Social Social Thread - Talk About Anything (You Are Allowed to Talk About)!

[dandan]

We've got 12 coins and one of those is heavier than the other 11. We've got a scale, and we want to know what's the heaviest coin only with 3 measurements. How we can do it?

divide it by two and check the two 6 coins stacks.
take the heavier one and divide by 2 and check the two 3 coins stack.
take 2 coins from the heavier 3 coin stack, if one is heavier, it is the heavy coin, otherwise, it is the coin we did not check.

the measurement problem is a really basic problem you learn about in data structures.
for n elements it can be solved in O(logn) (c*logn where c is a constant).

 

[NixxxoN]

Oh, It seems it can be done with 2 differernt ways then. The method i knew is to divide it by 3, then divide it by 2 and in the last measurement you can have only 1 coin in each side.

 

[dandan]

it does not matter how you divide it, you can also divide it by 4, if you see, the solution is in logn, the base is not given, as you can change log bases in a constant time, just divide by 2 is the most common way.

 

[Gammelnorsk]

22887

that was fun

if u want more good math puzzles get

colossal book of short puzzles and problems by martin gardner

 

[dandan]

here is a short probability question for you:
we have a stick 1m long.
we place 2 points, X and Y, on that stick such that X,Y~U[0,1] (means they have equal probability on every point) and their size is not consequential. moreover, there is no dependence between the two, placing one does not affect the placement of the other at all.
placing the two points divides the stick to 3 parts (even if X=Y there is a part between them with length 0).
what is the probability that there there is a part that is greater or equal to the sum of the other two parts.
have fun.

the answer:

Spoiler

3/4, i will give an explanation if someone is interested.

 

[NixxxoN]

I hate those scientific explainations O.o; Can you please translate this into normal english?

 

[Supreme Dirt]

I almost understand, an explanation would be kinda cool.


Also, I need someone to do me a favour. Can someone find for me the percentage at which fully charged charge shot kills from the centre of Dreamland?

 

[JaimeHR]

the stick is divided into 3 parts
case 1: part 1 is larger or equal thant the other two
case 2: part 2 is larger or equal thant the other two
case 3: part 3 is larger or equal thant the other two
case 4: all parts are equal
then chances are 3/4?
super confused
@_@ let's just p2p

 

[ballin4life]

We've got 12 coins and one of those is heavier than the other 11. We've got a scale, and we want to know what's the heaviest coin only with 3 measurements. How we can do it?

Try doing it without knowing whether the odd coin out is too heavy or too light.

here is a short probability question for you:
we have a stick 1m long.
we place 2 points, X and Y, on that stick such that X,Y~U[0,1] (means they have equal probability on every point) and their size is not consequential. moreover, there is no dependence between the two, placing one does not affect the placement of the other at all.
placing the two points divides the stick to 3 parts (even if X=Y there is a part between them with length 0).
what is the probability that there there is a part that is greater or equal to the sum of the other two parts.
have fun.

the answer:

Spoiler

3/4, i will give an explanation if someone is interested.

For simplicity, say X has to be between the 0 and 1/2 meter point (otherwise just flip the stick around). Obviously there is still a uniform distribution.

Now, if point Y is less than 1/2, then we the part that is after either point X or point Y will be greater than the other two (obviously because more than half the stick is going into one part). If the point Y is greater than 1-X, then the part after point X but before point Y will be greater than the other two. Otherwise, if the point Y is in between 1/2 and 1-X, there will be no part that is longer than the other two parts.

So what is the probability that point Y is between 1/2 and 1-X? Since it is a uniform distribution, it's just 1-X-(1/2) = 1/2-X. So given that we know where X is, the probability that there is NOT a part greater than the sum of the other two is 1/2-X.

Then we know that X is uniformly distributed between 0 and 1/2, so it has probability density 2 (since 2 times 1/2 equals 1) so we can integrate the function (1/2-X)2 (the probability function times the density function) from 0 to 1/2 to get an answer of 1/4. Since 1/4 is the probability that there will NOT be a part greater than the sum of the other two, there is a 3/4 chance that there will be a part greater than the sum of the other two.

Is there a simpler way to do it than this?

 

[The Star King]

Try doing it without knowing whether the odd coin out is too heavy or too light.

Yeah, this is what should have been asked. It's still possible, but WAAAY harder. I thought it was impossible for a really long time lol

inb4somebodygooglesitandspoilsitforeveryone

 

[dandan]

anyone came up with an explanation to the answer of my question yet?

 

[NixxxoN]

I lol'ed at this one

 

[Thino]

did someone ever do one with snails climbing on each other and starting to float to the sky?

cuz thats something I use to think back when I was a kid

 

[ballin4life]

anyone came up with an explanation to the answer of my question yet?

Well I did ...

 

[Robsta]

I'm not going to lie.
When I first heard that malva's real first name is Joe and not isai I was disappointed.

 

[TANK64]

if u want more good math puzzles get

colossal book of short puzzles and problems by martin gardner

ooOOo, why thank you

 

[SSB64-Jel]

So who here is going to get a 3DS on March 27th ???

 

[Dsc]

Definetaly me. Mgs3 and ocarina of time in the palm of your hands..in 3d. This my dream..***

 

[HellxBound]

Idk why I just spent 45 minutes working this heavy/light coin puzzle out... it's compelling.

You've got 12 coins total, you chuck 4 on each side and 4 are unweighed.

Two possible outcomes,
outcome a:
one side is heavier/lighter than the other:
then you remove 3 coins from the heavy side, move 3 of the coins from the light side to the heavy side, then move 3 of the unweighed coins on the light side
three things can happen
1) they now balance, which means one of the three removed coins from the heavy side was the heavy coin, so weigh any two of those 3, if one is heavier, it's the heavy coin, if they balance the 3rd one is the heavy coin
2) the heavy side is still heavy, which means that either the coin that stayed on the heavy side is heavy, or the coin that stayed on the light side is light, you pick either one and balance it against one of the other 10 coins and voila
3) the heavy side becomes the light side, which means that one of the 3 coins that went from the light side to the heavy side is the light coin, so take those 3 coins you moved and weigh any two of them, if one is lighter its the light coin, if they balance the unweighed one is the light

outcome b:
the original 4v4 balances, meaning the eight coins are all regular weight:
place 3 of the non-tested coins on one side, three of the identical coins on the other
again 3 things can happen
1) the untested coins are light, so you know one of these is the light coin, take two, weigh them against each other, if one is lighter then it is the light coin, if they are even the unweighed is the light coin
2) the untested coins are heavier, so you know one of these is the heavy coin, take two, weigh them against each other, if one is heavier then it is the heavy coin, if they are even the unweighed is the heavy coin
3) they now balance, which means it's the 12th coin, the only one that's never been on the scales, that's either light/heavy, so test it against any one of the 11 identical coins to determine if it's light/heavy

SHOW ME UR MOVEZ!

 

[NixxxoN]

Definetaly me. Mgs3 and ocarina of time in the palm of your hands..in 3d. This my dream..***

In a very small screen with a bad shaped controller. I'd rather play it on a TV+console but maybe thats just me
Dont get me wrong tho, DS and 3DS is cool

 

[TANK64]

SSF4 all DAI!
plus tons of 64 games in 3d.
plus Smash 64 is inevitable...maybe lol.

 

[Thino]

I like how people are so pumped up and suddenly forget about Nintendo's terribad online

even Kaillera/P2P is better

my wallet is safe

 

[Dsc]

In a very small screen with a bad shaped controller. I'd rather play it on a TV+console but maybe thats just me
Dont get me wrong tho, DS and 3DS is cool

But they're not ports. They're complete remakes with heavily updated graphics so its not like playing the n64/ps2 on a small screen with a weird controller.
I hope they remake majoras mask also.

 

[Peek~]

I lol'ed at this one

Why do I never save those, only got some sports ones

 

[ciaza]

If you want more comics like that just google "Troll Physics Funnyjunk" =).

There's some really good ones that makes you think.

 

[Sempiternity]

My friend has like six Facebook albums full (200 pics each) of the funny pictures he comes across on the webz, and there are tons of troll physics cartoons. Me, being the nerd I am, love disproving them! Some actually require a decent knowledge of physics to explain! There was one with Archimedes and a zeppelin that nobody got, but I reasoned that it's got to do with buoyancy between the two fluids (helium and air). Fun stuff!

 

[malva00]

latest NEWS is

big console Japanese tourney in Osaka or Kyoto on March 19th

That reminds me I should ask if I can put up the other tourney vids now >___>

 

[ciaza]

Darn I'll just miss it. I'm going to Japan in April.

 

[Peek~]

Handegg NFC/AFC Finals today

No smash today

DAT NATIONAL ANTHEM OH GOD

 

[AtotheZ]

So it turns out that in michigan that almost every brawl tournament we get a smash 64 side tourney/friendlies due to people actually playing. I just thought I would share.

 

[NixxxoN]

my fav trollphysics i've seen so far, some of the are hilarious

btw http://trollphysicscomic.com

 

[Peek~]

Handegg NFC/AFC Finals today

No smash today

DAT NATIONAL ANTHEM OH GOD

DAT 4th quarter wow

Bucsbro here, you guys made it to the playoffs over us and you made it to the final game, props

Spoiler

in b4 stop talking to yourself, its slower here on the weekends

 

[sharksquail]

US national anthem for S tier.

@Peek~
At least ur not a Falcons fan like me. Talk about embarrassed.

 

[Gammelnorsk]

helo every i arent the new guy is if around here haha greetingz~! from beLARUSE!

 

[Battlecow]

It doesn't surprise me that you responded this way, seeing as how you're constantly meatriding America on these forums. The thing is, I can never tell if you're being ironic or not.

Irony is for hipsters.

 

[ballin4life]

It's 5AM and I just finished my essay that's due tomorrow. Now I'm all awake and everything

lol @ putting football before school

 

[Sempiternity]

Where the hell do you live that it's 5AM!?

 

[Battlecow]

He's in England.

 

[th3kuzinator]

im going to japan on like march 1-march 13

lol.

 

[Sempiternity]

He's in England.

Ohhhhhhh, right. The Stanford avatar threw me for a loop, and I forgot he had travelled.