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-- Posted by Blackadder at 10:11 am on Dec. 10, 2006
Ok...These logic puzzles threads clutter up this forum, so I have decided to make a a single thread, WHERE ALL LOGIC PUZZLES ARE PLACED. If you have a LOGIC puzzle, post it here. Instead of making a new thread every time.... also, in attempt not to spoil it for others before you post the solution give everyone a little advanced waning. eg.
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the awnser is 3.
^ that way, we may have less chance of spoiling the fun for others....
Now thats Over, I'll post 3 puzzles: easy, medium, and hard.
 PUZZLE 1: (EASY) you are a prisoner in a foreign land. your fate will be determined by a little game. there are two jars, one with 50 white marbles, and one with 50 black marbles. at this point, you are allowed to redistribute the marbles however you wish (e.g. swap a black marble with a white marble, etc.): the only requirement is that after you are done with the redistribution, every marble must be in one of the two jars. afterwards, both jars will be shaken up, and you will be blindfolded and presented with one of the jars at random. then you pick one marble out of the jar given to you. if the marble you pull out is white, you live; if black, you die. how should you redistribute the marbles to maximize the probability that you live; what is this maximum probability (roughly)? 
PUZZLE 2 (MEDUIM) An acrobat thief enters an ancient temple, and finds the following scenario: 1. The roof of the temple is 100 meters high.
2. In the roof there are two holes, separated by 1 meter.
3. Through each hole passes a single gold rope, each going all the way to the floor.
4. There is nothing else in the room. The thief would like to cut and steal as much of the ropes as he can. However, he knows that if he falls from height that is greater than 10 meters, he will die. The only thing in his possession is a knife. How much length of rope can the acrobat thief get? And how?
PUZZLE 3 (hard) you're a cyborg in a pistol duel with two other cyborgs. you have been programmed to fire pistols with an accuracy of 33%. the other two cyborgs shoot with accuracies of 100% and 50%, respectively. the rules of the duel are one shot per-cyborg per-round. the shooting order is from worst shooter to best shooter. thus, you go first, the 50% guy goes second, and the 100% guy goes third; repeat. if a cyborg dies, we just skip his or her turn, obviously. what should you shoot at in round 1 to maximize your chances of survival over time?
*note, I have actually posted number 3 here before, but...I love the puzzle so much I post it again....
-- Posted by tell me again at 1:18 pm on Dec. 12, 2006
SOLUTIONS TO 1 AND 2
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. . 1. Best way to mix up marbles is to swap half of each bottle. Probability 1/2. 2. Climb to the top of one rope and cut the other one, climb down to 9m and cut as high as possible. Max length 100 + 9 (since at 10m he'll die from the fall) = 109m. Unless the 10m describes the lowest point of his body to the ground, which means that he'll be able to reach up to at least 2 more metres. But why would that be "medium"? Seems too easy. Did i miss something?
-- Posted by old american century at 7:19 pm on Dec. 12, 2006
Quote: from tell me again at 1:18 pm on Dec. 12, 2006
1. Best way to mix up marbles is to swap half of each bottle. Probability 1/2.
If you don't switch any marbles your probability is still 1/2 (you'll either get the all white jar, or all black jar). Plus, since you are blindfolded, you might be placing an already switched marble back into its original jar.
-- Posted by BrAysian at 7:54 pm on Dec. 12, 2006
Solution to 1
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I think my probability is a bit faulty on this, but if you put one white marble in one jar, you get a 50% chance of getting 100%. Leaving you with 50% chance of getting 49%. Then you average everything together or something like that. It just seems like a better chance than 50/50.
-- Posted by Apotheosis at 9:12 pm on Dec. 12, 2006
SOLUTION TO 1 . . . . . Put all marbles except one white one in one jar. The jar with one marble = win (100%), the jar with 50 black marbles and 49 white marbles = maybe win (49.49%), which gives you a combined 74.745% possibility of winning. old american century: You are not blindfolded during the redistribution.
BrAysian: You had the right idea, but math is not your forte.
-- Posted by Blackadder at 12:45 am on Dec. 13, 2006
Quote: from tell me again at 9:18 pm on Dec. 12, 2006
SOLUTIONS TO 1 AND 2
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. . 1. Best way to mix up marbles is to swap half of each bottle. Probability 1/2. 2. Climb to the top of one rope and cut the other one, climb down to 9m and cut as high as possible. Max length 100 + 9 (since at 10m he'll die from the fall) = 109m. Unless the 10m describes the lowest point of his body to the ground, which means that he'll be able to reach up to at least 2 more metres. But why would that be "medium"? Seems too easy. Did i miss something?
The reason the secound one is "meduim" is because there are several possible solutions; all of whiich leave you with 190+ metres... 109 metres is the "lazy man's solution"
On another note, Apothesis has solved problem 1, with the math AND reasoning correct...unlike the other guy :0
-- Posted by old american century at 12:50 am on Dec. 13, 2006
Quote: from Apotheosis at 9:12 pm on Dec. 12, 2006
old american century: You are not blindfolded during the redistribution.
Whoops.
-- Posted by steiny at 8:35 pm on Dec. 13, 2006
There are 10 stacks of coins, each stack has 10 coins in it. One stack is counterfeit. The real stacks weigh 100 grams, thus each coin weighs 10 grams, the counterfeit stack weighs 90 grams, thus each coin weighs 9 grams. You have a scale, that measures weight to the gram, you may only use it once. How do you figure out which stack is counterfeit?
-- Posted by Blackadder at 2:54 am on Dec. 14, 2006
Quote: from steiny at 4:35 am on Dec. 14, 2006
There are 10 stacks of coins, each stack has 10 coins in it. One stack is counterfeit. The real stacks weigh 100 grams, thus each coin weighs 10 grams, the counterfeit stack weighs 90 grams, thus each coin weighs 9 grams. You have a scale, that measures weight to the gram, you may only use it once. How do you figure out which stack is counterfeit?
solution:-
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hmmm...technically this might be cheating seeing as I kinda 'have' used the scales more than once. Put one coin from each stacks 1-5 on the scales [left]
Put one coin from each stacks 1-5 on the scales [right] (Remember which stack belongs to ech stack!) one side should be higher....that side has the fake coin. --- lets say, the left. remove 1 coin from each side - if the scales balence, the fake coin was the 'left' coin you just removed. if they remain unbalenced, repeat the process until the scales balence.
-- Posted by rchaneberg at 3:47 pm on Dec. 14, 2006
PUZZLE 3 (hard) you're a cyborg in a pistol duel with two other cyborgs. you have been programmed to fire pistols with an accuracy of 33%. the other two cyborgs shoot with accuracies of 100% and 50%, respectively. the rules of the duel are one shot per-cyborg per-round. the shooting order is from worst shooter to best shooter. thus, you go first, the 50% guy goes second, and the 100% guy goes third; repeat. if a cyborg dies, we just skip his or her turn, obviously. what should you shoot at in round 1 to maximize your chances of survival over time?
Solution
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first round:
You shoot at the Most accurate cyborg, so he has a 33% chance of dying next cyborg, assuming he's playing by the same rules has two options.
1:the 100% cyborg died - he shoots at you and has a 50% chance of killing you
2:the 100% cyborg lived - he shoots at the 100% cyborg(to maximize his own chances)
At this point the 100%cyborg has a 33% chance of being alive 100% cyborg(assuming he's alive), shoots at the 50% cyborg killing him, then you shoot at him again. Your survival chance would be 78% If the 50% cyborg killed the 100% cyborg, then you shoot him, with a 33% chance of success. And it goes on 50% vs 33% till one of them dies Edited for the space at the top
-- Posted by steiny at 4:03 pm on Dec. 14, 2006
Quote: from Blackadder at 5:54 am on Dec. 14, 2006
Quote: from steiny at 4:35 am on Dec. 14, 2006
There are 10 stacks of coins, each stack has 10 coins in it. One stack is counterfeit. The real stacks weigh 100 grams, thus each coin weighs 10 grams, the counterfeit stack weighs 90 grams, thus each coin weighs 9 grams. You have a scale, that measures weight to the gram, you may only use it once. How do you figure out which stack is counterfeit?
solution:-
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hmmm...technically this might be cheating seeing as I kinda 'have' used the scales more than once. Put one coin from each stacks 1-5 on the scales [left]
Put one coin from each stacks 1-5 on the scales [right] (Remember which stack belongs to ech stack!) one side should be higher....that side has the fake coin. --- lets say, the left. remove 1 coin from each side - if the scales balence, the fake coin was the 'left' coin you just removed. if they remain unbalenced, repeat the process until the scales balence.
unfortunately wrong sorry, its not that kind of a scale, we'll just say an electric scale that shows the exact weight of what you put on it and you can not take away or add coins u choose what you want on the scale and put it on it
-- Posted by Apotheosis at 11:08 pm on Dec. 14, 2006
SOLUTION
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Put ten coins from one stack, nine from another, eight from another, and so on until the last one. It should weight, without any counterfeits, 1000 grams. Thus, the difference in weight will tell you which stack is the counterfeit one--if it's 1g, it's the last one with only one coin in. If it's 2g, it's the one before that, with two coins in, and so on.
-- Posted by Blackadder at 5:44 am on Dec. 15, 2006
Quote: from rchaneberg at 11:47 pm on Dec. 14, 2006
PUZZLE 3 (hard) you're a cyborg in a pistol duel with two other cyborgs. you have been programmed to fire pistols with an accuracy of 33%. the other two cyborgs shoot with accuracies of 100% and 50%, respectively. the rules of the duel are one shot per-cyborg per-round. the shooting order is from worst shooter to best shooter. thus, you go first, the 50% guy goes second, and the 100% guy goes third; repeat. if a cyborg dies, we just skip his or her turn, obviously. what should you shoot at in round 1 to maximize your chances of survival over time?
Solution
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first round:
You shoot at the Most accurate cyborg, so he has a 33% chance of dying next cyborg, assuming he's playing by the same rules has two options.
1:the 100% cyborg died - he shoots at you and has a 50% chance of killing you
2:the 100% cyborg lived - he shoots at the 100% cyborg(to maximize his own chances)
At this point the 100%cyborg has a 33% chance of being alive 100% cyborg(assuming he's alive), shoots at the 50% cyborg killing him, then you shoot at him again. Your survival chance would be 78% If the 50% cyborg killed the 100% cyborg, then you shoot him, with a 33% chance of success. And it goes on 50% vs 33% till one of them dies Edited for the space at the top
Incorrect...try again.
-- Posted by old american century at 8:56 am on Dec. 15, 2006
Quote: from rchaneberg at 3:47 pm on Dec. 14, 2006
You shoot at the Most accurate cyborg, so he has a 33% chance of dying
According to the problem, "he has a 33% chance of getting hit." Since we haven't clarified how many shots each cyborg can take before "dying," I'd just say start firing away and wear a lot of armour.
-- Posted by Chava at 9:48 am on Dec. 15, 2006
number three seemed a little easy to me which means in all probability I have it wrong. You would shoot at the cyborg with the most amount of accuracy thus making you only 50% likely to be hit.
-- Posted by Blackadder at 10:34 am on Dec. 15, 2006
Quote: from Chava at 5:48 pm on Dec. 15, 2006
number three seemed a little easy to me which means in all probability I have it wrong. You would shoot at the cyborg with the most amount of accuracy thus making you only 50% likely to be hit.
wrong
-- Posted by old american century at 11:32 am on Dec. 15, 2006
you shoot at yourself and have a 2/3 chance of surviving. the other cyborgs shoot at each other because you are an idiot. at least one of them will die. then you hope you have better aim at your next shot at one of them.
-- Posted by medjai at 12:27 pm on Dec. 15, 2006
The 100% accuracy cyborg is going to aim at the 50% accuracy cyborg, the 50% accuracy cyborg is going to aim at the 100% accuracy cyborg. You do not shoot during the first round because there is a 33% chance you will lose the game, you pass up your turn. 50% accuracy cyborg shoots at 100% cyborg. From here, he hits or he misses. If he hits, the biggest threat is eliminated. If he misses, he is eliminated by the 100% cyborg. At this point, you shoot at whoever is remaining, this gives you the best possible odds in this situation.
-- Posted by medjai at 1:10 pm on Dec. 15, 2006
For Diego, I found this online so don't google it: Of three men, one man always tells the truth, one always tells lies, and one answers yes or no randomly. Each man knows which man is who. You may ask three yes/no question to determine who is who. If you ask the same question to more than one person you must count it as question used for each person whom you ask. What three questions should you ask?
-- Posted by Apotheosis at 3:05 pm on Dec. 15, 2006
Quote: from medjai at 4:10 pm on Dec. 15, 2006
For Diego, I found this online so don't google it: Of three men, one man always tells the truth, one always tells lies, and one answers yes or no randomly. Each man knows which man is who. You may ask three yes/no question to determine who is who. If you ask the same question to more than one person you must count it as question used for each person whom you ask. What three questions should you ask?
By "yes or no randomly", do you mean truth or lie randomly, or simply "yes" or "no" randomly?
-- Posted by medjai at 1:03 am on Dec. 16, 2006
Yes or no randomly, without respect to truth or falsehood.
-- Posted by Babiilnc at 8:05 am on Dec. 16, 2006
solution to the marbles:
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Feel the one of the white marbles. Place it in the black jar, and by feeling it, you will know where you placed it. Now pick it up and put it in back in the white jar. Repeat this. Now, when it comes to his time to choose which jar, he should just pick from the white jar. I don't know if that would work. I just thought of it.
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