Any known platform to post self made math questions

Question

Background

I am a class 10 student who is fond of maths. I like making math questions.

Question

I do not know of any platform where I can post these questions for others to practice and learn. I really want not to let them go unnoticed. Is there any well-known website or any other platform for this?

My questions require some critical thinking and are different from the ones which are found the textbooks that follow the syllabus.

Example Questions

Q - 1 Let the function $S(n)$ denote the sum of the first $n$ terms of Arithematic Progression. Given that the degree of $S(n)$ is $1$ and the first term of the AP is 10, find the $10^2$th term of the AP.

Q - 2 Let there be 2 squares, whose area is given by $[p(x)]^2$ and $[g(x)]^2$ for $x\geq0$, where $p(x)$ and $g(x)$ are quadratic polynomials.

It is given that $p(x) > g(x) \quad \forall x\geq0$

When the smaller square is placed on the larger square, such that it overlaps completely with the larger square then the area not overlapped by the smaller square is given by the polynomial $r(x) = 3x^4 + 20x^3 + 46x^2 + 44x + 15$

If the difference in side lengths of both squares is $3,8,15$ for values of $x$ as $0,1,2$, then find how many times $p(x)$ and $g(x)$ intersect on the graph. Also evaluate $\frac{p(12) - 1}{g(10)}$

Q - 3 Prove that for any natural number $x$, $1101$ cannot be the sum of $x$ and the number obtained by reversing the digits of $x$.

Q - 4 Prove that for natural numbers $a,b$ and $n$, $HCF(a^n, b^n) = [HCF(a,b)]^n$

Edit

Edit 1 - My problems are relatively straightforward for students who have taken specific courses that cover the required problem-solving techniques. My original intent was to look for an audience that had just learnt the basics and for whom these questions would require critical thinking, but now I realize I should leave that idea and post my problems for a general maths audience.

Answer 1

Perhaps reddit.com/r/mathriddles. The problems in the tag "easy" seem somewhat similar to the type of problems you posted, and they do get upvoted, which indicates that the community is receptive to them.

And of course nothing is stopping you from putting up a blog and posting the problems there, and/or making some YouTube videos about them.

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Something to aspire to: Math.SE has some tags where people often post problems that they believe are interesting & non-trivial in some way.

• "recreational-mathematics"
  For instance: What is the maximum volume that can be contained by a sheet of paper?

• "puzzle"
  For instance: How few $(42^\circ,60^\circ,78^\circ)$ triangles can an equilateral triangle be divided into?

• "contest-math"
  For instance: Find all functions $f$ such that if $a+b$ is a square, then $f(a)+f(b)$ is a square

I think the problems you provided here are too straightforward for Math.SE -- Q1 and Q4 look like standard textbook exercises, and I'll elaborate on Q2 and Q3 below. But perhaps you could try to create some more challenging problems to post there as well. It could be a good source of inspiration to continue developing your math chops! :)

• Q2 seems straightforward if you know how solve systems of arbitrarily many linear equations (which is covered at the beginning of Linear Algebra, and sometimes the end of Precalculus). You have $6$ unknowns ($3$ coefficients for each of $p$ and $g$) and $8$ linear equations ($5$ equations from equating the coefficients in $p(x)^2 - g(x)^2 = r(x),$ and $3$ more equations from the differences in side lengths for $x=0,1,2$), so you can just solve the system to find $p$ and $g$ exactly, and then the problem is essentially solved.

• Q3 looks a little bit more interesting but it's still straightforward for people who have taken an Introduction to Proofs course -- they'll naturally think of this number as having digits $abc,$ and arrive at \begin{align*} 1101 &= (a + 10b + 100c) + (100a + 10b + c) \\ &= 101(a+c) + 20b, \end{align*} and notice a contradiction: $a+c$ must end in $1,$ yet also $a+c=10$ (because $\frac{1101-(9)(20)}{101} \leq a+c \leq \frac{1101}{101}$).