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On April 10 2011 01:53 funk100 wrote:
I have one
this there is this village beside a mountin where all justice is decided by the accused picking one ball out of a bag with two in - one white one black- they then show the ball to the audience and justice is administerd. if the criminal picks the black ball they are thrown off the cliff (where the trails take place) if they pick the white ball they can walk free.
let us suppose that there is a man who has commited 10 murders but has continually, through chance, always picked the white ball and allways walked free. On the night of his 11th murder the brother of the murdered gets pissed as he wants justice, so he switches the bag so both the balls are black and so, he reasons he can get revenge. the murderer hears of this from the brother as he put his plan as his fb status and the murderer is a mutuall friend of him.
On the day the murderer manages to walk free from the cliff after the village agree he picked a white ball, how?
REMEMBER/rules
1) there are 2 black balls in the bag and they are not changed
2) he does not have a trick ball anywhere - he chooses a ball from the bag
3) the ball he chooses is the one he is represented by
4)where he is
+ Show Spoiler +just to clarify:
the ball he picks and actual show to the audience is also the ball he is represented by?
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for #6 everyone so far is WRONG (or at least, their answer is incomplete).
+ Show Spoiler + So if 100 blue eyed people leave on the 100th night, on the 101th day, all the brown eyed people would've realised that the only reason the 100 blue eyed people would've left is because they themselves (the blue eyed people) had realised that there are ONLY 100 blue eyed people on the island, and therefore had to leave. After this, the brown eyed people would all realise that each of themselves is also brown-eyed and would all leave on the 101st night.
On April 10 2011 01:53 funk100 wrote:I have one + Show Spoiler +
this there is this village beside a mountin where all justice is decided by the accused picking one ball out of a bag with two in - one white one black- they then show the ball to the audience and justice is administerd. if the criminal picks the black ball they are thrown off the cliff (where the trails take place) if they pick the white ball they can walk free.
let us suppose that there is a man who has commited 10 murders but has continually, through chance, always picked the white ball and allways walked free. On the night of his 11th murder the brother of the murdered gets pissed as he wants justice, so he switches the bag so both the balls are black and so, he reasons he can get revenge. the murderer hears of this from the brother as he put his plan as his fb status and the murderer is a mutuall friend of him.
On the day the murderer manages to walk free from the cliff after the village agree he picked a white ball, how?
REMEMBER/rules
1) there are 2 black balls in the bag and they are not changed
2) he does not have a trick ball anywhere - he chooses a ball from the bag
3) the ball he chooses is the one he is represented by
4)where he is
+ Show Spoiler +
He picks a ball, drops it off the cliff 'by accident' and says 'oops'. But to find the colour of the ball he chose, they look for the other ball that is remaining in the bag. A black ball is remaining so they all agree he chose the white ball.
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On April 10 2011 02:00 Tunks wrote:
How about an all time classic, just for those who haven't come across it before. Very simple if you know anything about maths though.
e
You are in the final round of a game show and are shown 3 doors. You will win whatever is behind the door you eventually choose. Behind 1 door is a car, and behind the other 2 are goats. You make your original choice and the presenter opens one of the other 2 doors to reveal a goat. He then gives you the chance to switch to the other remaining closed door, or to open your original choice. Should you switch?
+ Show Spoiler +
Yes. If you switch you have a 66.6% chance of winning the car, and if you don't switch you have a 33.3% chance. In the beginning when you picked the first door, you had a 66.6% chance of pickng a goat, and a 33.3% chance of picking the car. If you picked a goat (66.6%), he opens a goat door, so the other door has the car. If you chose a car first (33.3%), he opens a door with a goat, and the other door has a goat.
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+ Show Spoiler [q.5] +
5. Yes. A circle of radius 1 covers a square of exactly 2, since the width of the square is square root of 2, found using pythagorean theorem. A circle of radius 1/2, covers a square of exactly 1/2, using same calculations.
So 25 * 2 = 100 * 1/2 = 50. Both sets of circles can cover a rectangle of area up to 50.
+ Show Spoiler [q.13] +
13. Isn't that just binary numbers?
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for #1 i did
+ Show Spoiler +fill 5L jug, pour until full into 3L jug, empty 3L jug, pour the rest of the 5L jug into the 3L jug, fill 5L jug again, poor 1L to fill the 3L jug, than you have 4L 
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On April 10 2011 02:03 GQz wrote:for #6 everyone so far is WRONG (or at least, their answer is incomplete). + Show Spoiler + So if 100 blue eyed people leave on the 100th night, on the 101th day, all the brown eyed people would've realised that the only reason the 100 blue eyed people would've left is because they themselves (the blue eyed people) had realised that there are ONLY 100 blue eyed people on the island, and therefore had to leave. After this, the brown eyed people would all realise that each of themselves is also brown-eyed and would all leave on the 101st night.
no, they could have red eyes (or any other eye colour) they don't know there are only brown and blue eyed persons.
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Question:
What is the maximum number of times 10 lines can intersect in the same plane?
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Question 1: + Show Spoiler +1) This was an easy one. Fill up the 3 liter bottle. Pour into the 5 liter bottle. Fill the 3 liter bottle again. Fill the 5 liter bottle, you will have 1 liter left over. Empty the 5 liter bottle. Pour the 1 liter left over into the 5 liter bottle. Fill up the 3 liter bottle. Pour the 3 liters into the 5 liter bottle. Exactly 4 liters.
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On April 10 2011 02:03 GQz wrote:for #6 everyone so far is WRONG (or at least, their answer is incomplete). + Show Spoiler + So if 100 blue eyed people leave on the 100th night, on the 101th day, all the brown eyed people would've realised that the only reason the 100 blue eyed people would've left is because they themselves (the blue eyed people) had realised that there are ONLY 100 blue eyed people on the island, and therefore had to leave. After this, the brown eyed people would all realise that each of themselves is also brown-eyed and would all leave on the 101st night.
On this island there are 100 blue-eyed people, 100 brown-eyed people, and the Guru (she happens to have green eyes). So any given blue-eyed person can see 100 people with brown eyes and 99 people with blue eyes (and one with green), but that does not tell him his own eye color; as far as he knows the totals could be 101 brown and 99 blue. Or 100 brown, 99 blue, and he could have red eyes.
The ONLY thing YOU know is that SOMEONE on the island has blue eyes, nothing else
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On April 10 2011 02:14 ghrur wrote:
Question:
What is the maximum number of times 10 lines can intersect in the same plane?
+ Show Spoiler +
are you asking for the maximum number of intersection points between 10 (distinct) lines on a plane?
is it 1+2+3+4+5+6+7+8+9=45?
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6.+ Show Spoiler +On the first night if someone saw noone else with blue eyes they would know they had the blue eyes and they could leave. But since that doesn't happen everyone knows that noone sees 'no one with blue eyes'; ie. everyone sees at least 1 person with blue eyes. So on the second night someone who saw only one person with blue eyes would know that they also had blue eyes... So on the 100th night everyone who sees 99 people with blue eyes will know that they have blue eyes, so all 100 of them leave that night.
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On April 10 2011 02:03 C:Tahvo wrote:Show nested quote +On April 10 2011 02:00 Tunks wrote:
How about an all time classic, just for those who haven't come across it before. Very simple if you know anything about maths though.
e
You are in the final round of a game show and are shown 3 doors. You will win whatever is behind the door you eventually choose. Behind 1 door is a car, and behind the other 2 are goats. You make your original choice and the presenter opens one of the other 2 doors to reveal a goat. He then gives you the chance to switch to the other remaining closed door, or to open your original choice. Should you switch? + Show Spoiler +
Yes. If you switch you have a 66.6% chance of winning the car, and if you don't switch you have a 33.3% chance. In the beginning when you picked the first door, you had a 66.6% chance of pickng a goat, and a 33.3% chance of picking the car. If you picked a goat (66.6%), he opens a goat door, so the other door has the car. If you chose a car first (33.3%), he opens a door with a goat, and the other door has a goat.
+ Show Spoiler +
To be horribly pedantic, since I'm bored, the question ought to state that the presenter always gives the option to switch doors.
Perhaps he only gives you the option to switch when you've chosen the correct door? In that case you should never switch. Or perhaps he gives the option to switch 2/3 of the time when you choose the correct door, and 1/3 of the time when you choose the incorrect door? In this case you would be indifferent to switching, having a 50% chance of being right whether you switch or not.
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13. Can every natural number (e.g.1,2,3,...) be expressed as a sum of distinct powers of 2 (e.g.1,2,4,8,...)? If so, is that expression unique (ignoring order of the terms in the sum)?
What does distinct mean in this context?
+ Show Spoiler +All natural numbers can be expressed in binary.
But do you mean 5*2^0 = 2*2^1 + 1*2^0 ???
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So no one knows the answer to the xkcd one?
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+ Show Spoiler +
Yup. If you allow negative powers, you can represent any rational number too.
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On April 10 2011 02:39 eluv wrote:+ Show Spoiler +
Yup. If you allow negative powers, you can represent any rational number too.
+ Show Spoiler +
And if you allow infinite non-repeating decimals you can get all the numbers! Just like any other base! lol.
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On April 10 2011 02:39 gyth wrote:Show nested quote +13. Can every natural number (e.g.1,2,3,...) be expressed as a sum of distinct powers of 2 (e.g.1,2,4,8,...)? If so, is that expression unique (ignoring order of the terms in the sum)? What does distinct mean in this context? + Show Spoiler +All natural numbers can be expressed in binary.
But do you mean 5*2^0 = 2*2^1 + 1*2^0 ???
distinct meaning you cannot have 5 = 2+2+1, must do like 5 = 4+1.
and + Show Spoiler +binary is the right idea.
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On April 10 2011 02:35 PJA wrote:Show nested quote +On April 10 2011 02:03 C:Tahvo wrote:On April 10 2011 02:00 Tunks wrote:
How about an all time classic, just for those who haven't come across it before. Very simple if you know anything about maths though.
e
You are in the final round of a game show and are shown 3 doors. You will win whatever is behind the door you eventually choose. Behind 1 door is a car, and behind the other 2 are goats. You make your original choice and the presenter opens one of the other 2 doors to reveal a goat. He then gives you the chance to switch to the other remaining closed door, or to open your original choice. Should you switch? + Show Spoiler +
Yes. If you switch you have a 66.6% chance of winning the car, and if you don't switch you have a 33.3% chance. In the beginning when you picked the first door, you had a 66.6% chance of pickng a goat, and a 33.3% chance of picking the car. If you picked a goat (66.6%), he opens a goat door, so the other door has the car. If you chose a car first (33.3%), he opens a door with a goat, and the other door has a goat.
+ Show Spoiler +
To be horribly pedantic, since I'm bored, the question ought to state that the presenter always gives the option to switch doors.
Perhaps he only gives you the option to switch when you've chosen the correct door? In that case you should never switch. Or perhaps he gives the option to switch 2/3 of the time when you choose the correct door, and 1/3 of the time when you choose the incorrect door? In this case you would be indifferent to switching, having a 50% chance of being right whether you switch or not.
Well, I do suppose I'm assuming he asks you if you want to switch every time.
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On April 10 2011 02:45 susySquark wrote:
5 is either poorly worded or too vague. How big's the rectangle??
I.E. If the rectangle is the size 2 inches by 2 inches, 25 1 inch circles can easily cover it, and 25 1/2 inch circles can also obviously cover it.
The size of this rectangle is unknown, we only know that it can be covered by 25 disks or radius 1. This vagueness adds to the elegance of the solution, i.e. we don't know much about the rectangle, but we can still say something meaningful about it.
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EPT
