Think you're clever? Yami tests you...

[Yami Silver]

Answer 1: n(n-1)/2. It is simple combination.

That's it.

 

[Yami Silver]

Ok I'll try again. Also, I edited my post and did number 3.

K I think it's n/2 for the first one since it seems it's only one handshake lol

Quite close but a way to disprove you is what happens if n is odd? Therefore it cannot be n/2 because that is not an integer. If you want the solution, I can give it to you.

What did you do for 3?

 

[Yami Silver]

First one is easily n squared.

Third one only prime number 5 can equal to 24. And prime number 17 seems to fit. 289 - 1 = 288 and therefore 288 is basically 12 squared then double it. Not really that hard though .-.

Edit: Also, 19 also fits for number 3. .-.

You haven't really proved it for any prime number, you've only shown it for some. Try and factorise P squared minus 1.

 

[Yami Silver]

Good to hear man!

I knew you'd pick up STEP quickly - and I'm pretty sure you're going to get those 1s/S'

Not doing STEP III because I'm not doing FP2 for A Level but I'm doing STEP I and II. I is going very well, got an S in my first timed one. Haven't timed myself with II yet (it's not on my offer but doing it for bants)

 

[Dissonant Values]

Well Satan resides outside the known universe (or perhaps doesn't even exist) so he would not care about this contract. Satan is also a complete douche. Therefore, in this given case - or any other - it is never beneficial to sell your soul to Satan.

If we assume Satan accepts the standards, then my answer changes significantly. We must first look at what we gain/lose from selling Satan our soul. If Satan has our soul, do you mean he is in control of our lives? Or control us in the afterlife? Or we die? Idk, it's not very clear. If we define a soul as the spiritual or immaterial part of a human being or animal, then we no longer remain in our bodies once Satan has bought our soul. Therefore, it is beneficial at a point where we cannot do anything with our physical body (if it is dying, trapped imprisoned ect). But then what does Satan wish to do with our souls? No clue. Is it better off living in our bodies or being owned as immaterial beings by Satan?

Let's assume Satan is a douche, but not beyond formality or reason. The benefit from selling our soul is that we receive any sort of Earthly power or pleasure in the same strain as Goethe's Faustus. In this scenario our soul is the immaterial portion of our being (essence) and upon dying it is forfeited to Satan. It is then believed we will suffer some sort of torment, though not of the physical type.

 

[Chihaya]

I ain't tryna do no math when on vation from school. But wouldn't the first one be some kinda equation? Like n+1 or something haha idk

 

[Narushima]

Not doing STEP III because I'm not doing FP2 for A Level but I'm doing STEP I and II. I is going very well, got an S in my first timed one. Haven't timed myself with II yet (it's not on my offer but doing it for bants)

Don't worry, the II is the real jump, III isn't that much harder than II, just different material, so if you can master II you're pretty much done with STEP as far the challenge is concerned.

And it's probably not worth spending the time on III anyway, uni maths (introductory analysis and abstract/linear algebra will be the core of 1st year pure) is a lot more fun than STEP. When you're done with exams and school, have a look at some of that on the internet, it'll ward off your boredom much better than more STEP or BMO.

 

[~Ethereal~]

I haven't touched Maths since...2011. Sorry, my brain is dead.

 

[Yami Silver]

I ain't tryna do no math when on vation from school. But wouldn't the first one be some kinda equation? Like n+1 or something haha idk

Ok I'll try again. Also, I edited my post and did number 3.

K I think it's n/2 for the first one since it seems it's only one handshake lol

No haha. You can have another shot but I'll put the solution here:

Spoiler

Person A has n-1 many people to shank hands with.
Person B also has n-1 many people to shake hands with.
However, we're going to take away one from that because we've already counted the handshake AB when we counted person A's handshakes.
So then, as it stands, we have n-1 + n-2. Next we move onto person C.
Using the same logic, we say n-1 minus 2 more because we've already counted AC and BC.
Then we can say that we our solution is n-1 + n-2 + n-3... + 2 + 1 which is the sum for positive integers up to n-1. This simplifies to (n-1)/2

 

[~Ethereal~]

No haha. You can have another shot but I'll put the solution here:

Spoiler

Person A has n-1 many people to shank hands with.
Person B also has n-1 many people to shake hands with.
However, we're going to take away one from that because we've already counted the handshake AB when we counted person A's handshakes.
So then, as it stands, we have n-1 + n-2. Next we move onto person C.
Using the same logic, we say n-1 minus 2 more because we've already counted AC and BC.
Then we can say that we our solution is n-1 + n-2 + n-3... + 2 + 1 which is the sum for positive integers up to n-1. This simplifies to (n-1)/2

I am barely recognising them...oh my brain. :dead:

 

[Yami Silver]

Let's assume Satan is a douche, but not beyond formality or reason. The benefit from selling our soul is that we receive any sort of Earthly power or pleasure in the same strain as Goethe's Faustus. In this scenario our soul is the immaterial portion of our being (essence) and upon dying it is forfeited to Satan. It is then believed we will suffer some sort of torment, though not of the physical type.

Don't know what Goethe's Faustus is but oh wells.
So then, our deal is that by selling giving Satan the power to torture me as much as he wants after I die I can essentially get a wish? Would it not be best to wish for a body that never dies? For then I would be able to not be tortured in the afterlife.
However, your question was "at what point is it beneficial to sell your soul to Satan?". If we can't wish for an eternal physical body, then it is never beneficial (speaking of net welfare) because our torment would be for eternity and the value of it would be unbearable where as our gain would only be temporary.

 

[Yami Silver]

Don't worry, the II is the real jump, III isn't that much harder than II, just different material, so if you can master II you're pretty much done with STEP as far the challenge is concerned.

And it's probably not worth spending the time on III anyway, uni maths (introductory analysis and abstract/linear algebra will be the core of 1st year pure) is a lot more fun than STEP. When you're done with exams and school, have a look at some of that on the internet, it'll ward off your boredom much better than more STEP or BMO.

I was thinking to teach myself FP2 and have a go at some STEP III after my exams. Also, maybe looking at BMO2 and IMO (if I'm feeling brave lol)

 

[Legendary Saiyan]

You haven't really proved it for any prime number, you've only shown it for some. Try and factorise P squared minus 1.

Hmm... except for 2 and 3, we have 5,7,11,13,17,19,23,29,31,37,41, and I think it's endless from there.

 

[Yami Silver]

Hmm... except for 2 and 3, we have 5,7,11,13,17,19,23,29,31,37,41, and I think it's endless from there.

Ok, I'm going to put my solution in this spoiler:

Spoiler

P squared minus 1 can be written as (P+1)(P-1) (this is factorising the difference of two squares)
We then note that P is a prime greater than 3, so that P is not a multiple of 3.
P is not a multiple of 3. Therefore, P+1 or P-1 must be a multiple of 3.
This is because if we take any three consecutive whole numbers, one of them must be a multiple of 3.
Next we must prove that it is a multiple of 8.
The only even prime is 2. P > 3 > 2 Therefore, P is not even.
This means that P+1 and P-1 are both even.
If we take any two consecutive even numbers, one must be a multiple of 2 and the other must be a multiple of 4
Therefore, (P+1)(P-1) is a multiple of 8.
Because 8 and 3 share no common factors, we can therefore say that (P+1)(P-1) = P squared - 1 is a multiple of 24

 

[Dissonant Values]

Don't know what Goethe's Faustus is but oh wells.
So then, our deal is that by selling giving Satan the power to torture me as much as he wants after I die I can essentially get a wish? Would it not be best to wish for a body that never dies? For then I would be able to not be tortured in the afterlife.
However, your question was "at what point is it beneficial to sell your soul to Satan?". If we can't wish for an eternal physical body, then it is never beneficial (speaking of net welfare) because our torment would be for eternity and the value of it would be unbearable where as our gain would only be temporary.

You pretty much got the type of thinking I was trying to encourage. I wanted you to come up with a solution that didn't require deconstructing every aspect of the problem. Think Occams Razor.

Wishing for an eternal body would most assuredly be shot down by Satan but that's the right sort of thinking. The accepted answer to the question is we offer our soul to Satan as a minor because contracts involving minors are non binding unless made with the approval of a guardian. Satan is well versed in various aspects of rhetoric and law, but in his greed fails to remember this.

 

[Legendary Saiyan]

Ok, I'm going to put my solution in this spoiler:

Spoiler

P squared minus 1 can be written as (P+1)(P-1) (this is factorising the difference of two squares)
We then note that P is a prime greater than 3, so that P is not a multiple of 3.
P is not a multiple of 3. Therefore, P+1 or P-1 must be a multiple of 3.
This is because if we take any three consecutive whole numbers, one of them must be a multiple of 3.
Next we must prove that it is a multiple of 8.
The only even prime is 2. P > 3 > 2 Therefore, P is not even.
This means that P+1 and P-1 are both even.
If we take any two consecutive even numbers, one must be a multiple of 2 and the other must be a multiple of 4
Therefore, (P+1)(P-1) is a multiple of 8.
Because 8 and 3 share no common factors, we can therefore say that (P+1)(P-1) = P squared - 1 is a multiple of 24

Oh yeah... FOIL method... that explains why P squared minus 1 can be written like that... lol

 

[Yami Silver]

You pretty much got the type of thinking I was trying to encourage. I wanted you to come up with a solution that didn't require deconstructing every aspect of the problem. Think Occams Razor.

Wishing for an eternal body would most assuredly be shot down by Satan but that's the right sort of thinking. The accepted answer to the question is we offer our soul to Satan as a minor because contracts involving minors are non binding unless made with the approval of a guardian. Satan is well versed in various aspects of rhetoric and law, but in his greed fails to remember this.

That's cool. I've never studied philosophy but that was a nice little question there. Thanks =D

 

[Yami Silver]

Oh yeah... FOIL method... that explains why P squared minus 1 can be written like that... lol

Useful little trick:

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Here, a was P and b was 1.

 

[Legendary Saiyan]

Useful little trick:

You must be registered for see images

Here, a was P and b was 1.

Oh no I do remember how the foil method goes. I was just saying how I completely never thought of it xD

 

[Yami Silver]

Oh no I do remember how the foil method goes. I was just saying how I completely never thought of it xD

Oh, I never knew it was called the FOIL method. I thought it was called the difference of two squares lol