@math

That time a mathematical proof to an unsolved math problem was just casually posted anonymously to 4chan... Mathematicians found it some time later and realized, remarkably, a long outstanding problem in maths had finally been solved...

Sometimes life is funnier than fiction

100 Pots Puzzle

About a year and a half ago I presented the 100-pots puzzle, which is by far my favorite programming/logic/math problem I have ever come across. It took me a while to solve it the first time I heard it (most of the work day which is where I heard it). I also was at an advantage because the solution comes from a field of math I have particular expertise in, so most people will probably have a harder time solving it.

I donβt think anyone was able to solve it last time I presented it, and had to give the official answer, I could be wrong, I need to dig up the thread. @Absinthe however did write a simulation for it in python after I had posted the answer.

Anyway here is the problem for anyone who wants to take a stab.

All answers or hints must be CWβed

No tricks

First off some background. The problem is not a trick question, as much as it may seem like one. There is no play on words, no hidden exception. Everything in this problem is exactly how it is presented and the answer doesnβt rely on any slight of hand. Take this puzzle at face value.

The Puzzle

There is a room with 100 jars with lids on them all in a row. There is also a stack of papers, 100 papers each labeled 1 to 100. The papers are shuffled and one paper placed into each pot randomly.

You and your assistant are in an a joining room. Your assistant is allowed to enter the room, look in all 100 pots, and if they wish they can pick any 2 pots and switch the paper in them. They can only do this one time, they do not have to do this they can choose to also do nothing. At this point they leave the room, without talking to you.

Next, someone tells you a random number from 1 to 100. Your goal is to enter the room and open a pot that has that number in it. You are allowed to open, at most, 50 of the pots.

Whatever process you use to open those pots must guarantee that by the time you open the 50th pot that the number you were given will be found. Obviously your assistant didnβt know what the number is at any point.

What rules do you give your assistant, and what rules do you follow, to ensure you are successful?

@math #Math #Maths #Mathematics #Puzzle #Puzzles #logic #LogicPuzzles #Programming #algorithm #algorithms

I am way too excited by this novel little discovery of continuous complex fibonacci sequence.. I need to play with this!

Outlier looks pretty exciting. At first glance it appears to be something like Masterclass but for STEM, plus it counts as actual college credits for anyone in university. basically it is university level courses taught by famous experts in the field.

Also gets some brownie points from me for highlighting Hannah Fry as one of the instructors. She is awesome and has done a lot of great stuff over the years. I got to talk to a her a few times and she helped me out with some problems I was working on once or twice (not through outlier)... so cool they snatched her up.

https://www.outlier.org/ is the link for anyone who wants to check it out.

#Science #Math #Mathematics #learning #elearning @Science @math

Ok so yesterdays algorithm took a little more extra work than I had hopped to finally get into its final form but I **think** its there. I just need to run it through some tests to know for sure.

A new post I wrote explaining how to write an efficient Exponential Moving average with a finite length.

https://jeffreyfreeman.me/an-efficient-exponential-moving-average-of-finite-length/

#science #math #maths #mathematics #programming #DSP @Science

Early rough draft, haven't proof read it yet. But just wanted to share the math behind creating an efficient Exponential Moving Average with a finite length/cut off. I found this was needed for a project I am working on where the EMA much be determined by random access to various points in a time series and couldn't be calculated for the entire time series in one go.

I needed to modify the EMA for a finite back-length. The standard EMA is only really efficient when calculated sequentially for the entire time series. This implementation is an efficient design that allows for calculation at a point by using finite back-length.

This is an early draft, did not proof read it yet, just whipped it together, though pretty sure the math is close to the final form. I will publish it sometime tomorrow but want to share what I have and welcome and questions or feedback before I publish it.

https://beta.jeffreyfreeman.me/an-efficient-exponential-moving-average-of-finite-length/

#Programming #Math #Maths #Mathematics #algorithms #Science #QOTOJournal

A wonderful visualization of the often unknown Quaternions (a generalization of complex numbers into 4 dimensions).

Can you solve the riddle? My answer is under CW

1) First fill the 5L then pour that into the empty 3L until it is at the rim, now you have 2L of water in the 5L bucket and a full 3L bucket.

2) Pour out the 3 liter bucket leaving you with 2L in the 5L and an empty 5L

3) Pour the 2L from the 5L bucket to the 3L bucket leaving you with an empty 5L bucket and 2L in the 3L bucket

4) Fill the 5L bucket and pour it out into the 3L bucket until it is full. This leaves 4L in the 5L bucket, problem solved.

In case anyone is curious as to how to do some elementary statistics, in this case combinatorics, here is a quick little write up I did to explain the βn choose kβ paradigm.

Here is the is the question (from my cousin):

Math people

Can you help me ??

Letβs say

Hypothetically

You have 7 numbers

Between 1-99

The first 6 cant repeat but the 7th can

How many outcomes are possible?

This isnt a riddle or anything I just dont know how to do the math on something Iβm trying to figure out

Here is my answer:

For this weeks #FollowFriday I am going to do a groups addition.

@Electronics - An Electronics Group

@theamazingweb - A group about interesting and novel things on the internet.

@vim - A group for everything VIM

@funny - A group for humour and memes

@mnmlsm - A group devoted to discussing unix and related topics

@calligraphy - A group devoted to sharing and discussing calligraphy & handwriting

@FreeSoftware - A group for discussing Free and Open-source software

@math - Everything math!

@dogs - A group for sharing pictures of dogs, for any reason.

@Science - A group to discuss Science topics.

@photography - A group for sharing or discussing photograph.

So its been about a month since the QOTO Moderated Groups Server came online at groups.qoto.org. It adds group capability to the fediverse with an owner capable of moderating membership in the group unlike previous group servers which were completely unmoderated and open.

We have had some amazing groups form and overall the server seems to be the most popular on the fediverse, Iβm seeing more activity than the open-group servers which is great!

As such I wanted to share a list of a few groups I know of so far in case anyone is looking for a group to follow. Just follow the group as you would a user and you will be in the group and receive group posts in your timeline!

#Electronics #EE #VIM #Funny #Humour #meme #memes #unix #linux #Calligraphy #Handwriting #OpenSource #FreeSoftware #math #maths #mathematics #dog #dogs #doggo #Science #Photography #Pictures #FF

Hidden Markov P\'olya trees for high-dimensional distributions

Check this out...

#Math #Science #MachineLearning #AI #Statistics #CimputerScience #Algorithms #ComputerEngineering

QT: https://qoto.org/@arxiv_stats/105178202578254622

Looking for Math Helpβ¦

So met the guy who wrote this paper/post on a plane trip several years back where I was flying out on a business trip. Iβve done hundreds of them so they kinda all blend together and I didnt really remember who he was.

Anyway a few days ago he pops up into my emails, must be 4 years, maybe more, since the trip, and says he remembers me, apparently we talked some advanced math or something cause he knew I was the perfect guy to check out is NvNP math proof. Anyway, convinced him to come here and share it with all you guys, he could really use some feedback.

So yea, if you know any math or are just curious please check out @carlostomas βs paper attached as the quote/link on this post it would really help him out. Iβll be taking a look when I get a chance soon as well.

#math #maths #Mathematics #ComputerEngineering #Algorithms @math

What is everyone's favorite math equation? I think mine might be the laplace transform just because it is at the root of so much modern day science from relativity to electrical engineering and leads to a way of looking at and understanding the universe that really is a game changer.

Whats your favorite math equation?

Greetings!

In short, I am posting 3 documents, all geared towards a solution for the P versus NP problem.

The mathematics that governs the official solution has been presented to, and was subsequently endorsed by two separate mathematics journal editors.

Now I am presenting the mathematics to the public, and I got the suggestion to post here.

The reasoning behind three documents, is one is the official proof, which is written for professional mathematicians, and is very brief concerning certain ideas, and may not be obvious to even those with a strong mathematical background.

The next, is a version official proof, that obviates every point made in the official proof, and is much more verbose. It's a complete proof, and intended for those with a very strong mathematical background. It could be called properly the extended version of the official proof.

The other document is a basic mathematical overview, that is intended for anyone to read, so they can understand the mathematics that governs the solution.

It is chalk full of new mathematics, and has gotten great reviews from the readers I have thus far had. It is intended to be very informative for anyone with the slightest semblance of a mathematical background, and who wants to understand the official proof, and why and how it resolves the problem.

Any reviews and comments from the present community will be read.

I hope every well intended person has a great day. Likewise, enjoys reading the articles.

Basic mathematical overview of proof:

https://drive.google.com/file/d/1Y-GZKJbZKiAcqFm2ewdxX__PzyVpmNy1/view?usp=sharing

Official proof:

https://drive.google.com/file/d/1Q_LxHjsQgv7b3RrWnu7Jer23Jw1O7ZUc/view

Extended proof:

https://drive.google.com/file/d/1lhAILS01c7ROzcP2IcjwyiClsgchV8Pu/view?usp=sharing

Group

A moderated group for everything math!

Joined Oct 2020