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TitaniumAlloy
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posted September 11, 2007 02:02 PM |
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Ridiculous Puzzle
In light of FOG's Astronomical Puzzle which has a tangible answer and actually seems challenging, I thought the time was opportune to present (those who haven't heard it) with this puzzle:
Achilles and the Tortoise
Achilles, the fastest Greek in all of the land, was challenged to a footrace by a measly tortoise (well, measly in speed. he could talk, which is a fair claim. other than that, no redeeming features.)
The tortoise bet Achilles that he would beat him in the race so long as Achilles gave him a small head start.
Achilles, confident that he could easily catch up the small distance, agreed.
"Surely you are an insane, however verbose, tortoise. And soon to be a very poor, insane, verbose, tortoise."
"On the contrary, my good man." Said the tortoise, in perfect diction mind you. (did I mention the tortoise can talk?) "I am 100% sure I will win because unlike you, I've actually thought this through."
Achilles was taken aback.
"Go on then." He says.
"Well, suppose the race is 1km long, and I get a 100m head start. In order for you to overtake me and thereby win, you must first catch up the 100m."
"Easy."
"Maybe, you arrogant prick, but in the time it takes you to do so, I will have run a small bit further, maybe 10m. Hence, to overtake me, you must first catch up that extra 10m."
"Obviously."
"Yes, but in the time it takes you to catch up that 10m, I will have ran a small distance further, say, 1m (fast tortoise, I know), which you will then have to catch up. And so you see, in each moment you must be catching up the distance between us, and yet I – at the same time – will be adding a new distance, however small, for you to catch up again.”
"Oh dear."
"Yeah, you can never catch up. Hand over your money now, you damn hopscotch."
Obviously the race ensued and Achilles blitzed the tortoise hands down.
How is this possible?
We can observe this happening everyday, cars overtaking others, yet no one has found a complete flaw in the logic.
You can google to find an answer but none have yet entirely destroyed the thought experiment, so If you've heard it before or looked up something to ruin it maybe leave it to some people who haven't.
Of course no one will listen to this 
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JoonasTo
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posted September 11, 2007 04:38 PM |
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It's quite easy actually.
Yeah that was a fourth grade math lection problem actually
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Binabik
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posted September 11, 2007 07:53 PM |
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Quote:
In light of FOG's Astronomical Puzzle which has a tangible answer
Don't say "tangible" or William will start talking about electronic music.
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russ
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blah, blah, blah
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posted September 11, 2007 10:25 PM |
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Edited by russ at 22:26, 11 Sep 2007.
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Quote:
Don't say "tangible" or William will start talking about electronic music.
LOL!
Btw, as mentioned, it is at most a grade 4 math problem with the main idea that you should be able to deduct in a junior kindergarden (only that you would't be able to write down the official equation on paper back then). What's so complex about it that would require people to Google it up to ruin it?
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TitaniumAlloy
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posted September 11, 2007 11:54 PM |
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It's not the answer that's hard, it's how you get there for people who haven't seen it.
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william
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LummoxLewis
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posted September 12, 2007 05:14 AM |
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Quote:
Quote:
In light of FOG's Astronomical Puzzle which has a tangible answer
Don't say "tangible" or William will start talking about electronic music.
heh, closest song that is made from that word is "Tangent" by Tangerine Dream, poland concert, 1984 w00t.
sorry....lol....back to the thread
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TitaniumAlloy
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posted September 12, 2007 01:20 PM |
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he was talking about the actual word Tangerine..
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JoonasTo
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What if Elvin was female?
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posted September 14, 2007 08:12 AM |
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I meant that we had it on fourth grade in school.
Anyway they move simultaneously not in turns.
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TitaniumAlloy
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posted September 14, 2007 04:07 PM |
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Quote:
Anyway they move simultaneously not in turns.
Exactly.
It's the addition of infinite positive numbers adding up to a non infinite integer.
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frostwolf
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posted September 15, 2007 06:41 PM |
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Yeah, I remember doing this in the 6th grade. It was used as an example for the lesson about speed.
So yeah, by the time Achilles runs 100m, the turtle has run 110m, by the time Achilles runs 110m, the turtle has run 111m. At this point, Achilles will get ahead of the turtle. If Achilles runs 100m in 6 seconds (that's how much I got on my P.E exam in the 6th grade), this means he will run 1 km in about 1 minute. If the turtle would only be running at 7 seconds/100m, it would still be outrun by Achilles at the 700m line (which they will both reach after 42 seconds). And of course, the turtle would not be running at 100m/7sec.
Well, that was just coz noone bothered to do the math.
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TheDeath
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with serious business
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posted September 15, 2007 07:09 PM |
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Quote:
Exactly.
It's the addition of infinite positive numbers adding up to a non infinite integer.
Actually it's the addition of infinitesimall positive numbers (smaller and smaller). 
The turtle first gets 10m ahead. Then 1. Then 0.1m, then 0.01m.. and so on.
0.1 + 0.01 + 0.001 + 0.0001 + 0.00001 + ..... will never add up to 0.2
That's the time when both of them arrive at the same 'location'. Then obviously the turtle starts losing.
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russ
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posted September 17, 2007 04:11 PM |
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Edited by russ at 16:13, 17 Sep 2007.
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Quote:
If Achilles runs 100m in 6 seconds (that's how much I got on my P.E exam in the 6th grade)
WOW! This was a very good result! I belive that Asafa Powell (who currently holds the 100m running record only ran it in 9.74 seconds), and he was a fully grown man at the time. But you ran it in 6 seconds in grade 6!!! WOW!!! 
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TitaniumAlloy
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posted September 18, 2007 03:09 AM |
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lmao.
That's like this guy in my class trying to claim he got 22 for 50m Butterfly
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