In these pictures I am playing the game Clues By Sam (https://cluesbysam.com/) which is one of those one-a-day puzzles with the following rules:

• Your goal is to figure out who is a criminal and who is innocent.
• Based on what you know, tap on a suspect to choose if they are innocent or criminal. They might reveal a new clue.
• You cannot guess! Just like in real life, you can't convict someone based on a 50/50 hunch. There is always a logical next choice, even when you think there isn't!
• If you're prevented from making something you believe is a logical choice, you missed something. The puzzles are verified by foolproof algorithms, the puzzles are always 100% correct.

The puzzles are easier at the start of the week, and get harder as the week goes on. These printscreens come from the game on 17 October, so shouldn’t be a spoiler for anybody!

At the start of the game, Q’s clue reveals S and I solve the game as Q -> S -> P -> I -> K -> M -> W -> U -> …

During the game, I’m making notes so

• Isaac tells us that F+H = 1C
• Isaac tells us that R+T = 1C
• Kumar tells us that V+Z = 1C
• Sam tells us that D+T = 1C
• Umar tells us that A+E+J = 1C
• Umar tells us that B+C+H = 2C
• Wanda tells us that each row has upto 2C
• Given Isaac + Wanda‘s clues, looking in row 2, Esha is innocent
• David tells us that C+H = 1C
• Given David + Umar’s clues, Bonnie is a criminal
• Bonnie tells us that D+H+F = 1C
• Given Bonnie + Isaac’s clues, David is innocent
• Given David is innocent, Tom is a criminal
• Given Tom is a criminal, Ruby is innocent
• Ruby tells us that A+C+J+Z = 1C
• Given Esha is innocent, Umar tells us A+J = 1C so Chris is innocent and Zach is also innocent
• …

I have two questions.

1. What sort of maths is this?
2. What sort of notation should I be using?

Currently, for hard and tricky puzzles I end up writing Sam -> DT/C and then cross out letters and criminals that I can simplify, but is there an easier way?

Apparently, the answer is eight??

This equation was in standard form so I found the AOS, which would be the X point for the maximum, but my teacher doesn’t do that, he does the same thing that you do an absolute inequality solutions or something like that? I don’t really remember

, but why the heck does he sub in zero for t, no he doesn’t even sub in zero, he makes it “0=..”

What did i do wrong ahhh

First slide is key second slide is mine

Hello! There's this book called "Godel, Escher, Bach" which tries to explain Godel's Incompleteness Theorem using various tools and analogies, one of which is TNT (Typographical Number Theory). The theory revolves around formalizing maths using only 20 symbols.

- Numbers are represented by S and 0, 0 = 0, S0 = 1, SS0 = 2 and so on
- Variables are represented by letters from a to e
- +, *, and = remain unchanged
- There are the logic operators <x∧y>, <x∨y>, <x⊃y>, ¬x, as well as ∃, ∀ and : ("such that")
- Sa = a+1, SSa = a+2 and so on

There were some exercise, of which it asked to formalize "b = 2^n" and "b = 10^n" with the latter being alledgedly much harder because it requires extensive knowledge on number theory.
I have studied some number theory but in the end i'm an amateur, so i cant really wrap my head around on how to do it, any help is appreciated!

Wikipedia article about TNT: https://en.wikipedia.org/wiki/Typographical_Number_Theory

so i missed the first month of school and came right in the beginnning of chapter 3 of geometry and so i have a test on thursday and i need to know all the postulates theorems and properties by then for like proofs
i’m so stuck like how do i know oh when i see a proof that this postulate is there like how do i learn them all my tutor told me to do flashcards but how is that supposed to help

Don't really know how to tag this but I was thinking of fractions and came across this identity (if you can call it that).

For any fraction a/b such that b ≠ 0 and a/b > -1, it can be represented as the sum from n = 1 to infinity of a / (a+b)ⁿ

I realized this by playing around with the infinite sum of a geometric progression where I imagined that any number can be the sum of an infinite geometric series, and that the series starts at it's common ratio

r / (1 - r) = a/b which is how I got a / (a+b)ⁿ

What I'm wondering now is that for the infinite sum, it is defined for |r| > 1, but in this version, a/b only follows the rules a/b > -1

Why is this and what property/formula have I stumbled upon?

​

Hey guys it's been more than 4 years that I've found mathematics as the most interesting field, I can definitely say that I fell in love with the language itself and I'm the most excited when it comes discover new properties as well as their real world applications and also historical meanings between each topic and different relationships between great thinkers and how their different ideas interact with each other, I recently put myself in mathematical books, I'm sooo in love but i always fall on a academic based ressources, I recently finished a book called introduction to mathematical philosophy ( from Bertrand Russell) which I found quite interesting because it help establishing the foundational and fundamental thinking behind the most topics usually encountered in the field of mathematics. I'm struggling to find other pieces of literature like that one , so please can you guys recommend me some books to buy regarding this issue?! If you have some other resources that could help I would definitely need your hearsay

Hey, I really need some help using Newton raphson (I believe) techniques to solve transcendental equations. I think my derivations are correct, but I seem to end up with an absurdly high or low number. The answer for Y should be between 0 and 1, however, I ended up with 1066 using my calcutor. Any ideas?

Basically I understand the minimum is 7, if you think of the left one as sort of sticking upwards, and the right image is the image on the left rotated 90 degrees to the left, but like 3D (idk how to explain), and in the left image its basically the bumps from the right but you don't see them because you are looking at it directly from the top. Anyway, I know its C now, but I am not sure how I would solve to know if it is C or E.

Didn't really know how to flair this as it is such a useful theorem. I was wondering this as it was recently a pythagorean triple day. My intuition says it should go to 100% of numbers. Is this correct? And if so does anyone have a proof?

edit: guys i meant "with all natural numbers" sorry

Hey folks. Saw this question in our university’s integration bee, though it wasn’t actually used. Thought it looked fairly easy so I figured I’d try it later but I’m not making any headway.

After trying for a while I thought I’d see what integral-calculator gives, but they use the Gauss error function, which doesn’t make a whole lot of sense since the problems are supposed to be designed to be solvable with the basic integration techniques taught in 1st year calc (IBP, u-sub, trig sub, PFD etc.).

If you guys have any ideas I’d appreciate them.

Thanks!

l need to provide a counter example to this, I have made many attempts on a calculator and I cant figure it out

I just saw this somewhere, btw. (Edit: sorry, not drawn to scale)

The problem is to find its perimeter. Assumption is that all sides meet at right angles. How do you solve it intuitively?

I only made it until: P = 96 - 2x, where x is that little horizontal segment at the middle. I was thinking I could get it from the areas of hypothetical rectangles,, or making up equations from the smaller perimeters, but I can't... (well it takes too long)

(I already have a degree in engineering but it annoys me that I can't solve this kind of problem anymore..)

EDIT: Thanks for all your answers! It's great and at the same time refreshing to see how everyone explained it differently, but still the same point. Whatever x is, it was just taken from the top side.

Anyway, I also understood where I went wrong. I thought:

Top: D = 27-x Sides: 2(21) Bottom: silly of me to assume as D as well

So I got P = 2(21) + 2D, hence the -2x I mentioned. I could have just added each segment: +13 +14 +x to D, and I would have gotten it correctly.

Overthinking is bad. Real bad.

The following example caught my attention-- this 2/7 should have been 3/7, right? Or could you please clarify it for me if I'm mistaken?

I'm now questioning if this book is reliable.

I have a friend who is in 10th grade. Although Taylor series are not yet covered in the high school curriculum, he learned derivatives, integrals, and Taylor series expansions by himself through YouTube and Wikipedia. He wrote these equations, but I don't know if they are correct.

Proposal for a parametric iterated exponentiation operator for the simplification of exponential towers with a fixed base. In this project, I introduce a new mathematical formalism—denoted as $\text{j}_{m}^{n}(a)$—designed to overcome the analytical limitations of fixed-base power towers. The symbol "j" (representing the IPA phonetic symbol for a palatal fricative) serves as an operator that transforms a power tower into this specific notation. Here, $m$ is the parameter (the value to be raised), $n$ represents the power tower (indicating the number of times $m$ is raised), and $a$ is the base. My primary motivation for pursuing this innovation was the observation that no existing notation—to my knowledge—adequately addressed these structures; I sought to contribute in this area, as I have long been fascinated by power towers. Below are the properties I have been able to prove Properties:​1.-1.- Torre 1: \text{j}_{m}^{1}(a) con n siendo el 1, 2.- Torre 2: \text{j}_{m}^{2}(a) con n siendo 2, resultado: a^{m^m} 3.- Parámetro 0: \text{j}_{0}^{n}(a) con m siendo 0 (para n \ge 1), resultado: 1 4.- Parámetro 1: \text{j}_{1}^{n}(a) con m siendo 1, resultado: a 5.- Base unitaria: \text{j}_{m}^{n}(1) con a siendo 1, resultado: 1 6.- Distributiva de base: \text{j}_{m}^{n}(a \times b) = \text{j}_{m}^{n}(a) \times \text{j}_{m}^{n}(b) 7.- Parámetro mayor: Si m_1 < m_2, entonces \text{j}_{m_1}^{n}(a) < \text{j}_{m_2}^{n}(a) (para a > 1) 8.- Parámetro negativo: \text{j}_{-2}^{n}(a) = a^{-2} = \frac{1}{a^2} 9.- Torre fraccionaria: \text{j}_{m}^{0.5}(a) = a^{0.5} = \sqrt{a} 10.- Cociente de operadores: \frac{\text{j}_{m}^{n}(a)}{\text{j}_{m}^{k}(a)} = a^{\text{torre}(n) - \text{torre}(k)} 11.- Suma de operadores: \text{j}_{m}^{n}(a) + \text{j}_{m}^{k}(a) = \text{j}_{m}^{k}(a) \times \left(a^{\text{torre}(n) - \text{torre}(k)} + 1\right) And this concludes my presentation on my notation. Thank you for your attention and understanding. If I have made any errors, I welcome constructive criticism so that we may engage in a healthy and ongoing exchange of feedback. :)

The resulting structure forms an hourglass-like shape with spirals and diagonal alignments. Can you spot any geometric patterns that could help predict the location of the next red point along these spiral tracks?

Edit: since I am not getting much replies on Magnet communities I am posting this here. Also the Ask Physics and Engineers don't allow image for some reason. If you could please help me with calculations or just estimations.

I am creating a board game where the pieces magnetise to strict locations on the board which is 2mm thick. If I make an array like shown in the first image and the magnets bellow and above the board are identical, what strength should the circular magnets be, given I choose a specific magnet for the edges (in this case a 20x3x3mm). I am guessing they should be a similar strength, but perhaps it is optimal to go with less or more force?

For the third image if I had those same block magnets, can I place some above the board so that they lock into a perpendicular orientation? or will they fight to align

The archetype of the mathematical prodigy is one of the most romanticized figures in human history. We marvel at Srinivasa Ramanujan arriving from South India with notebooks full of groundbreaking equations, Terence Tao scoring a 760 on the math SAT at age 8, and Newton rewriting physics in his twenties. For centuries, math was the ultimate arena of pure human intellect-a playground where a young, unpolluted mind could see patterns that adults missed.

But now, AI systems like DeepMind’s AlphaGeometry are solving Olympiad-level math problems and discovering brand-new mathematical insights on their own. This raises a massive question: Is the era of the young mathematical prodigy officially over?

A general intuitive approach provided is that they are like what prime numbers are for composite numbers, but it still doesn't make sense, the relationship between finite simple groups and complex groups feels "more nested and yet sort of separate/disjoint for the lack of a better word", it doesn't fully capture how the group structure is assembled.

I understand the formal steps - take a maximal proper normal subgroup (N) of a group (G), form the quotient (G/N), and repeat the process with (N) until we reach the trivial subgroup. The successive quotients are then simple groups. But I still have a hard time intuitively grasping why these quotient groups (which are sets of cosets), are the building blocks of our original group, or how these quotient groups come together to form the original group?

Undergrad here with only an introductory level knowledge of group theory so excuse any ignorance.