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Triangles, bitches
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See post (rounded to the nearest percent)
100%
11%
 11%  [ 1 ]
75%
0%
 0%  [ 0 ]
67%
0%
 0%  [ 0 ]
50%
0%
 0%  [ 0 ]
33%
0%
 0%  [ 0 ]
25%
22%
 22%  [ 2 ]
0%
33%
 33%  [ 3 ]
You didn't put the real answer up, you cheating bastard...
33%
 33%  [ 3 ]
Total Votes : 9

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quack_tape
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PostPosted: Sun Dec 27, 2009 3:25 am    Post subject: Triangles, bitches Reply with quote

Okay, I have a quiz.

You have a rod with length L. You make three cuts [EDIT: 2 cuts] at a distance R from one side where R is a random number between L and 0. What is the probability that you will be able to make a triangle by connecting the tips of the three new rods?

I will be very disappointed in certain members of this forum if they aren't able to get this.
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Last edited by quack_tape on Sat Jan 02, 2010 11:06 pm; edited 1 time in total
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Spock_Logic147
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PostPosted: Sun Dec 27, 2009 3:35 am    Post subject: Reply with quote

If you make 3 cuts then you have 4 new rods...or I misunderstand what you're asking.

Also, when you say make 3 cuts at distance R from one end, does that mean make the first cut R away from the end and then cut again R distance away from the first cut?

Please clarify.
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psy_wombats
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PostPosted: Sun Dec 27, 2009 4:50 am    Post subject: Reply with quote

I came to the same conclusion as SL...
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quack_tape
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PostPosted: Sun Dec 27, 2009 5:09 am    Post subject: Reply with quote

Shit, two cuts.

I'm sick and tired, give me a break. Rolling Eyes

Although you should have been able to give me an answer for both situations...also, given that the title is "Triangles, bitches" and I mention the word "three" about a billion times, I think it'd be easy to guess.


Quote:
Also, when you say make 3 cuts at distance R from one end, does that mean make the first cut R away from the end and then cut again R distance away from the first cut?

No. I don't even understand how you could get that from my prompt.
If I made a cut that was L/2 units away from one end of a bar that was L/3 units long, what would happen? The universe would collapse. That's what would happen.

Bah, now I need to get back to college application essays *grumble, grumble*
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"This is rather as if you imagine a puddle waking up one morning and thinking, 'This is an interesting world I find myself in - an interesting hole I find myself in - fits me rather neatly, doesn't it? In fact it fits me staggeringly well, must have been made to have me in it!'"
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quack_tape
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PostPosted: Sun Dec 27, 2009 5:11 am    Post subject: Reply with quote

Actually, I'm not even sure if it would even make a difference (assuming we lower the limit to the length of the remaining bar) I'll have to figure it out at some time other than midnight.
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Million Dollar Horse

"This is rather as if you imagine a puddle waking up one morning and thinking, 'This is an interesting world I find myself in - an interesting hole I find myself in - fits me rather neatly, doesn't it? In fact it fits me staggeringly well, must have been made to have me in it!'"
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JMickle
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PostPosted: Sun Dec 27, 2009 3:12 pm    Post subject: Reply with quote

i'm pretty sure its a very small chance, from what i can work out.

actually, i'm not even sure you can do anything other than an equilateral triangle :/
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quack_tape
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PostPosted: Sun Dec 27, 2009 3:48 pm    Post subject: Reply with quote

Cut two pieces with lengths of L/3, and one with L/4. Ta da!

Also, who said 100%? I must kill them.
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Million Dollar Horse

"This is rather as if you imagine a puddle waking up one morning and thinking, 'This is an interesting world I find myself in - an interesting hole I find myself in - fits me rather neatly, doesn't it? In fact it fits me staggeringly well, must have been made to have me in it!'"
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Aulos
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PostPosted: Sun Dec 27, 2009 6:02 pm    Post subject: Reply with quote

You simply said triangle. Can't you make always make a triangle with those segments, regardless of their length? Laughing
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quack_tape
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PostPosted: Sun Dec 27, 2009 6:29 pm    Post subject: Reply with quote

I knew someone was going to say that, so that's why I specified it as the tips of the new rods. By the way, you can consider the rods infinitely thin if you're looking for another loophole.
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Million Dollar Horse

"This is rather as if you imagine a puddle waking up one morning and thinking, 'This is an interesting world I find myself in - an interesting hole I find myself in - fits me rather neatly, doesn't it? In fact it fits me staggeringly well, must have been made to have me in it!'"
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Aulos
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PostPosted: Sun Dec 27, 2009 6:50 pm    Post subject: Reply with quote

The wording of that is tricky. You can still take that to mean you are joining the rods, at the tips.
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quack_tape
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PostPosted: Sun Dec 27, 2009 7:22 pm    Post subject: Reply with quote

huh?

How about instead of complaining about the wording you try to figure out the answer?
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Million Dollar Horse

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JMickle
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PostPosted: Sun Dec 27, 2009 7:39 pm    Post subject: Reply with quote

quack_tape wrote:
How about instead of complaining about the wording you try to figure out the answer?

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JMickle
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PostPosted: Sun Dec 27, 2009 7:40 pm    Post subject: Reply with quote

quack_tape wrote:
Cut two pieces with lengths of L/3, and one with L/4. Ta da!

Also, who said 100%? I must kill them.
that would make L = 11/12L

unless you are allowed to scrap part of the rod, in which case one of the percentages you put is the right answer.
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Gregshank
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PostPosted: Sun Dec 27, 2009 8:35 pm    Post subject: Reply with quote

the answer is 25%

the 50% of the time greater than 1/2L doesnt work cause the thing wouldnt be long enough

the 25% of the time under 1/4L doesnt work cause it wouldnt actually fit together ( 2R cant be less than 1/2 L )

everything else, the remaining 25% works, it forms an isosceles triangle
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Gregshank
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PostPosted: Sun Dec 27, 2009 8:36 pm    Post subject: Reply with quote

oh wait i think i misunderstood the problem
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Gregshank
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PostPosted: Sun Dec 27, 2009 8:48 pm    Post subject: Reply with quote

Nevermind, my first logic still works considering

is the same as

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quack_tape
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PostPosted: Sun Dec 27, 2009 10:08 pm    Post subject: Reply with quote

JMickle wrote:
quack_tape wrote:
Cut two pieces with lengths of L/3, and one with L/4. Ta da!

Also, who said 100%? I must kill them.
that would make L = 11/12L

unless you are allowed to scrap part of the rod, in which case one of the percentages you put is the right answer.


Oops. I meant 3/10x2 and 4/10... I always seem to do shit like this...

Greg is right (although his logic is a bit difficult to understand if you don't know the answer) The answer is 25%. I figured that psy would get it first, but Greg was a close second.

It's a bit difficult to explain, but I'll give it a shot:
-After you make the first cut, there's a fifty percent chance that the second cut will be put in the bigger of the two resultant rods. If it isn't, one of the sides will be too long and the triangle won't form.
-The next part is difficult to explain: Assuming that you are putting the second cut in the bigger rod, you will cut that rod into a left and a right piece. You have a 50% chance of cutting one of these two pieces too long.
--Now, that sounds weird. Think about it like this: There is a "sweet spot" in the middle of the big bar that you get after the first cut that you can cut into and still get a triangle. This sweet spot will decrease linearly as the length of said rod increases. When the length of the long bar approaches L, the sweet spot approaches encompassing 0% of the bar. As the length of the bar approaches L/2, the sweet spot approaches encompassing 100% of the bar. 0%+100%/2=50%

50%* 50% = 25%

By the way, I was surprised that no-one tried making a program to test this out...scientifically challenged buffoons...
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Million Dollar Horse

"This is rather as if you imagine a puddle waking up one morning and thinking, 'This is an interesting world I find myself in - an interesting hole I find myself in - fits me rather neatly, doesn't it? In fact it fits me staggeringly well, must have been made to have me in it!'"
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Gregshank
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PostPosted: Sun Dec 27, 2009 11:50 pm    Post subject: Reply with quote

to be completely honest it was kinda easy as soon as i saw it i thought about it for like 5 to 10 min, solved it, then went back to read the other posts
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quack_tape
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PostPosted: Sun Dec 27, 2009 11:58 pm    Post subject: Reply with quote

Good. I won't tell you how long it took me because it would make you sad (hint: less time than it takes to read my explanation).
...of course, I did test my hypothesis, just to make sure.

Follow-up question: what is the probability that we would be able to make a quadrilateral with 3 random cuts? Is there a formula that we could use to determine the chance of us being able to do this with N cuts?
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Million Dollar Horse

"This is rather as if you imagine a puddle waking up one morning and thinking, 'This is an interesting world I find myself in - an interesting hole I find myself in - fits me rather neatly, doesn't it? In fact it fits me staggeringly well, must have been made to have me in it!'"
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Gregshank
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PostPosted: Mon Dec 28, 2009 1:19 am    Post subject: Reply with quote

hypothesis:
% = 1/(2N)

If people care about how i arrived at this i will explain.
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