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PeteH

Math problem: Zeno's paradox

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I have three bags of marbles:

1 - has 6 black marbles
1 - has 6 white marbles
1 - has 3 black and 3 white marbles

all are labeled incorrectly with the lables (no particular order here) "Black" "White" "Mixed"

1 - What is the mininum number of marbles you pick to be able to move the labels to the correct bag?

2 - From which bag or combination of bags did you pick how many marbles from? in what order?



I have no freakin' clue...I've lost all my marbles.
:D
My reality and yours are quite different.
I think we're all Bozos on this bus.
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8 pirates and a monkey are marooned on an island. The pirates collect coconuts and agree to divide them up in the morning.

During the night a pirate wakes up and thinks his colleagues will steal his share, so he takes and hides 1/8 of the coconutrs, throws a coconut to the monkey, and returns to sleep. Shortly after another pirate wakes up, takes 1/8 of the remaining coconuts and hides them, throws one of the remainder to the monkey, and goes back to sleep.

Then another pirate awakes and does the exact same thing. And then the next, and then the next, etc. until each pirate has done it.

In the morning they share the remaining coconuts equally, and finding a remainder of one, they give it to the monkey.

What is the smallest number of coconuts they could have started with?




I still have no idea what the smallest number of coconuts is [:/] Can someone help :)
Dave

Fallschirmsport Marl

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8 pirates and a monkey are marooned on an island. The pirates collect coconuts and agree to divide them up in the morning.

During the night a pirate wakes up and thinks his colleagues will steal his share, so he takes and hides 1/8 of the coconutrs, throws a coconut to the monkey, and returns to sleep. Shortly after another pirate wakes up, takes 1/8 of the remaining coconuts and hides them, throws one of the remainder to the monkey, and goes back to sleep.

Then another pirate awakes and does the exact same thing. And then the next, and then the next, etc. until each pirate has done it.

In the morning they share the remaining coconuts equally, and finding a remainder of one, they give it to the monkey.

What is the smallest number of coconuts they could have started with?




I still have no idea what the smallest number of coconuts is [:/] Can someone help :)


Diophantine equations are a challenge, aren't they?
...

The only sure way to survive a canopy collision is not to have one.

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ahhh, the master replies. :)



Well, start at the end of the problem. The monkey took the remainder of 1. The smallest number that can be divided by 8 with a remainder of 1 is 9, so assume they had 9 coconuts when they awoke in the morning. Therefore they had 10 before the last pirate gave one to the monkey in the night. But 10 cannot be 7/8 of an integer as required so the assumption was wrong. Next Try 17 left in the morning (divisible by 8 with remainder 1). Is 18 7/8 of an integer? (no). So try 25, 33, 41

41 works! (41+1 = 42, and 42 is 7/8 of 48.

So now you know that 48 is the smallest number that could have been there when the last pirate awoke. He took 48/8 = 6, gave 1 to the monkey, leaving 41 (divisible by 8 with remainder 1).

And work your way all the way to the beginning like this.

A computer helps!
...

The only sure way to survive a canopy collision is not to have one.

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I have three bags of marbles:

1 - has 6 black marbles
1 - has 6 white marbles
1 - has 3 black and 3 white marbles

all are labeled incorrectly with the lables (no particular order here) "Black" "White" "Mixed"

1 - What is the mininum number of marbles you pick to be able to move the labels to the correct bag?

2 - From which bag or combination of bags did you pick how many marbles from? in what order?



I have no freakin' clue...I've lost all my marbles.
:D



I'm thinking this one's more of a language riddle than mathematical, the key being that *all* the bags are mislabeled. We know the bag labeled "mixed" must contain either 6 white or 6 black marbles, otherwise it wouldn't be mislabeled. If we pull one marble from it, we'll know which it is. We then replace the "mixed" label with the correct label ("white" or "black"), and ensure that the labels on the other two bags are moved.

Blues,
Dave
"I AM A PROFESSIONAL EXTREME ATHLETE!"
(drink Mountain Dew)

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this made my brain bleed, and i figure its wrong but I'll give it a shot.

nevermind
:S:|


damn, I know better. You cant have anything other than a whole coconut here.
Goddam dirty hippies piss me off! ~GFD
"What do I get for closing your rig?" ~ me
"Anything you want." ~ female skydiver
Mohoso Rodriguez #865

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took 48/8 = 6, gave 1 to the monkey, leaving 41



you are a physisist ( or something like that):S but not a mathematichen ( or something like that):S.

It just don't work [:/]



Start with 48. Take away 48/8 (=6) leaves 42. Give one to monkey, leaves 41.

41/8 = 5 remainder 1. Give one to monkey. All gone, QED.
...

The only sure way to survive a canopy collision is not to have one.

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I have three bags of marbles:

1 - has 6 black marbles
1 - has 6 white marbles
1 - has 3 black and 3 white marbles

all are labeled incorrectly with the lables (no particular order here) "Black" "White" "Mixed"

1 - What is the mininum number of marbles you pick to be able to move the labels to the correct bag?

2 - From which bag or combination of bags did you pick how many marbles from? in what order?



I have no freakin' clue...I've lost all my marbles.
:D



I'm thinking this one's more of a language riddle than mathematical, the key being that *all* the bags are mislabeled. We know the bag labeled "mixed" must contain either 6 white or 6 black marbles, otherwise it wouldn't be mislabeled. If we pull one marble from it, we'll know which it is. We then replace the "mixed" label with the correct label ("white" or "black"), and ensure that the labels on the other two bags are moved.

Blues,
Dave



Make it more complicated by making the bags initially unlabeled, and asking how many marbles need to be picked in order to label them correctly.
...

The only sure way to survive a canopy collision is not to have one.

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Make it more complicated by making the bags initially unlabeled, and asking how many marbles need to be picked in order to label them correctly.



are the drawn marbles returned to the bag or not?



Look, just forget the marbles, the coconut problem is the real killer. Now how many did the pirates start with?
Dave

Fallschirmsport Marl

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In the morning they share the remaining coconuts equally, and finding a remainder of one, they give it to the monkey.



Ok. Let's works backwards. 9/8 = 1 each plus 1 for the :ph34r:
Then we have 9 * 8 + 1 = 73 (last pirate)
Then we have 73 * 8 + 1 = 585 (7th pirate)
Then we have 585 * 8 + 1 = 4681 (6th pirate)
Then we have 4681 * 8 + 1 = 37449 (5th pirate)
Then we have 37449 * 8 + 1 = 299593 (4th pirate)
Then we have 299593 * 8 + 1 = 2396745 (3rd pirate)
Then we have 2396745 * 8 + 1 = 19173961 (2nd pirate)
Then we have 19173961 * 8 + 1 = 153391689 (1st pirate)
So the smallest number they could have started with is
153391689:)
Dave

Fallschirmsport Marl

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