#get math answers

[papercoach]

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[gascreates]

a new star

[peach-pot]

ok my turn

[chongoblog]

Have you heard of the Sum and Product Puzzle, aka the "Impossible Puzzle" because it initially seems like there isn't enough information to go on? I think I have the answer, and I'm mad about it.

I hadn't so I looked it up and here's Wikipedia's summary of it

There's also an explanation, but I didn't look. I wanna figure this out myself.

So let's break it down.

"P does not know X and Y" means that X and Y are not both prime. If they WERE both prime, then P would know the two numbers right away. So if S KNOWS FOR CERTAIN that P doesn't know X and Y, that means that the sum of X and Y can't be made up of two prime numbers. So, for example, the sum can't be 20, since if X and Y are 1 and 19, P would get 19 and be able to easily deduce the values of X and Y.

So we have a bound for the sum here, so we just need to find all numbers that can't possibly be the sum of two primes. I tried to get a good list of all numbers that aren't the sum of two primes through trial and error, but I after I found the first few I just let the OEIS do the rest of the work for me

So our possible sums are: 11, 17, 23, 27, 29, 35, 37, 41, 47, 51, 53, 57, 59, 65, 67, 71, 77, 79, 83, 87, 89, 93, 95, and 97.

Now that doesn't narrow it down a TON, but we can probably do something with this. Now that P knows that these are all of the possible sums, they know FOR CERTAIN what X and Y are. Very interesting. That tells me a lot about the product.

So let's say X is 4 and Y is 7. Then P is 28, and S is 11. Now, other factors of 28 include 2 and 14, which add up to 16 (not on the list), so we could just say that and call it a day, but there's something else that perplexes me. What if P is 24? The factors of 24 are 6x4, 8x3 and 12x2, which give us sums of 10, 11, and 14, and 11 is the only one on the list, so we have new X and Y values for S = 11 that could also apply. And since the S mathematician said he knew what X and Y were upon hearing that P knew, we can safely say S isn't 11, since X&Y could have multiple possibilities.

So, simply put, we need a value of S where there's only one possible P that could work for it. On one hand that still sounds like a LOT of guess and check work, but on the other, I feel like there's a way to find this solution without that.

Doesn't matter. I did the guess and check work anyway, granted it was actually easier when I got to the higher numbers, since most possible factors of P went over the sum of 100, which is one of our limitations. Easiest way to find these unique products is to find the largest prime number (lower than the sum) and use that as one of our two values.

So the conversation goes as such.

S sees that their sum is 17. Knowing that 17 can't be reached as a sum of two primes, S says "P does not know X and Y", which tells P that the sum is one of those numbers we saw up there. P's product is 52, he figures and he only knows two numbers whose sum add up to one of those numbers. So he says "NOW I know the value of X and Y". S hears that and figures that it has to be that one EXACT combination.

X and Y add up to 17 and multiply to make 52 which means that X and Y are 4 and-

...

GOD DAMMIT

[darcyolsson]

aled mention in heartstopper now they're at 6th form makes me feel unwell .... i think i sent you an ask about this forever ago but i literally feel like i'm grieving a dead character when he's Right There. he's coming up on probably the worst year of his life and his friends have no idea!! they'll have no idea when it happens!! and my osemanverse timeline knowledge is a little scattered but i'm pretty sure at this point in heartstopper aled's sister has already left home? so he's all alone with his mother and literally no one knows and he hasn't even met frances yet ....... aled last you are everything to me

LITERALLY EXACTLYYYYY...... aled's prescence in heartstopper is such an unexpected sad detail :( i always think ab that moment where aled and charlie discuss daniel but aled first has to explain who daniel is. and it's framed very casually but like daniel is such a massive part of aled's life! and yet charlie doesn't even know about his existence!!!!???!!! ALED TALK TO YOUR FRIENDS PLEASE... THEY LOVE YOU...........

and yes you're right that carys is already gone by this point-- she left when they were 15, and currently it's nick's 18th birthday (september) in the comic which means aled had his 16th birthday the month before (august). the worst thing that could happen to him has already happened and now it is only going to get worse for a few years. and all we can do as a reader is just watch him deteriorate in the background of someone else's story bc he's not yet at a point where he can do anything about it. incredibly upsetting

[faithfulpuppy]

Something I've seen a lot of in the Locked Tomb fandom is John's irreverence/sense of humour held as evidence that he is and always was a piece of shit - his response to Wake's questions about the bombs, his general attitude in the Nona flashbacks. (This is not a defence of John's actions, so bear with me.)

This is a cultural barrier I've encountered before with New Zealand humour - Americans in particular have taken offence to my 'attitude' when I was making what would be considered a very chill joke here, and I think it's no coincidence that a large portion of the tlt fandom seems to be American. New Zealand humour is very, very dry and irreverent and relies mainly on sarcasm, understatement and self-deprecation. We're not overly sophisticated or witty. Delivering a very serious statement deadpan is considered very funny. We're (especially men) discouraged from showing honest emotions and often cope with tragedy by making casual remarks that are almost callous at times. This all frequently comes off as rude or disrespectful to non-New Zealanders, especially via text with no vocal/body language indicators. I've gotten in trouble online more than once before over it.

I think part of the reason I interpreted John as less sinister than a lot of other people on my initial read is because his humour and manner seem very normal and non-threatening to me. When he says flippant shit that other people jump on as "See? He has no heart he's evil he doesn't care about others!" I'm like what? He was just- that's what I'd have said too? That's just how kiwis talk? This is not always true of course - sometimes he goes too far because he's dead inside - the line about Sydney's tram service is, while in line with New Zealand humour, deeply disturbing. But I think it's really important that he's not just Some Guy, he's Some Kiwi Guy and to someone who's grown up in New Zealand his manner of speech is very familiar and not the evidence of coldness/evilness it's often perceived as by others.

[doodle-do-wop]

What the Elvin equivalent of your dad yelling at you about math homework over the kitchen table for Foxfire?

[miyamoratsumuu]

just got to make it to friday just got to make it to friday just got to make it to friday justgottomakeittofriday justgottomakeittofriday justgottomakeittofriday

[papercoach]

📚 Study environment matters! Create a dedicated study space with good lighting and minimal distractions. 📖 Your focus will improve, and so will your grades! ✨

[girlcockholmes]

i love blocking people for stupid reasons. yesssss i can guarantee i will never have to interact with you this is so good for me ❤️

[hecksupremechips]

It’s something only kinda implied but I love how Junpei is really smart and actually does know random bullshit information like everyone else does but he just like. Doesn’t use it unless he wants to end an argument

[stars-of-radiance]

Um, actually the EXACT time that the train collision would occur is 6:20:46.153846 repeating AM, Brennan

[beatcroc]

Hi Mecha Sonic, are you a fan of them gosh dang chilli dogs? 🌭

[unnonexistence]

btw if i'm ever rambling about math on here and you have questions about it, you are ALWAYS welcome to ask. always. everyone has a different level of math education they're working from & math has a lot of technical terms & frankly i just forget stuff a lot so my rambling might not be all that coherent to begin with.

worst case is idk how to answer your question. more likely you will get some sort of explanation because it means i get to ramble more.

[moldwood]

i wish i had normal "phone calls are impossible, my friends secretly hate me, i'm wearing the wrong outfit to the wrong place" anxieties and not "if your five year plan succeeds and you move to france, everyone is going to hate you because even though you have worked so hard and you learnt the language and you're not a tourist and you are a genuine + kind person, your accent is just embarrassing" anxieties

[applesaucesomething]

Some recent deltarune wips that i dont really like that much but meh