#ITS. MATH STUFF-

[lorebird]

In which Ford struggles so badly to relate to other people that he wonders if he’s really human at all. The more isolated he becomes, the harder it is to reconcile with his own humanity.

[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

[statementlou]

hey some very smart people (my babes @captainrayzizuniverse and @goldcrumble) have cracked a 28 Clothing pattern check this out: Drop 1 and Drop 2 came out August and November last year and were both Collection 01 (labeled on the clothing tags); Drop 3 (this July) is Collection 02...

...which suggests a possible pattern of one collection consisting of two drops close together late in the year per year, which feels consistent with teasing items from the next drop in the promo for this recent one; so we would see Drop 4- the second half of Collection 02- in October or November, and then another long wait until the second half of next year for more?

[askblueandviolet]

[avocado62524]

[aimasup]

throws up my hands in mock resignation but also a hint of frustration Okay Valentino is a cool villain I guess

He's like. Genuinely unsettling. Wish the show struck a better balance with his character sometimes (like sometimes when he's onscreen I have to skip over because I feel queasy and sometimes he's so unsubtle he feels more like a prop than a guy who's going to be a Huge Deal in s2)

[thatsamonkey]

barely 3 weeks into school and i already have an f in 2 classes i think my only choice is to revolutionize the world

[nonconstories]

Here, you think that LAST fantasy was weird? Try this shit on for size. Imagine a ~* VillainCon *~, where supervillains expo their latest advancements in EVIL, including torture devices. Imagine a cute little sidekick getting kidnapped and used to demonstrate some kinda tentacle beast engineered specifically for rape, screaming as their costume gets ripped off and the thing fucks them in every hole. Imagine a famously badass heroine getting mind controlled into a grinning, bimbo housewife on a demo stage, her captor charging the audience for the pleasure of fucking her mouth. Imagine a small group of civilians getting turned into hypersexualized anthro creatures and auctioned off as henchmen/personal sex slaves.

The Renaissance Center doesn't invite VillainCon back for the next year and most of the presenters got their ASSES KICKED afterwards BUT by god did the convention itself turn a profit!

[vse-kar-vem]

quick bojč!!! 💓💓💓

[reef-sys]

math is currently the #1 trending thing on tumblr

what

[rainc0at]

brassic questions im haunted by: what the fuck was the wanking contest? why the FUCK do these "professional thieves" never silence their phones when they're robbing? why does dylan continue to take class a's?

[chongoblog]

Hey you’re a math guy right? And you like Balatro right? I’ve had this math question related to Balatro but I can’t phrase it properly to get a satisfactory answer from google so I was wondering if you or a follower could help? Anyway here goes:

In Balatro there is a deck called the Plasma Deck which “balances” your chips and your mult so that they are equal in order to increase your score. I understand that mathematically given two positive numbers x and y when multiplied together will have an increasing total as x and y approach each other given their sum is constant. What I REALLY want to know is that if for any given sum of x and y where each integer permutation with the same sum is equally likely, what is the expected increase in score from balancing and is it thus worth it to double score requirements?

Tl;dr for any given total T where x and y are positive integers and sum to T and where each permutation of x and y are equally likely, what is the expected increase in value from x times y to (T/2)^2

So I am familiar with the Plasma Deck. Despite note having unlocked it yet it's definitely the one I'm most excited to unlock for this exact reason.

That said, let's talk about the question at hand. I can fix a more sophisticated explanation for this at another point in time, but here's my answer for now. If you're expecting an equal distribution of possible positive integers x and y, then no, the expected increase in score isn't double. For example, let's say T is 20 and p is the product of these values.

As you can see, out of all of these outcomes, only two of them are less than half of (T/2)^2 (which is 100 in this case). Which, if we were expecting an equal distribution of possible x and y values, would make the idea of doubling the score requirement seem incredibly unbalanced. However, that's where the strategy comes in. If you can make a build where you x and y values are 1 and 19, then the Plasma Deck more than quintuples your value, making the doubling of the score requirement seem like a breeze. So the strategy of Plasma Deck is basically to hard focus either x (chips) or y (mult)

Maybe if I have time I'll see if there's some sort of equation discussing this (there almost certainly is) but until then I am tired

[lesbicosmos]

me and one of my best friends only have one subject together now, so we tend to spend the time we're not working talking about our current favourite tv shows, it's kinda our thing

it's really funny right now though because she's yapping about the new season two of her show (rings of power) while im yapping about the unjust cancellation of season two of mine (dead boy detectives)

[amoneki-ramblings]

In the Amon stays in CCG AU Shironeki will get jealous with Haise because Haise gets to talk/work/eat with Amon and he doesn't??? 😭😭 Guy be sitting in a chair chanting "it should have been me"

WAIT THIS IS SO FUNNY?? I also spent way too much time on this um?? Enjoy

[crushedsweets]

creeped timelines

hopefully this is readable once i post UODATE(;Itsnot ITS NOT READABLE 💔

[floralfractals]

Hi everyone, I wanted to write a quick update to you guys :)

I made this blog in March of 2021. At the time, I followed my first math course on fractals and dynamics, and had just discovered a tool to make my own awesome fractals. This blog started out as a place to share the art I was making as a coping mechanism during covid, but as I quit making them after a few months, this blog died pretty quickly. In 2022, I decided to start posting regularly again (mostly just shitposts though), just so that the effort I put into this blog wouldn't go to waste.

Then, in the beginning of this year, I started writing my thesis. I posted one (1) shitpost about him (my well-known and popular son), and got 10s of thousands of notes. Every morning I would wake up to another crowd of people who loved the graphs, or were baffled by them, and I got showered in asks to elaborate on him.

Truth be told, 2023 has been a very heavy year for me. A lot of things happened in my personal life, and I lost a dear friend to suicide. It became so difficult for me to keep writing on my thesis, and the project that should have been finished in June this year has now been taking 4 months too many. My mental health has suffered greatly, I haven't been able to take any breaks, and life has just been generally difficult. I have spent nights not being able to sleep because I wanted to finish my bachelor's thesis so bad, but my supervisors would keep demanding more work, more edits, and more drafts. At some point, I even considered quitting my studies and finding a job.

The community has helped me to keep going. Mathematicians and non-mathematicians alike who sent me genuinely interested questions, made me laugh in the notes, created fanart (??? I'm still baffled by this but the people who did this are the coolest in the world) and generally made me feel for the first time that mathematics isn't a universally hated subject. On some days, the only reason I was able to keep going and the only thing keeping me from experiencing burn-out was the support I got through this blog.

Today, 10/12/2023, I turned in my thesis. Thank you so much for your support!