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 Post subject: Re: Logic Puzzles
PostPosted: Fri Aug 02, 2013 7:23 pm 
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I'm more concerned with the "why" aspect of the question.


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 Post subject: Re: Logic Puzzles
PostPosted: Fri Aug 02, 2013 7:40 pm 
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The males are the runts of the pack but the breeder does not wish to put them down.

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 Post subject: Re: Logic Puzzles
PostPosted: Sat Aug 03, 2013 12:46 am 
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50% is what it should be, but due to random selection of the gamete process it's not accurate, the other reason could well be that they are the smallest and youngest, unable to get enough milk, hence why the breeder will wish to put them up for adoption.

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 Post subject: Re: Logic Puzzles
PostPosted: Sat Aug 03, 2013 6:41 am 
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Spoiler:
At first glance, it might appear that the chance is 50%, but drawing a chart of possible combinations allows us to come to the conclusion that the probability of the second puppy being male when we know at least one is male is 33%.

The normal possibilities for a set of two puppies are:
M/M
M/F
F/M
F/F

Since we know one of the puppies is male, we can strike out F/F. That leaves us with three combinations.

That's the mathematical solution based on the probability theory - which is why we get 33%.

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 Post subject: Re: Logic Puzzles
PostPosted: Sat Aug 03, 2013 7:27 am 
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Correct, Norroen! Your turn :)


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 Post subject: Re: Logic Puzzles
PostPosted: Sat Aug 03, 2013 8:03 am 
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A quickie:
A 15-storey house has an elevator. There are 4 people living on the first storey, and on which subsequent storey the number of tenants increases twofold. Which of the elevator's buttons is the one pressed most frequently?

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 Post subject: Re: Logic Puzzles
PostPosted: Sat Aug 03, 2013 9:13 am 
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The first storey? People need to come down.


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 Post subject: Re: Logic Puzzles
PostPosted: Sat Aug 03, 2013 10:09 am 
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Spoiler:
Yes, 1 is indeed the most pressed button, irrespective of how the tenants are distributed among the storeys.

Your turn, Sinister! :)

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 Post subject: Re: Logic Puzzles
PostPosted: Sat Aug 03, 2013 9:05 pm 
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I don't know any logic puzzles. :( So my turns up for grabs.


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 Post subject: Re: Logic Puzzles
PostPosted: Sat Aug 03, 2013 10:08 pm 
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I'll take it then :). Let's do another "hats" puzzle.

Six children chose to participate in a puzzle in which the first child to solve it correctly would get an ice cream. The other children would get nothing. The children were told that they were to be given either a black or white hat to wear. They would be unable to see the colour of their own hat, but could see the colour of the hats of the other children. To solve the puzzle correctly, a child must guess the colour of their own hat. They were told that there was at least one black hat and one white hat, but were not given any other information. Three of the children were given black hats, and the remaining three were given white hats. Being very intelligent children, they all spent some time considering the puzzle before simply guessing. Are any of the children able to solve the puzzle, and if so, how?

Edit: Originally the children were just told that there was at least one black hat. I have changed it so that they have now been told that there is at least one black hat and at least one white hat. The answer to the puzzle is still essentially the same.


Last edited by Moeboid on Sun Aug 04, 2013 6:13 pm, edited 2 times in total.

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 Post subject: Re: Logic Puzzles
PostPosted: Sun Aug 04, 2013 4:26 am 
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Spoiler:
Cheap shot, but they where given the hats instead of having them put on their heads, and already know the colors


Spoiler:
A more through shot.

There are six children each unaware of the 50/50 chance they have of having one or the other color. So we may correctly assume that one in a white hat will see two others in white hats and three in black. One in a black hat will see three in white and two in black. Assuming that they are not allowed to commune with each other it would seem impossible to make a decision based on deduction. Something tells me there is one of those painfully obvious answers in there. Maybe in one of the little details of the question.

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 Post subject: Re: Logic Puzzles
PostPosted: Sun Aug 04, 2013 1:06 pm 
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A long shot:

Spoiler:
The children were intelligent enough not to guess straight away. This means they were silent for quite some time. The smartest child would realize that this silence stems from an inability to answer. Why are they unable? Let's assume that the child is wearing a black hat. It sees 3 white hats and 2 black hats. The fact that no one else is answering, means that all the other children are seeing the same as it: 3 hats of one color, and 2 of the other. Had it been different, one of the children would have been able to make a deduction. Sadly, I can't make any of the other deductions myself, so I can't prove this answer. It's probably wrong anyway.


Another shot:

Spoiler:
The child that waited until all the others had guessed can figure out the solution based on the guesses of the other children. Through careful consideration, it can deduct what each of the other children were seeing.

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 Post subject: Re: Logic Puzzles
PostPosted: Sun Aug 04, 2013 4:59 pm 
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Spoiler:
I am rather wondering why the children 'were told that there was at least one black hat' , since they can see one another perfectly well anyway. Image.
It could be the requirement necessary for all possible combinations, to eliminate the all-white hat combination.

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 Post subject: Re: Logic Puzzles
PostPosted: Sun Aug 04, 2013 6:07 pm 
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That's a nice starting point, Mars :p

Edit: I have changed the puzzle so that now the children are aware that there is and at least one white hat as well as at least one black hat. With this addition, the answer to the puzzle is essentially the same.


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 Post subject: Re: Logic Puzzles
PostPosted: Sun Aug 04, 2013 7:56 pm 
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Spoiler:
Let's assume a child is wearing a black hat. S/he knows that the maximal possible number of both black and white hats is 5 (because the puzzle states that at least one of the hats is white and at least one of the hats is black). The child sees 3 white hats and 2 black hats. Thus, the child sees 3 white hats out of the possible 5 and 2 black hats out of the possible 5. S/he deduces that the probability of his/her hat being black is higher and risks saying that his/her hat is black. Which turns out to be right, allowing the other children to guess the colour of their own hats as well.

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 Post subject: Re: Logic Puzzles
PostPosted: Sun Aug 04, 2013 8:03 pm 
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Incorrect. Only the first child to guess gets an ice cream.


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 Post subject: Re: Logic Puzzles
PostPosted: Sun Aug 04, 2013 8:07 pm 
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So they have to shout in chorus to get their share?Image

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 Post subject: Re: Logic Puzzles
PostPosted: Sun Aug 04, 2013 8:13 pm 
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... I don't know what would happen if they shouted in chorus... ... ... *brain explodes*


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 Post subject: Re: Logic Puzzles
PostPosted: Sun Aug 04, 2013 8:29 pm 
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Spoiler:
I'm going to guess(and be wrong) that none of the children can solve the puzzle on their own, and thus none of them gets an ice cream. Moot point anyway, I ate it long before this started. :P

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 Post subject: Re: Logic Puzzles
PostPosted: Sun Aug 04, 2013 8:31 pm 
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Incorrect.


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 Post subject: Re: Logic Puzzles
PostPosted: Sun Aug 04, 2013 8:35 pm 
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Spoiler:
So each child, by virtue of seeing the other children, renders useless the fact they were told there was at least one of each hat, as they can clearly see that. Are they allowed to take off their hat to look at it, then? :lol:

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 Post subject: Re: Logic Puzzles
PostPosted: Sun Aug 04, 2013 8:41 pm 
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No lol; they are not allowed to take their hat off and look at it :p.

I should point out that without any information on how many hats of each colour there were, they puzzle would not be solvable. Even if one child could see five white hats, without knowing whether there was at least one black hat, they couldn't reasonably deduce that their own hat was black; they could only guess.


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 Post subject: Re: Logic Puzzles
PostPosted: Mon Aug 05, 2013 12:57 am 
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Something tells me the two details, ice cream and one black and white hat, are very important points.

Spoiler:
One of the children says 'blow this,' takes the ice cream and leaves.


Spoiler:
srsly. The children are not allowed to take off the hats so one looks in a mirror to find out.


Spoiler:
No information was given on the ones who distributed the hats. One of the children distributed them and knows his color.


We can come to the conclusion that is impossible to answer the hat from deduction and there is some other kind if reasoning to figure it out.

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 Post subject: Re: Logic Puzzles
PostPosted: Mon Aug 05, 2013 5:20 am 
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Moeboid wrote:

I should point out that without any information on how many hats of each colour there were, they puzzle would not be solvable. Even if one child could see five white hats, without knowing whether there was at least one black hat, they couldn't reasonably deduce that their own hat was black; they could only guess.


That's what I was talking about earlier. Either it's a common condition for all possible hat combinations, or that's where the trick lies.Image

Since the stake here is one ice-cream, teamwork is out of the question. Every child is out for him/herself to get the preciousss.Image

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 Post subject: Re: Logic Puzzles
PostPosted: Mon Aug 05, 2013 6:13 am 
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Even if the children aren't told there is at least one black and one white hat, since they are given three of each they would know there's at least one of each. Right? I mean there's nothing separating them or keeping them from just forming a circle and looking at all the other hats.

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