteen O's, three P's, one Q, fourteen R's, twentynine S's, twentyfour T's, five U's, six V's, seven W's, four X's, five Y's, and one Z. Funny you should bring that up... I'm one of the eight people that independently came up with that sentence, as a result of a challenge in Scientific American in the mid80s. It took quite the computer search, at the time. The challenge was posed by Lee Sallows, who had built a custom computer to do a bruteforce search to construct a similar sentence, stepping through all possibilities. It took months of run time to find a solution. He was so proud of his accomplishment, he declared that it couldn't have been accomplished with just software, and challenged anyone to prove different. Several of us did. Exhaustive search for this kind of problem is just stupid.


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bhearn

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Mon Oct 11, 2010 2:16 pm 

Joined: Tue Aug 11, 2009 2:44 pm

Kelvin Stott wrote: This is a wellknown effect of auctions called "winner's curse". Yes, but the effect is highly magnified when you make the 2ndplace bidder pay too.


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bhearn

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Mon Oct 11, 2010 4:03 pm 

Joined: Tue Aug 11, 2009 2:44 pm

bhearn wrote: Iranon wrote: ... Anyway, the BanachTarski paradox:
Consider the unit sphere in 3 dimensional space. It is possible to divide the sphere up into finitely many pieces (you can get away with only 5 pieces, in fact), and reassemble the pieces ("reassemble" here essentially means what it should mean  only rigid motions, i.e. rotating and sliding) into TWO copies of the unit sphere. ... And the BanachTarski Paradox (which is truly wonderful) is only a true statement if you use the axiom of choice. Some mathematicians use this fact as an argument against the axiom of choice! Today's xkcd is highly relevant:


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gingervergo

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Mon Oct 11, 2010 4:11 pm 

Joined: Fri Mar 06, 2009 9:23 pm


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Monopoly

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Mon Oct 11, 2010 4:14 pm 

Joined: Sun May 17, 2009 1:33 pm Location: USA, North America, Planet Earth, Solar system, Milky Way galaxy, Universe


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kastellorizo

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Tue Oct 12, 2010 3:00 am 

Joined: Fri Nov 04, 2005 12:31 am Location: Greece, Australia, Thailand, India, Singapore.

bhearn wrote: Iranon wrote: Since Russell's paradox has been thrown out there, I feel like I should add the BanachTarski paradox into the mix, for fans of mathematics here on TP. Of course, neither of these are really paradoxes, Russell's paradox is only a paradox to philosophers who don't really understand how axiomatic set theory works, and the BanachTarski paradox is just a true statement which intuitively seems false if you've never been exposed to measure theory. Well, Russell's Paradox was certainly a mathematical paradox at the time it was discovered; that's one reason there is axiomatic set theory! And the BanachTarski Paradox (which is truly wonderful) is only a true statement if you use the axiom of choice. Some mathematicians use this fact as an argument against the axiom of choice! Indeed the BanachTarski Paradox is a very interesting case. But we need to consider something important: density. Yes, density. It may not make sense for infinite sets, but it is the "rate of distribution of points" which changes. Something like thinking that [4 in the power of "infinity 1"], "goes faster" to infinity than [2 in the power of "infinity 1"]. Note that I used the term "infinity 1" to ensure that the powers used are of the same "rate". (i.e. [4 in the power of "infinity 1"] could be equal, lower or higher than [2 in the power of "infinity 2"], depending on the relation between "infinity 1" and "infinity 2") I mean, since we have defined the term "density" for the finite cases, we are required to do the same for the infinite cases. And if we don't, then, as seen, many paradoxes may pop up. That said, the properties of the infinity density *do not* have to be the same with the finite one. The starting point would be defining the simplest of all infinities. This simplest infinity has neither the lowest nor the fastest "rate", but it can be a nice starting point. Finally, for the "density" to make sense, we also need a "point of reference". For example, when we compare two infinities from the same set (e.g. fractals) it *does* matter how deep we have gone. The 11 and onto homomorphism (i.e. isomorphism) seems naked without the notions of "density" and "point of reference". Yes, it works perfectly for finite isomorphisms, but isomorphisms between infinite sets are by definition more complex and demanding, so a more careful approach and a new theory is required. Pantazis PS. I love this talk, I almost drove crazy one of the Professors when I was undergraduate, and when I showed to him some "new" theory, he could not tell me the reason it was right or wrong. LOL
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Jorbs3210

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Tue Oct 12, 2010 6:22 pm 

Joined: Thu Jun 03, 2010 2:25 pm Location: Farmington, NM

Jorbs3210 wrote: How many grains of sand does it take to make a heap of sand? We can safely say two things. 1. A million grains of sand is a heap of sand. 2. We can take one grain of sand out of the pile, and it will still be a heap of sand. So, if we continue to take grains of sand out of the pile, we end up with one grain of sand. Is this a heap of sand? Better yet, if we take away the last grain of sand, is the nothingness remaining still a heap of sand?
_________________ Autism Speaks can go away. I have Autism. I can speak for myself.
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Jared

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Wed Oct 13, 2010 2:39 am 

Joined: Mon Aug 18, 2008 10:16 pm Location: Somewhere Else

Jorbs3210 wrote: 2. We can take one grain of sand out of the pile, and it will still be a heap of sand. Not if a heap of sand is 1,000,000 grains as you defined previously. Then it's 999,999 grains, which is one short of a heap.


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APJ

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Wed Oct 13, 2010 4:23 am 

Joined: Sat Jul 11, 2009 1:09 pm Location: My House

Jared wrote: Jorbs3210 wrote: 2. We can take one grain of sand out of the pile, and it will still be a heap of sand. Not if a heap of sand is 1,000,000 grains as you defined previously. Then it's 999,999 grains, which is one short of a heap. Yeah, this 'paradox' has always irritated me. You can't specify what a heap is and then later choose that you decide by looking. If 1,000,000 is an arbitrary number though, you are deciding that it's a heap just by observation, so every time you remove a grain you should decide whether it's a heap or not. Of course it would be boring, and people would have different interpretations of what a heap is, but nobody would ever reach 1 or 0 as suggested. Alex
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Sjoerd

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Wed Oct 13, 2010 4:53 pm 

Joined: Mon Sep 29, 2008 9:41 am Location: Spijkenisse, the Netherlands

Everything somehow leads to 4 in the end. for example:
92. Ninetytwo has 9 letters nine has 4 letters.
But not only numbers equal 4 in the end, even things Like: Drewseph's Chopasaurus. Those two words are made up of 20 letters Twenty is made up of 6 letters Six is made up of 3 letters. Three is made up of 5 letters. Five is made up of 4 letters and there's 4 again.
Can you come up with a word, thing, or number that does not lead to 4?
_________________
OlivĂ©r Nagy wrote: 43,252,003,274,489,856,000. Or the full number in Hungarian is: NegyvenhĂˇromtrilliĂłkĂ©tszĂˇzĂ¶tvenkĂ©tbilliĂˇrdhĂˇrombilliĂłkĂ©tszĂˇzhetvennĂ©gymiliĂˇrdnĂ©gyszĂˇznyolcvankilencmilliĂłnyolcszĂˇzĂ¶tvenhatezer )


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PuzzleMaster6262

Post subject: Re: Enigmas, Riddles, and Paradoxes... (post yours here!) Posted: Wed Oct 13, 2010 5:01 pm 

Joined: Sun Jun 13, 2010 1:00 am Location: Colorado

Sjoerd wrote: Can you come up with a word, thing, or number that does not lead to 4? 3.1415926535897932384626433... Or what about $, â‚¬, ÂŁ, and ÂĄ? (the symbols, not what they represent ) In my opinion, everything ends with g.
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