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Problems unlock one after another, from simple all the way to genius. Every one you solve adds XP.

1,198 problems
9 difficulty levels
+5 to +405 XP per problem

All problems

Showing 529–576 of 1,198

4.31Geometry
Locked
Law of cosines – triangle with 60° angle
Difficulty 4 of 9+80 XP
4.32Functions
Locked
Functional equation f(x + 1/x)
Difficulty 4 of 9+80 XP
4.33Combinatorics
Locked
5 boys and 3 girls in a row – no two girls adjacent
Difficulty 4 of 9+80 XP
4.34Arithmetic
Locked
Number of divisors of 10!
Difficulty 4 of 9+80 XP
4.35Arithmetic
Locked
Largest integer n with n² < 1000
Difficulty 4 of 9+80 XP
4.36Equations
Locked
Product of three consecutive integers equals 120
Difficulty 4 of 9+80 XP
4.37Probability
Locked
Probability of at least 2 red balls
Difficulty 4 of 9+80 XP
4.38Geometry
Locked
Sum of sin²(1°) + sin²(2°) + … + sin²(90°)
Difficulty 4 of 9+80 XP
4.39Combinatorics
Locked
Sum of k · k! for k = 1 to 6
Difficulty 4 of 9+80 XP
4.40Algebra
Locked
Symmetric ratio when a + b + c = 0
Difficulty 4 of 9+80 XP
4.41Arithmetic
Locked
Smallest prime p with p | 2^p + 1
Difficulty 4 of 9+80 XP
4.42Combinatorics
Locked
Making change for $1 using 1¢, 5¢, 10¢
Difficulty 4 of 9+80 XP
4.43Algebra
Locked
Minimum of x² + y² given xy = 100
Difficulty 4 of 9+80 XP
4.44Equations
Locked
Positive integer solutions of 2^x = x²
Difficulty 4 of 9+80 XP
4.45Algebra
Locked
Modulus |1 + i|⁸
Difficulty 4 of 9+80 XP
4.46Algebra
Locked
Recurrence aₙ₊₁ = aₙ + 2n
Difficulty 4 of 9+80 XP
4.47Combinatorics
Locked
Coefficient of x³ in (1 + x + x²)⁴
Difficulty 4 of 9+80 XP
4.48Arithmetic
Locked
Primes of the form n² + 1 for n = 1 to 10
Difficulty 4 of 9+80 XP
4.49Combinatorics
Locked
Alternating binomial sum
Difficulty 4 of 9+80 XP
4.50Arithmetic
Locked
Perfect squares or cubes up to 1000
Difficulty 4 of 9+80 XP
4.51Equations
Locked
A logarithm inside a logarithm
Difficulty 4 of 9+80 XP
4.52Functions
Locked
An exponential through two points
Difficulty 4 of 9+80 XP
4.53Geometry
Locked
The other end of a segment
Difficulty 4 of 9+80 XP
4.54Probability
Locked
A random three-digit number
Difficulty 4 of 9+80 XP
4.55Equations
Locked
Fours and eights with exponents
Difficulty 4 of 9+80 XP
4.56Calculus
Locked
Seats in an amphitheatre
Difficulty 4 of 9+80 XP
4.57Geometry
Locked
How far is the centre of the circle
Difficulty 4 of 9+80 XP
4.58Combinatorics
Locked
One coefficient of a binomial expansion
Difficulty 4 of 9+80 XP
4.59Equations
Locked
Three powers of two
Difficulty 4 of 9+80 XP
4.60Functions
Locked
Exact values of trigonometric functions
Difficulty 4 of 9+80 XP
4.61Geometry
Locked
A perpendicular and the y-axis
Difficulty 4 of 9+80 XP
4.62Probability
Locked
Swapped digits in the record
Difficulty 4 of 9+80 XP
4.63Equations
Locked
Tangent and angles in degrees
Difficulty 4 of 9+80 XP
4.64Calculus
Locked
From the second and the fifth term
Difficulty 4 of 9+80 XP
4.65Geometry
Locked
The angle of two lines
Difficulty 4 of 9+80 XP
4.66Combinatorics
Locked
A 5-out-of-35 lottery
Difficulty 4 of 9+80 XP
4.67Equations
Locked
A sum of two distances
Difficulty 4 of 9+80 XP
4.68Functions
Locked
The inverse of a logarithmic function
Difficulty 4 of 9+80 XP
4.69Geometry
Locked
The side opposite the third angle
Difficulty 4 of 9+80 XP
4.70Probability
Locked
Two cards and an ace
Difficulty 4 of 9+80 XP
4.71Equations
Locked
When a fraction is not positive
Difficulty 4 of 9+80 XP
4.72Calculus
Locked
Double it, minus one
Difficulty 4 of 9+80 XP
4.73Geometry
Locked
A cuboid with a square base
Difficulty 4 of 9+80 XP
4.74Combinatorics
Locked
Anagrams of a magic word
Difficulty 4 of 9+80 XP
4.75Equations
Locked
A square root and a check
Difficulty 4 of 9+80 XP
4.76Calculus
Locked
Weekly savings
Difficulty 4 of 9+80 XP
4.77Geometry
Locked
A cuboid diagonal and the base
Difficulty 4 of 9+80 XP
4.78Probability
Locked
Two shooters, one target
Difficulty 4 of 9+80 XP

Solve problems

All problems

Law of cosines – triangle with 60° angle

Functional equation f(x + 1/x)

5 boys and 3 girls in a row – no two girls adjacent

Number of divisors of 10!

Largest integer n with n² < 1000

Product of three consecutive integers equals 120

Probability of at least 2 red balls

Sum of sin²(1°) + sin²(2°) + … + sin²(90°)

Sum of k · k! for k = 1 to 6

Symmetric ratio when a + b + c = 0

Smallest prime p with p | 2^p + 1

Making change for $1 using 1¢, 5¢, 10¢

Minimum of x² + y² given xy = 100

Positive integer solutions of 2^x = x²

Modulus |1 + i|⁸

Recurrence aₙ₊₁ = aₙ + 2n

Coefficient of x³ in (1 + x + x²)⁴

Primes of the form n² + 1 for n = 1 to 10

Alternating binomial sum

Perfect squares or cubes up to 1000

A logarithm inside a logarithm

An exponential through two points

The other end of a segment

A random three-digit number

Fours and eights with exponents

Seats in an amphitheatre

How far is the centre of the circle

One coefficient of a binomial expansion

Three powers of two

Exact values of trigonometric functions

A perpendicular and the y-axis

Swapped digits in the record

Tangent and angles in degrees

From the second and the fifth term

The angle of two lines

A 5-out-of-35 lottery

A sum of two distances

The inverse of a logarithmic function

The side opposite the third angle

Two cards and an ace

When a fraction is not positive

Double it, minus one

A cuboid with a square base

Anagrams of a magic word

A square root and a check

Weekly savings

A cuboid diagonal and the base

Two shooters, one target