You're trapped on an island, with no way out.

Out of nowhere, a native appears and gives you two bags, one containing 20 red balls, the other containing 20 blue balls. Thanks to a plot hole, the native speaks English.

The native tells you, "Mix and match the balls as much as you like, but the transfer must remain the same. For example, if you take out five red balls and place them in the bag with blue balls, then they must be replaced with five blue balls, keeping the ratio at 20:20.

After you are finished, you must select one ball from each bag. A blue ball means instant death. If you happen to choose two red balls, you will live and be able to leave the island."

What is the appropriate ratio for each bag? Why?

5/19/2008 12:00:28 AM

10:10

durr

[Edited on May 19, 2008 at 12:01 AM. Reason : ]

5/19/2008 12:01:20 AM

17

5/19/2008 12:01:23 AM

without giving it much thought, I'd say half and half in each bag. seems like it would give you the best probability of pulling out the correct colored ball from each bag.

5/19/2008 12:01:44 AM

Apparently the answer is 11:9.

But I can't find that answer on the internet. That answer comes from the source.

There's another question where it's 50 of each color, but you can put as many as you want in each container. The obvious answer to that is to put one red marble in a jar and put the other 49 in with the blues.

5/19/2008 12:03:38 AM

Why 11:9 instead of 10:10??

5/19/2008 12:04:13 AM

42

5/19/2008 12:04:50 AM

Quote :

"Apparently the answer is 11:9."

No

Quote :

"The obvious answer to that is to put one red marble in a jar and put the other 49 in with the blues."

Would that not make your odds lower than if it were 25:25 in each jar?

[Edited on May 19, 2008 at 12:05 AM. Reason : ]

5/19/2008 12:04:54 AM

all i wanna know is why the native is giving you blue balls?


how long have you been trapped on the island?

5/19/2008 12:05:03 AM

Quote :

"Would that not make your odds lower than if it were 25:25 in each jar?"

There's no ratio stipulation in the second question.

Therefore if you have a red marble in the jar, that's a 100% chance of getting a red ball from container one and a 49/99 chance from the second container.

5/19/2008 12:06:28 AM

49/99 is less than .5

1.49/2 < 1.5/2

[Edited on May 19, 2008 at 12:08 AM. Reason : ]

5/19/2008 12:07:16 AM

i hate riddles. i hate math. and i hate red and blue colored balls.

5/19/2008 12:07:43 AM

but it's more than .25, which would be your total odds by keeping everything 25:25.

.5*.5 = .25

1.00*(49/99) approximately equals .5

5/19/2008 12:08:51 AM

i dont know the answer, but i do agree that blue balls=death

5/19/2008 12:08:59 AM

Quote :

"1.00*(49/99) approximately equals .5"

But it doesn't equal .5, 1.5/2 does.

5/19/2008 12:09:35 AM

i pretty much hate this whole thread except the first post when he says "thanks to a plot hole"

[Edited on May 19, 2008 at 12:09 AM. Reason : .]

5/19/2008 12:09:43 AM

I predict this thread will become another "will the airplane take off?" thread

5/19/2008 12:11:09 AM

^^ haha dnl with the win

5/19/2008 12:12:09 AM

Quote :

"i pretty much hate this whole thread except the first post when he says "thanks to a plot hole""

I figured I would be barraged with ad hominem comments about the native speaking English, rather than people focusing on the solution, which I'm still arguing with my friend is 10:10, but he says it's 11:9 because it was a bank interview question that his friend took and knew the answer only because his friend got it wrong and didn't get a job at a bank.

5/19/2008 12:19:37 AM

Are you trying to say this guy didn't get a job because he got the answer "wrong"

5/19/2008 12:21:05 AM

I mean...it's third party information...on t-dub.

Take it however you want to.

5/19/2008 12:26:32 AM

its not 11:9

then you'd have 11 red balls and 9 blue balls in one bag and 11 blue balls and 9 red ones in the other

you'd have a better chance of getting a red ball in one but a better chance of getting a blue ball in the other this would reduce your odds to 24.75% of getting two red balls 50.5.% chance of getting a red and a blue and 24.75% chance of getting 2 blues

if you did 10:10 you'd have a 25% chance of getting 2 red balls 50% of getting a red and a blue and a 25% of getting 2 blues

5/19/2008 12:27:35 AM

I keep wanting to justify it as a P(A|B) situation...but I can't and my Excel spreadsheet gives me those numbers.

5/19/2008 12:28:41 AM

You don't need an Excel spreadsheet. You need a small bit of common sense and a seventh grade education.

5/19/2008 12:31:52 AM

Burn.

5/19/2008 12:34:09 AM

here are the probabilities of pulling 2 red balls for each value
20 red balls in one bag 0%
19 4.75%
18 9%
17 12.75%
16 16%
15 18.75
14 21%
13 22.75%
12 24%
11 24.75%
10 25%

5/19/2008 12:40:11 AM

look in the bag briefly then tell him there aren't 20 balls in one of them, when he looks at it, swiftly kick him in the balls then grab his head with both hands and smash it into your knee.Then lock his head under your arm and twist it as hard as you can until you hear a cracking noise.

5/19/2008 12:40:16 AM

take enough of the balls out of one bag to get a good swing in and beat the e'erloving christ out of the native

unless they're like nerf balls

but what the hell is he doing with nerf balls?

5/19/2008 12:41:38 AM

or don't worry about it and challenge death to battleship when he comes to get you after the native has killed you off

5/19/2008 12:43:17 AM

i was going to suggest that but i wasn't sure that bag was tough enough material or the balls dense enough to use it as a bludgeon.

5/19/2008 12:43:53 AM

Uh, all red balls in one, all blue balls in the other?

I'd blow the loser if he gave that as a solution but apparently that's not an option.

5/19/2008 12:48:25 AM

Quote :

"After you are finished, you must select one ball from each bag. A blue ball means instant death. If you happen to choose two red balls, you will live and be able to leave the island.""

^ that guarantees death

5/19/2008 12:50:47 AM

you move one ball.

you take a blue to the red, then a red to the blue. When placing the red in the blue bag, place it on top gently to remember the orientation.

Select it first, and then select any but the one blue you put in the red bag.

Also, I would score each ball I moved, just in case (since it wasn't disallowed)

5/19/2008 1:21:11 AM

Quote :

"You're trapped on an island, with no way out. Out of nowhere, a native appears and gives you two bags, one containing 20 red balls, the other containing 20 blue balls. Thanks to a plot hole, the native speaks English."

ftw

5/19/2008 1:28:31 AM

A=1, B=2, C=3...H=8

9/11 = .818181 = HAHAHA

5/19/2008 2:25:57 AM

^^^To your horror, after you were allowed to move the balls, the native shakes the bags and mixes the red ball in with all the blue ones.

5/19/2008 2:53:38 AM

really all the choices here should result in

"You were eaten by a grue."

5/19/2008 2:56:44 AM

At no point in the riddle was it implied that the choice had to be random. It just says "You must select one ball from each bag." If anything, "select" implies a conscious decision to withdraw a specific ball.

I'll assume this was just an error in your retelling of it, but I'm a language guy, not a math guy, and I'm going to stick to my strong suits.

5/19/2008 3:40:51 AM

Quote :

"At no point in the riddle was it implied that the choice had to be random."

At no point in this thread was it implied that at some point in the riddle it was implied that the choice had to be random.

5/19/2008 8:22:23 AM

Quote :

"You're trapped on an island, with no way ou"

the correct answer is to never give up hope of being rescued. tom hanks showed us this.



10:10 is the best. you cant get higher than a .25 shot at life if the pick is random. unless you can switch the balls between the picks, then you can do 19/20 both picks.

5/19/2008 8:28:19 AM

Ernie swoops in and proves why he still works the quikee mart. lol

5/19/2008 8:55:07 AM

i'd move at least one over, and just look in the bags when i picked.

5/19/2008 9:07:17 AM

just don't shake up the bag and draw off the top of the one where you are moving the red balls to and draw from the bottom of the one where you are moving the blue balls to


sorta like what Noen said

5/19/2008 9:13:13 AM

what if this riddle took place on a plane taking off from a treadmill?

5/19/2008 9:33:32 AM

^ that depends if the plane started moving the same time as the treadmill. if the treadmill had achieved full momentum (plane was moving backwards at full speed for treadmill) then it would have had a more difficult time taking off. it would have had negative airspeed and have had to overcome it. at least i think that works like that.

5/19/2008 9:36:53 AM

so what ratio of red and blue balls would you suggest for the given scenario?

5/19/2008 9:58:22 AM

it's slightly different b/c the odds change once you remove a ball.

5/19/2008 10:05:04 AM

^ but you are only picking once from each bag, so successive picks are meaningless.

^^ just club the dude with the bag of balls and throw him out of the plane.

5/19/2008 10:21:39 AM

you want to stack the odds for one of the picks slightly even so

5/19/2008 10:26:29 AM

no you dont, because then you have worse odds for the second pick. 10:10 in both is 0.5*0.5 = 0.25. 12:8 and 8:12 is 0.6*0.4 = .24. and it gets worse the worse the odds for one. 19:20 and 1:20 is .95*.05 = .0475.

5/19/2008 10:29:09 AM