Weekly problem archive

Problem of the Week.

Every Monday, a fresh problem from the Think-Nth tutors. Sometimes a calculus curio, sometimes a number-theory gem, sometimes a competition classic. Submit your solution by email — the best gets published with attribution.

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This week

The unfinished sum

\sum_{k=1}^{n} k^2 = \frac{n(n+1)(2n+1)}{6}

Induction

Last week

A friendly integral

\int_{0}^{\pi/2} \frac{\sin x}{\sin x + \cos x} dx

Calculus

Two weeks ago

Rank in disguise

\text{rank}\begin{pmatrix} 1 & 2 & 3 \\ 2 & 4 & 6 \\ 3 & 6 & 9 \end{pmatrix} = ?

Linear Algebra

Three weeks ago

Small gaps

p_{n+1} - p_n \le 246

Number Theory

Four weeks ago

The medical test paradox

P(\text{sick} \mid +) = ?

Probability

Five weeks ago

Power of a point

PA \cdot PB = PC \cdot PD

Geometry

Six weeks ago

Diagonalise

Av = \lambda v

Linear Algebra

Seven weeks ago

Lagrange's Theorem

|H| \; \big| \; |G|

Abstract Algebra

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