popsjumper 2 #101 August 8, 2005 Quote 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. My reality and yours are quite different. I think we're all Bozos on this bus. Falcon5232, SCS8170, SCSA353, POPS9398, DS239 Quote Share this post Link to post Share on other sites
speedy 0 #102 December 20, 2005 Quote 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 Quote Share this post Link to post Share on other sites
kallend 2,117 #103 December 20, 2005 Quote Quote 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. Quote Share this post Link to post Share on other sites
speedy 0 #104 December 20, 2005 ahhh, the master replies. Dave Fallschirmsport Marl Quote Share this post Link to post Share on other sites
kallend 2,117 #105 December 20, 2005 Quote 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. Quote Share this post Link to post Share on other sites
livendive 8 #106 December 20, 2005 Quote Quote 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. 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) Quote Share this post Link to post Share on other sites
yardhippie 0 #107 December 20, 2005 this made my brain bleed, and i figure its wrong but I'll give it a shot. nevermind 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 Quote Share this post Link to post Share on other sites
wildblue 7 #108 December 20, 2005 Quote What is the volume of the remaining rock in the planet? 0.5236it's like incest - you're substituting convenience for quality Quote Share this post Link to post Share on other sites
speedy 0 #109 December 20, 2005 Quote took 48/8 = 6, gave 1 to the monkey, leaving 41 you are a physisist ( or something like that) but not a mathematichen ( or something like that). It just don't work Dave Fallschirmsport Marl Quote Share this post Link to post Share on other sites
DrewGPM 0 #110 December 20, 2005 Quote Diophantine equations are a challenge, aren't they? I come up with 134,217,721 coconuts...is that correct? I built the equation based on http://mathworld.wolfram.com/MonkeyandCoconutProblem.html Quote Share this post Link to post Share on other sites
kallend 2,117 #111 December 20, 2005 Quote Quote took 48/8 = 6, gave 1 to the monkey, leaving 41 you are a physisist ( or something like that) but not a mathematichen ( or something like that). 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. Quote Share this post Link to post Share on other sites
kallend 2,117 #112 December 22, 2005 Quote Quote Quote 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. 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. Quote Share this post Link to post Share on other sites
jumper03 0 #113 December 22, 2005 Quote 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?Scars remind us that the past is real Quote Share this post Link to post Share on other sites
speedy 0 #114 January 27, 2006 Quote Quote 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 Quote Share this post Link to post Share on other sites
wildblue 7 #115 January 27, 2006 Good necro.... it's like incest - you're substituting convenience for quality Quote Share this post Link to post Share on other sites
speedy 0 #116 January 27, 2006 So what! You still don't know how many coconuts they started with do you? Dave Fallschirmsport Marl Quote Share this post Link to post Share on other sites
wildblue 7 #117 January 27, 2006 Quote So what! You still don't know how many coconuts they started with do you? 134,217,720it's like incest - you're substituting convenience for quality Quote Share this post Link to post Share on other sites
livendive 8 #118 January 27, 2006 Quote 134,217,720 That ends up without a coconut for the monkey at the end. Blues, Dave"I AM A PROFESSIONAL EXTREME ATHLETE!" (drink Mountain Dew) Quote Share this post Link to post Share on other sites
speedy 0 #119 January 27, 2006 Quote Quote So what! You still don't know how many coconuts they started with do you? 134,217,720 Sorry, but 134,217,720 divided by 8 does not leave 1 left over for the . Try again Dave Fallschirmsport Marl Quote Share this post Link to post Share on other sites
happythoughts 0 #120 January 28, 2006 Since they are pirates (thieves and killers by job description), morality is not an issue. Instead of removing coconuts, why not remove pirates? Keep knocking off the other pirates until he has all the coconuts. Problem solved. Quote Share this post Link to post Share on other sites
speedy 0 #121 January 28, 2006 Quote 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 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 Quote Share this post Link to post Share on other sites
speedy 0 #122 January 28, 2006 forget that , it's the wrong answer Dave Fallschirmsport Marl Quote Share this post Link to post Share on other sites