Quadratic equation with ten 1-s and ten 2-s.

The powers of mutually inverse numbers added to √3.

A single---line solution of a trigonometric equation

A simply evaluated monstrous sum.

Another calculus problem from Putnam 2005 competition.

A simple problem with a smart solution. Can we cover a 10×10 square with 1×4 tiles?

The exact value of cos(π/7) cos(2π/7) cos(4π/7) cos(8π/7) cos(16π/7) cos(32π/7)

Putnam 2005. Another application of Feynman's trick. Integral of ln(x+1)/(x²+1) in (0,1).

Integral of sin(x)/x in the interval (0,1). Feynmans' trick not involving complex numbers.

An equation containing 2023 exponentiations of x and number π

A segment dividing the median in given ratio

The Christmas Tree Problem

Geometric proofs of some non-geometric facts. Algebraic identities.

The least number with sum of digits equal to 10 in numeric systems base both 10 and 8.

In triangle ABC find point К so that triangles AKB, BKC and AKC have same area. Two methods.

Ratio of the sum of inverse cubes of all positive integers to the ones neither multiples of 2 nor 3.

Find the positive (real) root of an equation: ∛(20x+22) − ∛(20x−2) = 2

Three powers of 4 added to a perfect square

Another motion problem solved in a purely arithmetic way

Is ⌊(44+√2022)¹⁰⁰⁰⁰⁰⁰⌋ even or odd?

A 4th degree equation for integers: x²+x=y⁴+y³+y²+y. Unusual solving method.

Sum of low factorials equal to a perfect square. (A classic maths problem)

A tricky arithmetic problem to solve in mind.

A problem from American Math Competition involving absolute values.

A system of equations leading to ... Egyptian triangle

Fast proof of triangle inequalities for real numbers

Nested square roots evaluated to an integer

A 115-year-old trigonometric equation

Another geometric problem about finding the value of an angle.

Six integral parts (floors) summed up to 12345

An equation with numerous nested square roots

Kettering University Math Olympiad missing solutions

A mathematical joke, involving fractional and integral parts

Four Factorials in One Equation

Solve the equation x²+x²/(x+1)²−3=0 (wordless)

A mere arithmetic (English subtitles)

System of simultaneous equations (East Germany, 1980)

Mathematical pursuit problems (English subtitles)

Three Linked Squares

A square turned around its vertex

System of simultaneous equations (allegedly by Ramanujan)

Solve in integers: x²+y²+z²=x²y²

The area of a trapezium

Split clock face into 3 matching parts

Циферблат — на три равные части!

To grasp the immensity! About infinitely tall power towers. (English subtitles)

For a given set, write a code to list all subsets of given size.

Anomalous Cancellations in Depth

Let's prove the obvious!

Inscribed Hexagon. When the drawing matters.

Coding Challenge. Can you do it in a single loop?

Three segments in a triangle

2021 American Math Competition (AMC) 12B. Part III. Problems 18-21

2021 American Math Competition (AMC) 12B. Part II. Problems 11-17

2021 American Math Competition (AMC) 12B. Part I. Problems 1-10

The hardest task of Russia's 2020 Unified State Exam is made even harder but more consistent.

Napoleon's Theorem

Three Tangent Circles

2020 Australian Mathematical Olympiad. All solutions from Day 1

Невозможно возможно ... и объяснимо (продолжение темы канала Valery Volkov)