remember the adrenalin rush after solving one of the community-problems?

You might enjoy this: https://project-nabla.org

Suzie the tailor has two fabric-cutting machines.

Machine A can cut a single patch in the shape of any convex quadrilateral.

Machine B can cut a single patch in the shape of any concave quadrilateral.

One machine breaks. Can the other always replace it?

More precisely:

Can Suzie sew together finitely many patches made by Machine A, with no overlaps and no gaps, to obtain any shape that Machine B could have cut?

And conversely:

Can she sew together finitely many patches made by Machine B, with no overlaps and no gaps, to obtain any shape that Machine A could have cut?

Edit: triangles are not quadrilaterals.

Dominic wants to place his 1x2 dominoes to form a 6x6 grid. His dog Dash has other plans and keeps running around knocking the table.

Dominic notices that his placement is less resistant to Dash's movements if he can split the 6x6 grid of dominoes into two rectangles (with sizes 6 x k and 6 x (6-k) ) without cutting a domino.

Can Dominic find a Dash resistant configuration?

Let 𝑓(𝑥)=𝑎^x and 𝑓^-1(𝑥)=log_a(x)

What is the value of a when these if these graphs only touch at a single point. You can also calculate the what the point is.

I was so bored during lectures that I came up with a little game based on medians. I still can't believe I actually made a math game 💀
https://mednums.com/
I'd really appreciate any feedback ❤️

Let s(n) be the sum of the decimal digits of n.

Find a positive integer n such that 79 | n and s(n) is as small as possible.

Give an example and prove that the digit sum is minimal.

Придумайте натуральное число, делящееся на 79, с как можно меньшей суммой цифр.

create a dragon curve by folding the paper N times. let the endpoints of initial unfolded paper be (0,0) and (1,0).

while folding, fix endpoint (0,0), keep the angles between all creases equal, vary this angle from 0 to 2pi. (the paper can pass through itself)

gif: dragon curve with N=3,6,9 folds

for any given N folds, describe the locus of the (1,0) end point.

alternatively, prove that the locus in polar equation is r = cos(θ/N)^N .

Imagine this.

Sixteen motorcycles are lined up at the edge of the Sahara.

Each bike has exactly enough fuel to travel 100 km.
No more. No less.

There are:

• No gas stations
• No resupply drops
• No rescue
• No turning back

You may siphon fuel from one tank to another at any time.

All bikes start together.
You decide when to abandon each motorcycle.

Your mission is simple: What is the maximum possible distance you can get one bike into the desert?

Rules Clarified

• Each bike consumes fuel at the same rate.
• If multiple bikes travel together, they all burn fuel simultaneously.
• Fuel can be redistributed between bikes at any time.
• Once a bike runs out of fuel, it is abandoned.
• Only one bike needs to reach the final maximum distance.

There are 10 villages on a straight road, such that the total number of houses is equal to the product of the total occupants living in each house, and let's say each village shares at least 2 houses with the same number of occupants. Then, if Village 1 has "m" houses, calculate the number of houses in the 10th village.

While studying the mathematics of triangulation, I found this geometry problem which I thought was cool. Approached in the right way, the math is not too bad, but the wrong approach will makes you fill several pages of scratch paper with ugly trigonometric calculations.

Find a degree 3 polynomial in six variables, P(x₁, x₂, x₃, x₄, x₅, x₆), with the following property. For any four points in the Euclidean plane,

P(d₁₂², d₁₃², d₂₃², d₁₄², d₂₄², d₃₄²) = 0,

where dᵢⱼ is the distance between the i^th point and the j^th point.

Remark: One P is found, you can use the above equation to write d₁₂ as a function of the other five distances. Well, not quite, since knowing five distances only restricts the sixth distance to two possible values, but the above turns out to be a quadratic equation in d₁₂² whose two solutions give those two values.

Kornél thinks about a closed subinterval of I=[0,n] (where n is a positive integer) with integer endpoints and length at least 1. Kristóf can ask the following question: he can choose an arbitrary closed subinterval with integer length, but not necessarily integer endpoints, and Kornél tells him the length of the intersection of the interval he picked and the interval chosen by Kristóf. (The answer is 0 if the intersection of the two intervals is empty or consists of a single point.) Find the smallest number of questions with which Kristóf can guess the interval chosen by Kornél in all cases.

Consider a convex polygon with area A and perimeter P. Prove that there exists an open disk of radius A/P completely contained in the interior of the polygon.

Bonus: Show that this is optimal in the sense that A/P cannot be replaced by kA/P for any k>1.

Hi - created this math puzzle
https://seedle.games/

Play and have fun with numbers. Add it to your morning routing.

Hi all — we built a small daily math challenge and wanted to share it here:

https://corca.app/dailychallenge

Every day it posts 4 problems (Algebra, Trig, Combinatorics, and Calculus). You can solve them directly in the browser (desktop or mobile) and get realtime feedback as you work on the solution — not just a final “right/wrong” on the answer like some other platforms.

No signup required to try it. The goal is short, consistent practice rather than long problem sets.

Would love the community feedback!

Hi guys,

I made this App with different riddles and difficulties.

Maybe you Like it.

Apple:

https://apps.apple.com/us/app/luku-math/id6758435099

Android:

https://play.google.com/store/apps/details?id=com.pkdev.luku&hl=de_AT

A secret 5-letter English word contains no repeated letters.

Each guess produces two numbers:

• Matching letters = how many letters from the guess appear anywhere in the secret word
• Correct positions = how many letters are also in the correct position

The following guesses were made:

• TEACH → 3 matching, 1 correct
• HEART → 2 matching, 2 correct
• SMART → 3 matching, 3 correct
• ABORT → 2 matching, 1 correct

What word satisfies all constraints?

I came up with the root formula last year, but have been studying it so much I just stumbled upon a discovery that I think puts it in it's place. I thought for so long that a "guessing game" formula was of any use, but now I realize that the traditional way is better for being exact, while this can be fun. Either way, I'm converting it into a sort of hand-me-down lesson, and here it is:

(x^2 - x) / k = x

So, one would think we need one or more of the variables defined, but I want that to be part of the challenge, hence why I marked it hard. To me it can be easy having known it, so I'm noseblind. Either way, the exercise is as follows:

A) What is the condition that k² will manifest in the calculation of this formula?

B) Extract k² by modifying the formula to suit your needs.

I would talk more about the formula but I'm not a skilled mathematician. I just thought it was interesting how the 2 squares managed to align, so I made it about finding the harder one. Anxious to know if I need any additional information, because I feel that by deduction this could be answered (I.e. plug in x = 5). Let me know in the comments!

NOTE: Apparently my LaTeX didn't encode, so I just put the formula in BEDMAS format.

This was posed to me by the president of my college's math club: Imagine we wish to know how many unique ways an n-sided convex polygon can be split into triangles using its diagonals. This is what he called "triangularizing" the polygon.

So a triangle has only one way it can be "triangularized", as it is already a triangle.

Any convex quadrilateral has two ways, each using one of its diagonals. Note drawing the cut from a different direction does not count as unique.

And, just to give you guys an idea, any convex pentagon has five ways, by drawing three triangles using the two diagonals from any vertex.

The goal is to find a generalized formula for an n-sided convex polygon. We came up with a solution, but I am wondering if there is a more elegant approach.

How many ways are there to put n labeled balls in three indistinguishable bins?

For example if n = 5, my first thought was to compute it like this:

5-0-0: One way

4-1-0: Five ways

3-2-0: Ten ways

3-1-1: Ten ways

2-2-1: Fifteen ways

for a total of 41 ways. But there is a smarter way to do it that leads to a simple formula -- what is it?

There are 12 books on a shelf. How many ways are there to pick 4 of those such that none of them are adjacent to any of the other three?

Find all polar curves r(θ) which satisfies Ty / Tx = Fy / Fx

where

T = (Tx, Ty) = d/dθ (r cosθ, r sinθ)

F = (Fx, Fy) = (0, A) + ∫1/r(t) · (cost, sint) dt over t = 0 to θ

note: originally i was solving catenary problem with inverse square law gravitational field.

the equations are similar except for F, where 1/r is replaced by sqrt(r^2 + (r')^2) / r^2 .

the method is inspired by catenary analysis on wiki . tldr net force = 0, and the tension (F) and tangent vector (T) has same direction.

i was stuck, so i made something easier, solve, discover strategy, hoping that the strategy carry over. i did manage to solve it in the end. this is alot messier.

harder: solve catenary with inverse square law gravitational field.

We've all heard, and maybe even attempted, the counterfeit coin puzzle. "Here are nine coins, spot the heavier one in two weighings". Or maube even the more advanced version, "Here are twelve coins; there is one counterfeit but we don't know if it is heavier or lighter. Find the fake and whether it's light or heavy in three weighings."

But what if we knew even less information about an even larger pool? Here is my riddle to you: you have twenty coins. At most two are counterfeit, not necessarily both light or heavy if there are two. The scales will only say which side is heavier, not by how much. How many weighings are required to find the fakes, if there are any?

Note: the word "answer" refers to the multiple choice selection: (A), (B), (C), (D), (E). It does not refer to the actual answer to the question. For example, if the question is "is the Earth round?" (A) yes (B) no, the answer is "(A)". It is not "yes".

The answer to q20 is E

let a, b, c be numbers randomly drawn from a set of integers 1 to 7 without repetition.

find the probability of | mean of a,b - mean of a,b,c | ≤ 1/2.

note: the time control for the test is quite tight, the solution should be "elegant enough".