Home Featured Math Problems Featured Math Problems. A growing archive of favourite problems from Think-Nth educators. Sometimes a calculus curio, sometimes a number-theory gem, sometimes a classic puzzle.
To submit a solution, email your working (a photo of handwritten work is fine) with the problem title in the subject line. We read every submission and publish the clearest one with the student's first name, only where permission is given.
Featured problem
The unfinished sum ∑ k = 1 n k 2 = n ( n + 1 ) ( 2 n + 1 ) 6 \sum_{k=1}^{n} k^2 = \frac{n(n+1)(2n+1)}{6} k = 1 ∑ n k 2 = 6 n ( n + 1 ) ( 2 n + 1 ) Induction
From the archive
A friendly integral ∫ 0 π / 2 sin x sin x + cos x d x \int_{0}^{\pi/2} \frac{\sin x}{\sin x + \cos x} dx ∫ 0 π /2 sin x + cos x sin x d x Calculus
From the archive
Rank in disguise rank ( 1 2 3 2 4 6 3 6 9 ) = ? \text{rank}\begin{pmatrix} 1 & 2 & 3 \\ 2 & 4 & 6 \\ 3 & 6 & 9 \end{pmatrix} = ? rank 1 2 3 2 4 6 3 6 9 = ? Linear Algebra
From the archive
Small gaps p n + 1 − p n ≤ 246 p_{n+1} - p_n \le 246 p n + 1 − p n ≤ 246 Number Theory
From the archive
The medical test paradox P ( sick ∣ + ) = ? P(\text{sick} \mid +) = ? P ( sick ∣ + ) = ? Probability
From the archive
Power of a point P A ⋅ P B = P C ⋅ P D PA \cdot PB = PC \cdot PD P A ⋅ P B = P C ⋅ P D Geometry
From the archive
Diagonalise Linear Algebra
From the archive
Lagrange's Theorem ∣ H ∣ ∣ ∣ G ∣ |H| \; \big| \; |G| ∣ H ∣ ∣ G ∣ Abstract Algebra
Enjoying these?
Get a tutor who thinks like this. Tell us your course and goals. We'll match you with the right tutor and put a first session on the calendar.
Think-Nth manages educator matching, scheduling and program support rather than operating as an open tutor marketplace. See how Think-Nth works →
Think-Nth
Managed online mathematics tutoring
A mathematics education company providing managed online tutoring, structured learning, and progress monitoring.
info@think-nth.org +1 484-761-0224 Online worldwide Monday–Saturday, by appointment (US Eastern Time) Learn Families Company Schools & Support Personalized Mathematics. Visible Progress.
Currency USD GBP EUR AED INR SGD AUD CAD © 2026 Think-Nth. All rights reserved. Math-only support • Personalized tutor matching • Progress monitoring • Global curriculum experience