This guy on YouTube shorts named Poijz for a few days has been hunting a shiny Rayquaza in emerald across 6 games at the same time. The odds for a shiny in that game are 1/8192. He is at about 31500 total encounters (not resets of all 6 games) as this is posted. I commented “that is so unlucky to be at almost 4 times odds” and like 3 people told me it’s not how it works.

The math I did was that even though it is 6 games at the same time, the odds are still 1/8192 for each game. So with 8192*4 to get 32768, he is about 1000 encounters or a little more than 200 resets to 4 times odds. And I’ve asked them to explain and they just called me an idiot and say I know nothing about stats so what am I doing wrong?

Tried to have a crack at this month's Jane Street Puzzle and Ive hit a wall.

Problem: "Two random points, one red and one blue, are chosen uniformly and independently from the interior of a square. To ten decimal places^(1), what is the probability that there exists a point on the side of the square closest to the blue point that is equidistant to both the blue point and the red point?

1. (Or, if you want to send in the exact answer, that’s fine too!)"

My first thought was that you can find the point of intersection between the side closest to the blue point and the perpendicular bisector of the red and blue points. Where I'm lost is figuring out the probability such a point exists for two random points.

I quickly wrote up a Monte Carlo simulation in Python (it's as slow as you would think) but I could only reasonably simulate ~100 million trials before runtime on my computer got too out of hand. I can reasonably predict the probability to four decimal places but Jane Street asks for ten. My solution is too inefficient.

I'm not very well versed in probability theory so it would be much appreciated if anyone could point me in a direction that might get me closer to a solution. The fact they suggest there could be an exact solution makes me feel that brute force is not the best approach, even if it was computationally viable for me

Hi everyone,

I have a repeating 7 width by 8 hight hexagonal grid. There are 56 spaces to be filled with 9 types of elements (elements #1 to #9). Top loops around and connects to bottom and right to left, so each cell has 6 neighbors always. I need to figure out an algorythm I can use to tile this repeating pattern with 9 types of elements such, that no two simmilar element is closer than 3 spaces away and there are close to equal number of elements of each time (margin of 1 is acceptable. For example, when I tiled it with no method I had space left for extra element #4 and extra element #9)

I tried arranging them with these rules and couldn't do it: there are multiple instances where 2 elements of the same type are reachable with just 2 jumps.

Any help or pointers on finding a methodology to solve this would be greatly appreciated.

Hello,

In an LPP, to select the Key column(Pivot column) we calculate Zj-Cj or Cj-Zj; where Cj are the coefficients of the Max equation.

My doubt is: In some tutorials Zj-Cj is selected and in some others its Cj-Zj.

Is it the same?

After we calculate Zj-Cj/Cj-Zj we select the most positive/most negative etc according to whatever method we are doing(Simplex, Big M, Two Phase).

Is this selection different for Zj-Cj and Cj-Zj?

Thank you.

I’ve asked so many people about this question, and nobody seems to know the answer. This is my last attempt, asking here one more time in hopes that someone might have a solution. Honestly, I’m not even sure where to begin with this question, so it's not that I'm avoiding the effort—I'm just completely stuck and don’t even know how to start

Plz stop shadowbaning my post

I know no odd perfect numbers have ever been discovered, and are unlikely to, but have any been found that have been close? Like, say, just a couple digits out?

In Calculus we first learn that simple definition of differentials as dy = f'(x)dx, which allow us to treat the derivative as fractions and use things like U-Substitution in integrals.

However, is there any deeper definition to dy and dx as infinitesimals, that really turn derivatives into a quotient of differentials and integrals as sums of products with infinitesimals that results in an area, in a way that is equivalent to the Calculus we learn in college?

My attempt: https://ibb.co/TKZQGL3

The question: https://ibb.co/GdPv0X8

I'm asking for a second opinion because I've just started analysis and some of these proofs feel like I'm guessing a lot, because of the "choose" parts of the proofs

I believe for part (b) I need to use the max() function, right? Because need to choose an n which is greater than N

And also I need to use the ceiling function when I choose L+1 because n needs to be a natural number right? Or does n not have to be a natural number? Its confusing because it doesn't really say in the definition of the limit whether n should be a natural number or any real number strictly greater than N, which indeed is a natural number

The graph of f", the second derivative of the continuous function f, is shown below on the interval [0,Pi/2]. On this interval f has only one critical point which occurs at x=pi/16. Which of the following statements is true about the function f on the interval [0, Pi/2]?

A) f has a relative minimum at x=pi/16 but not an absolute minimum

B) The absolute minimum of f is at x=pi/16

C) f has a relative maximum at x=pi/16 but not an absolute maximum

D) The absolute maximum of f is at x=Pi/16

https://preview.redd.it/y3q7z4dlhxzd1.jpg?width=1560&format=pjpg&auto=webp&s=793ec291ac8328951a35fbda74d1576cf775f5a3

So I'm leaning towards choice C here but I'm not 100% certain. From the graph of f", we can say that f' is increasing on the interval [0,Pi/2] which would give us positive slopes and also that f is concave up on the is interval. I'm not sure if I completely understand what is going on with this question so if someone that understands can shed some light on it, I would greatly appreciate it. Thanks!

PS. Sorry about the bad graph but it's supposed to be nice and curvy and looks something like a sine or cosine graph.

I've got a geometric sequence where the sum is 375,000; the first term is 83,335; and there are 9 terms.

Plugging that into the relevant formula gives me 375,000 = 83,335 * (1-r^9) / (1-r)

I can get a value for r from an online calculator, but I want to know how to calculate that value.

I've tried manipulating the equation algebraically in every way that I can think of, but I can't find a way to solve for r. Do I need more advanced math than algebra to find the answer? Am I overlooking something simple/obvious?

Two criteria:

A) The function approaches 0 as x tends to infinity (asymptomatically approaches the x-axis), and it also approaches infinity as x tends to 0 (asymptomatically approaches the y-axis).

B) The function approaches each axis fast enough that the area under it from x=0 to x=infinity is finite.

The function 1/x satisfies criteria A, but it doesn't decay fast enough for the area from any number to either 0 or infinity to be finite.

The function 1/x^2 also satisfies criteria A, but it only decays fast enough horizontally, not vertically. That means that the area under it from 1 to infinity is finite, but not from 0 to 1.

SO THE QUESTION IS: Is there any function that approaches both the y-axis and the x-axis fast enough that the area under it from 0 to infinity converges?

Hi everyone,

I'm working on a project where I need a formula to compare the construction years of different buildings to a singular building and output a similarity score between 0 and 1. This is important for automatically identifying buildings most comparable to the one I’m valuing.

Goal: Small differences in construction years should result in high similarity scores, while larger gaps should reduce the score—especially for buildings from very different time periods (e.g., decades apart). For this I've already tried using exponential functions put I'm comming across a problem.

The problem: The formula needs to be less sensitive to year differences as the building I'm valuing gets older. For instance, comparing buildings from 1400 and 1500 should yield a higher similarity score than comparing buildings from 1900 and 2000, even though both comparisons involve a 100-year difference. Without this adjustment, small score differences between older buildings would make them weigh too little in the overall score, leading to it possibly comparing buildings from 1400 to buildings built in recent years if all other variables are more comparable. Also there are probably barely any well comparable buildings from the 1400's since old buildings are quite rare. Ideally, the function would adapt based on the construction year of the building I'm comparing others to.

Thanks in advance for your help!

Exactly what the title says.

I have tried some arguments but didn't see any hope at all.

Here are the arguments.

1. If there is a surjective mapping then it won't be injective and also one element of B might be mapped to 2 or more elements of A I tried this assumption.

2. I tried proving that the existence of a surjective mapping might compromise the surjectivity of the maps from A to B hence causing a contradiction.

If any of the mentioned approaches can be used for a proof then please guide or give me hints. I would like to finish the proof myself.

Estaba pensando en que tal como el ultimo teorema de fermat que dice que para n>2 no existe ningun par de numeros tal que x^n+y^n=z^n, pero, ¿existe algun teorema o se ha hecho algun avance en una extension donde mientras vaya aumentando el valor de n tambien aumenten las variables?, es decir, para n=3 que sea a^3+b^3+c^3=d^3 y para n=4 sea a^4+b^4+c^4+d^4=e^4 y asi consecutivamente, por lo que podria escribirse algebraicamente la ecuacion de la siguiente manera

https://preview.redd.it/mi64sntkpwzd1.png?width=123&format=png&auto=webp&s=98a9b13640bd97970be8c321c4e5ef397c5a0b60

In the new version of the game Kill Team there is an ability that requires both players to roll 5 dice. And for each match between them, the opponents model will take D3 damage.

So what are the odds for 0 matches 1 match 2 matches Etc.

For clarity if one person rolled 5 1s and the other only rolled 1 1, that would only be 1 match.

As part of a physics project I’m modelling a beam which produces particles with a normally distributed velocity, and which decay after an exponentially distributed time. For the purposes of finding the expectation value of the number of particles detected by a detector screen, I’d like to find the distribution of the decay positions using d = v*t. Is there a type of probability distribution which does exactly this?

The Markov numbers are the positive integers a such that there exist positive integers b and c such that a^2 +b^2 +c^2 =3abc.

For example, 1 is a Markov number because 1 +b^2 +c^2 =3•1•bc has infinitely many integer solutions with b and c being the consecutive odd-indexed Fibonacci numbers: (1, 1) and the permutations of (1, 2), (2, 5), (5, 13), etc.

8 is not a Markov number because 64 +b^2 +c^2 =3•8•bc has no integer solutions by 2-adic method.

27 is not a Markov number because 729 +b^2 +c^2 =3•27•bc has no integer solutions by 3-adic method.

64 is not a Markov number because 4096 +b^2 +c^2 =3•64•bc has no integer solutions by 2-adic method.

The only square Markov numbers are 1 and 169.

But I'm stuck with 125, 2197, 4913, (not 15625 since 15625=125^2 ), 24389, etc.

Main question: How do you prove that 1 is the only Markov number that is also a perfect cube?

Hi, I did shitty in high school and now I'm in in my 30s. I've been in the workforce since I've graduated highschool. When I graduated, I was not college bound at all. Yet now I'm in the position where I have college fully funded.

I'm interested in computer science but I know year one semester one I would get slammed by Calculus 1.

What's the best pathway to Calculus 1? Like not knowing calculus, but being prepared with all the prior knowledge of mathematics to be able to follow along?

I know in high school, you generally do algebra 1, geometry, algebra 2, and then maybe high school calculus in your senior year. I'm not totally sure, but I think there's a class on just trigonometry.

One thing I have to admit. I love Khan academy. I haven't totally followed through with all their instruction on algebra, but it's free and available for me to start back up whenever I need to. I'm thinking maybe I just need to relearn high school algebra and study pre-calculus. Or take those courses in college and then just cram Calculus in the the last two years of school. It gets me wondering if I need to jam a geometry and trig course in there too.

Either way, I'm rambling. What do I need to do before college or in college to get the adequate amount of calculus I need for a CS major?

The number k=2^n^2+2 -1 is prime for n=0 (k=3) and n=±1 (k=7). The number k is given by the formula M(n^2 +2), where M(x)=2^x -1 is the x-th Mersenne number. Hence n^2 +2 is prime. It is easy to check in the OEIS that n^2 +2 is greater than 57885161. Also n^2 +2 cannot be 74207281, 77232917, 82589933 or 136279841, so these Mersenne exponents don't work. Also, n must be congruent to 3 modulo 6, i.e., n=6m+3 for some (nonnegative) integer m. So the question in the title is equivalent to the following:

Main question: Is there any (nonnegative) integer m such that M((6m+3)^2 +2) is prime?

The matrix in question.

I am told to reduce the system of equations Ax=b (see image) into row echelon form. But how am I supposed to do so when almost everything is an uknown? The image above is the only information I am given.

For example, If I change the places of the 1st and 2nd rows, I can't guarantee that it is in echelon form if α = 1 and β = 0. Is there any "generalized" echelon form for a matrix like this, or do I have to divide it into case by case basis depending on the values of α and β?