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.

********SOLUTION*******

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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.

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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)?

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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?

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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?

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*note, I have actually posted number 3 here before, but...I love the puzzle so much I post it again....

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The truth is what money can be made from a lie.

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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?

Post edited at 1:20 pm on Dec. 12, 2006 by tell me again

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1. Best way to mix up marbles is to swap half of each bottle. Probability 1/2.  

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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.

Post edited at 9:14 pm on Dec. 12, 2006 by Apotheosis

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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?

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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

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The truth is what money can be made from a lie.

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old american century: You are not blindfolded during the redistribution.

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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?

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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.

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The truth is what money can be made from a lie.

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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?

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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

Post edited at 5:07 pm on Dec. 14, 2006 by rchaneberg

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Deus ex Machina

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Quote: from steiny at 4:35 am on Dec. 14, 2006

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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?

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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.  

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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

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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?

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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

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Incorrect...try again.

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The truth is what money can be made from a lie.

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You shoot at the Most accurate cyborg, so he has a 33% chance of dying

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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.

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