Puzzle for the Day

[complicatedliar]

The sum of five real numbers is 7; the sum of their squares is 10. Find the minimum and maximum possible values of any one of the numbers.

If you a require a hint, ask and you shall receive.

First to the solution shall be monarch for the day! :-)





[OOC: If your character is particularly good at maths but the player isn't, drop me a line and I can see about coming up with a googling hint.]

Comments

[see_my_back]

Monarch of what?

[several hastily written scribbles have been crossed out. Only bits of the equations are visible.]

a + b + c + d + e = 7
a2 + b2 + c2 + d2 + e2 = 10
a + b + c + d = 7 − e
a2 + b2 + c2 + d2 = 10 − e2
If x = (1, 1, 1, 1) and y = (a, b, c, d) then-

This is assuming math isn't too different between your world and mine, right?

[complicatedliar]

Monarch of Maths, of the Institute, whatever you'd like since it's really just a point of pride.

Mathematics has always been presumed as a universal language. I suppose we'll test that out here.

[see_my_back]

I see.

I guess we'll test that theory. 1 and 1.8?

[complicatedliar]

Excellently done! Today, the prize is yours.

[see_my_back]

Monarch of this institution? Though lately it sounds like I'll have to defend my title if people keep claiming territories. I'm not sure I'm up for that responsibility. Thank you for the information though, it's good to know that some things translate no matter what world it is.

[complicatedliar]

There does seem to be a bit of that going around, yes. So far everyone but we happy few seem to be leaving maths alone, at least.

And I'm always happy to talk maths.

[see_my_back]

I'm happy just to be top of the class for a day. I was worried I'd gotten rusty without my usual studies.

Good to know! I'm Sakura, by the way. Haruno Sakura.

[complicatedliar]

I've heard others express similar concerns. Hopefully we can all work together to stay sharp.

A pleasure to meet you, so to speak. I am Lingormr.

[see_my_back]

I'm all for that. I've been thinking of putting a daily study group together actually, but I was worried there wouldn't be enough interest. Maybe it's worth a try though.

You too. I haven't seen your name around the bulletin before. Are you new?

[complicatedliar]

I think it certainly is. The worst that could happen is no one shows up, but I doubt that would be the case. The young man I spoke with yesterday, Peter, also mentioned studies, so perhaps he would be interested as well.

I arrived yesterday.

[see_my_back]

You know Peter too? Teen, kind of lanky, messy brown hair? He'd be a really good person to have on board, we've spoken before a few times at least.

Oh wow, really new then. It's a few weeks for me, but let me know if you have any questions. Being a new person here can be really intimidating for a lot of people.

[complicatedliar]

Peter was actually the first person I met upon my arrival. Well, the first person that counts at least, if you take my meaning. He seems very nice.

I appreciate the offer. So far I feel as if I lack information so badly that I'm just absorbing everything and not yet prepared to ask intelligent questions.

[see_my_back]

I think I'm starting to. Maybe I'll try to set something up then- or at least see who might be interested. Couldn't hurt at least.

If you get to the point of needing questions answered, just drop me a note. Or you can see me in person if you like. I'm about average height, 15 years old, shoulder length pink hair, green eyes, easy to find. I have a copy of an old primer someone posted on the bulletin once and it's reasonably helpful. Just make sure to be careful, things can get pretty dangerous around here if you're unprepared.

[complicatedliar]

Perhaps we shall meet some time, then. I'm quite tall, have black hair and green eyes, and I look, oh, about twice your age. :) Do say hello.

A primer. Interesting. I've been warned several times about things being dangerous, so I am being cautious. I'm not the sort to seek out fights anyway.

[see_my_back]

Noted! Thank you, I'm sure I will. :)

That's a good plan to have. Do you know how to fight? There are also some people here willing to teach self-defense, if you need some tips.

[complicatedliar]

Not really, no. I'm a bit of a useless mess at that sort of thing, if I'm to be honest. I'd much rather avoid fighting entirely, or run away, as awful as that no doubt sounds. I made a much better scholar than I did a Viking.

[see_my_back]

Not awful no. It depends on what you're fighting for. There's no need to rush in and get yourself hurt for no reason if running away is a better option. What's a Viking? A sort of fighter from your world? I definitely know how it feels to have to balance study and physical combat skills. One always seems to suffer.

[complicatedliar]

Vikings are warriors and raiders. It's a profession of sorts, I suppose. Travel to far-off places, fight with people you don't like, and take all their things. In my experience that's the reason most people fight. Or for fun. I'm not really interested in either.

There simply aren't enough hours in the day, what with needing to sleep and all.

[see_my_back]

I can see why you might not enjoy that. But I think there's a lot of other reasons to fight. Here for instance, we aren't fighting to take anything but our own freedom back. Or to get back home.

Either way, take care. I've seen too many people disappear or end up on the wrong end of a fight in this place. I'd hate to miss out on more math problems in the future.

[complicatedliar]

This is very true. One must always be prepared to defend one's self, or friends. Loved ones as well, should you have any. I can understand how some might wish to return home. I am not among that number.

I shall do my best to be careful. :)

[Bottom portion folded]

[vulpinisms]

You've certainly found a way to pass the time here. Does 'monarch of the day' basically just include bragging rights?

Clarification question. You're asking for the minimum and maximum possible values, but they need not be in the same set of numbers that would satisfy the conditions?

Re: [Bottom portion folded]

[complicatedliar]

Yes. You get the warm glow of satisfaction that goes with knowing you're very good at maths and have beaten everyone else to the solution. :)

I'm not certain what you're asking. In order for the solution to fit, they must be in the set of real numbers. Since the variables are basically interchangeable place holders, effectively I'm just asking for the minimum and maximum value for all of the possible numbers that make up the solution.

[Folded]

[vulpinisms]

Ah, I see. You've answered my question, though now that I think about it, it wouldn't have made any sense. It's been a while since I've done problems like this.

I'll hazard a guess then. 1 and 1.8?

Re: [Folded]

[complicatedliar]

Quite the accurate guess, my friend. Write it publicly and claim your prize.

I shall try to come up with something a little more challenging tomorrow. ;-) I wouldn't want to bore you.

[Folded, previous note with answer removed]

[vulpinisms]

That's quite alright, I think. I'll let someone else have the bragging rights. The person above me looks like they're on the right track.

Well, I'll look forward to it then.

Re: [Folded, previous note with answer removed]

[complicatedliar]

A gentleman as well as a scholar, I see.

Re: [Folded, previous note with answer removed]

[vulpinisms]

Well, not quite. We both know I was first, after all.

[Previous notes removed]

[complicatedliar]

Our little secret, friend.