[Maths_Lover]

Gosh! They're expensive! No marimba for me...

[bananarama2]

(Original post by Maths_Lover)
After spending a considerable amount of time getting distracted by YouTube, I have decided that I would really like a marimba.

17th birthday present.

WTH Why?

They are expensive. Most percussion instruments are. A good triangle can set you back £50.

[Emissionspectra]

Anyone got any tips for solving Physics problems in general?

[Maths_Lover]

(Original post by wcp100)
WTH Why?

They are expensive. Most percussion instruments are. A good triangle can set you back £50.

... I want to play one.

I guess...

[bananarama2]

(Original post by Emissionspectra)
Anyone got any tips for solving Physics problems in general?

Jot down what you know...

[chickenonsteroids]

(Original post by Emissionspectra)
Anyone got any tips for solving Physics problems in general?

Write down the information your given. Mix it into a bowl of equations and let it bake for a few minutes. Let it cool down on the paper then write down your final answer.

[Llewellyn]

(Original post by VictorDeLost)
Question for anyone who has read the last book in The Hunger Games trilogy.
What did you think about the ending?

I read some reviews on amazon and some of them are just.....extreme. Was the ending really that rubbish?
One reviewer went as far as saying, "The ending was the most disappointing and sadly has ruined the series for me. I would recommend imagining your own version".

The books get progressively worse. I've never talked to anyone with a different opinion. Having said that, I only discuss literature with ~10 people at most.

[Llewellyn]

(Original post by VictorDeLost)
Yes, the second one in particular is disappointing.
However, despite the books getting progressively, the ending of the third book is at least satisfactory, no?

Whether or not I recommend doing so, I strongly suspect you're going to read the 3rd book. I can't really comment on how the ending will satisfy you. You may have some idea what you think will -or want to- happen, it may be interesting to see how that compares to Collins' ending. I won't give away spoilers though

I don't like the series, at all. The first book was interesting, but I thought the idea (not just the plot but also the characters) had a lot more potential than what they were actually developed into. The series is also poorly written, maybe because it's aimed at a slightly younger audience than it should be, or maybe because plot trumps writing style nowadays. Still, there are worse books. I'd give the series as a whole a 3.5/10 and the first book a 7/10.

[berryripple]

(Original post by Llewellyn)
Sorry, I meant wouldn't* ask that of anyone

Which exam board are you with?

I'm with AQA on specification A; doing Hardy and Victorian literature
you?

[Llewellyn]

(Original post by berryripple)
I'm with AQA on specification A; doing Hardy and Victorian literature
you?

AQA specification B, still with a healthy amount of Thomas Hardy, but we're doing more modern literature alongside coursework focused on tragedy.

I'm still not sure if I like Hardy's poetry. Everyone else seems to hate his "drivel" by this point Good luck with revision and exams though

[ElMoro]

Guys, I'm going to a taster day tomorrow and we're going to have lectures. Do you think it'd be weird if I recorded them with a dictaphone?

[Llewellyn]

(Original post by ElMoro)
Guys, I'm going to a taster day tomorrow and we're going to have lectures. Do you think it'd be weird if I recored them with a dictaphone?

Yes. But I'm sure you could do it discretely.

Alternatively, you could bring a pen and paper and jot down notes.

[Llewellyn]

Here is an interesting logic question. You don't require knowledge of any maths or philosophical techniques to answer this.



You are one of 3 Senior executives in a company. The CEO is going to retire, but before he retires he has to choose a successor. The CEO decides to choose whichever candidate is the smartest, and so decides on a fair intelligence test.

The 3 of you are gathered into a blank room and seated, facing each other. There are 5 hats shown to you; 3 Black and 2 White. You are all blindfolded, and 1 hat is placed on each of your heads, then the remaining hats are removed from the room.

The CEO tells you that the candidate who can correctly deduce the colour of their hat without removing it will be his successor. Any incorrect guesses will lead to that person being fired. The blindfolds are then removed.

You see the other 2 candidates are both wearing black hats. You know they are both smart and want the job, however after some time you realise that they cannot deduce the colour of their hat, or are unwilling to guess.

What is the colour of your hat? Why?

[bananarama2]

(Original post by Llewellyn)
Here is an interesting logic question. You don't require knowledge of any maths or philosophical techniques to answer this.



You are one of 3 Senior executives in a company. The CEO is going to retire, but before he retires he has to choose a successor. The CEO decides to choose whichever candidate is the smartest, and so decides on a fair intelligence test.

The 3 of you are gathered into a blank room and seated, facing each other. There are 5 hats shown to you; 3 Black and 2 White. You are all blindfolded, and 1 hat is placed on each of your heads, then the remaining hats are removed from the room.

The CEO tells you that the candidate who can correctly deduce the colour of their hat without removing it will be his successor. Any incorrect guesses will lead to that person being fired. The blindfolds are then removed.

You see the other 2 candidates are both wearing black hats. You know they are both smart and want the job, however after some time you realise that they cannot deduce the colour of their hat, or are unwilling to guess.

What is the colour of your hat? Why?

Spoiler:

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Black. Let them be 1, 2 and 3.

1=black
2=black
3=?

Suppose 3 has a white hat.

2 Wouldn't know if his hat is black or white. This uncertainty implies to 1 that his must black because he can see 3 and is his was white, 2 would know.

Hence contradiction so the answer must be black.....I think

[Llewellyn]

(Original post by wcp100)

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Black. Let them be 1, 2 and 3.

1=black
2=black
3=?

Suppose 3 has a white hat.

2 Wouldn't know if his hat is black or white. This uncertainty implies to 1 that his must black because he can see 3 and is his was white, 2 would know.

Hence contradiction so the answer must be black.....I think

Your reasoning is not complete.

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Yes, in the hypothetical situation 3 has a white hat, both 1 and 2 could not deduce their colour on that information alone, because both 1 and 2 could be either black or white. (If 1 and 2 see one black, one white, that still leaves two black, one white left)

But in the hypothetical situation where 3 has a black hat, both 1 and 2 could not deduce their colour on that information alone, because both 1 and 2 could be either black or white. (1 and 3 see two black. But that still leaves one black, two white left).

You could conclude that 3 has either a black or white on contradiction alone. Thus, that is not enough.

(Original post by wcp100)

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Could you just say black. Then none of them would be certain?

No, there is only one solution, and you should be completely certain of it.

Sometimes it helps to come back to these types of problems after a break.

[bananarama2]

(Original post by Llewellyn)
Your reasoning is not complete.

Spoiler:

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Yes, in the hypothetical situation 3 has a white hat, both 1 and 2 could not deduce their colour on that information alone, because both 1 and 2 could be either black or white. (If 1 and 2 see one black, one white, that still leaves two black, one white left)

But in the hypothetical situation where 3 has a black hat, both 1 and 2 could not deduce their colour on that information alone, because both 1 and 2 could be either black or white. (1 and 3 see two black. But that still leaves one black, two white left).

You could conclude that 3 has either a black or white on contradiction alone. Thus, that is not enough.

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Could you just say black. Then none of them would be certain?

[bananarama2]

(Original post by Llewellyn)
Your reasoning is not complete.

Spoiler:

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Yes, in the hypothetical situation 3 has a white hat, both 1 and 2 could not deduce their colour on that information alone, because both 1 and 2 could be either black or white. (If 1 and 2 see one black, one white, that still leaves two black, one white left)

But in the hypothetical situation where 3 has a black hat, both 1 and 2 could not deduce their colour on that information alone, because both 1 and 2 could be either black or white. (1 and 3 see two black. But that still leaves one black, two white left).

You could conclude that 3 has either a black or white on contradiction alone. Thus, that is not enough.

No, there is only one solution, and you should be completely certain of it.

Sometimes it helps to come back to these types of problems after a break.

I was proposing there was than one solution.

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I meant black is the only case where the other two of them aren't certain and so is the only solution.

[chickenonsteroids]

(Original post by Llewellyn)
Here is an interesting logic question. You don't require knowledge of any maths or philosophical techniques to answer this.

fair intelligence test.

There are 5 hats shown to you; 3 Black and 2 White.

The CEO tells you that the candidate who can correctly deduce the colour of their hat without removing it will be his successor. Any incorrect guesses will lead to that person being fired. The blindfolds are then removed.

You see the other 2 candidates are both wearing black hats. You know they are both smart and want the job, however after some time you realise that they cannot deduce the colour of their hat, or are unwilling to guess.

What is the colour of your hat? Why?

Spoiler:

Show

This really annoyed me for a little bit. But that's why it's fun

Since it's fair... it can't be unfair right?

The answer is that you're wearing a black hat. If he gave you a white hat then the others would see one white hat and one black hat. So that would mean 1 = white, 1 = black 1 = ?. But it'd be too easy for one if the people to see they're wearing a black hat if there were 2 black hats and 1 white hat. So that'd be unfair for you (the subject of the problem)

So that way for it to be fair all of you would need to be wearing a black hat.

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I want more ... even though that'll be the only one I can figure out

[Llewellyn]

(Original post by chickenonsteroids)

Spoiler:

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This really annoyed me for a little bit. But that's why it's fun

Since it's fair... it can't be unfair right?

The answer is that you're wearing a black hat. If he gave you a white hat then the others would see one white hat and one black hat. So that would mean 1 = white, 1 = black 1 = ?. But it'd be too easy for one if the people to see they're wearing a black hat if there were 2 black hats and 1 white hat. So that'd be unfair for you (the subject of the problem)

So that way for it to be fair all of you would need to be wearing a black hat.

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I want more ... even though that'll be the only one I can figure out

That is one correct conclusion. It is surprising how many people will miss that though. Well done.

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Interestingly, using that reasoning, you can immediately determine that you are wearing white. In fact, you can do it before the blindfold is removed.

This was my reasoning:

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Consider a situation, R where there are one black and two white hats. In this case, the person with a black hat on would immediately deduce that he was wearing black. We can therefore immediately discount this case.

Consider a situation where there are two black hats and one white hat. If a candidate saw one white and one black, he would know after a moment's consideration that he was wearing black. He knows this because R is not true, as another candidate has not yet given out an answer.

Therefore if a candidate sees a white hat they will almost immediately be able to deduce that they themselves are wearing black.

Now consider a situation where all three hats are black. Based on the information provided, no candidate can infer the colour of their hat. However, given that another candidate does not come to the "black because I see 1 or 2 white" conclusion, then it becomes obvious that all 3 candidates are wearing black.

The problem with this problem is:

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We assume that the other candidates are smart, but we also assume that they are not smart enough to realise that the only fair test is 3 black. We also assume that they will not have come to my conclusion after a fair amount of time.

(Original post by wcp100)
I was proposing there was than one solution.

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I meant black is the only case where the other two of them aren't certain and so is the only solution.

You have come to the right answer, and one of the methods is through certainty. I think I'm not interpreting your reasoning correctly though.

[Llewellyn]

This is another good question.


There are 32 coins randomly arranged on a table. 16 are Heads, 16 are Tails. You are sitting down at the table with a blindfold and gloves on. You can move the coins and you can invert them (so a tail becomes a head and vice versa). You have no way of telling which coins are heads and which are tails. You must create two groups of coins under these conditions. There must be the same number of heads in each group. How will you do this?

Hint:

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Consider a simplified version. Say you have 2 coins on a table, 1 head, 1 tail. How would you make sure you get two groups with an equal amount of heads?

And for 4 coins, 2 heads, 2 tails?

And for 32 coins?