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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 481–528 of 1,198

3.113Geometry
Locked
A tangent parallel to a side
Difficulty 3 of 9+45 XP
3.114Arithmetic
Locked
Eighteen divisors
Difficulty 3 of 9+45 XP
3.115Equations
Locked
A product of four brackets
Difficulty 3 of 9+45 XP
3.116Functions
Locked
A price in steps of fifty cents
Difficulty 3 of 9+45 XP
3.117Geometry
Locked
The foot of an altitude and a point of contact
Difficulty 3 of 9+45 XP
3.118Combinatorics
Locked
Books as rewards
Difficulty 3 of 9+45 XP
3.119Algebra
Locked
Cube roots in the denominator
Difficulty 3 of 9+45 XP
3.120Functions
Locked
A parameter from the least value
Difficulty 3 of 9+45 XP
3.121Geometry
Locked
A diagonal as a diameter
Difficulty 3 of 9+45 XP
3.122Logic
Locked
Divisible by exactly one
Difficulty 3 of 9+45 XP
3.123Equations
Locked
An equation with the unknown in the denominator
Difficulty 3 of 9+45 XP
3.124Functions
Locked
The smallest triangle cut off
Difficulty 3 of 9+45 XP
3.125Geometry
Locked
The common part of two discs
Difficulty 3 of 9+45 XP
3.126Arithmetic
Locked
Terminating decimals
Difficulty 3 of 9+45 XP
3.127Algebra
Locked
A sum of two cube roots
Difficulty 3 of 9+45 XP
3.128Functions
Locked
How often f(f(x)) = 0
Difficulty 3 of 9+45 XP
3.129Geometry
Locked
The gap under two discs
Difficulty 3 of 9+45 XP
3.130Combinatorics
Locked
Cards that differ by seven
Difficulty 3 of 9+45 XP
4.1Arithmetic
Locked
Units digit of 7^100
Difficulty 4 of 9+80 XP
4.2Arithmetic
Locked
Remainder of 2^50 divided by 7
Difficulty 4 of 9+80 XP
4.3Arithmetic
Locked
Divisibility by 3 or 7
Difficulty 4 of 9+80 XP
4.4Arithmetic
Locked
Sum of divisors of 360
Difficulty 4 of 9+80 XP
4.5Algebra
Locked
Common ratio of geometric series
Difficulty 4 of 9+80 XP
4.6Geometry
Locked
Area of triangle with sides 13, 14, 15
Difficulty 4 of 9+80 XP
4.7Algebra
Locked
Logarithmic equation
Difficulty 4 of 9+80 XP
4.8Combinatorics
Locked
Combinations – committee of 4 from 10
Difficulty 4 of 9+80 XP
4.9Probability
Locked
Probability of sum 8 on two dice
Difficulty 4 of 9+80 XP
4.10Arithmetic
Locked
Numbers with exactly 3 divisors
Difficulty 4 of 9+80 XP
4.11Functions
Locked
Composite function f(f(2))
Difficulty 4 of 9+80 XP
4.12Arithmetic
Locked
Largest prime factor of 2310
Difficulty 4 of 9+80 XP
4.13Combinatorics
Locked
3-digit palindromes
Difficulty 4 of 9+80 XP
4.14Algebra
Locked
Arithmetic sequence – find a₁₀
Difficulty 4 of 9+80 XP
4.15Algebra
Locked
Telescoping sum
Difficulty 4 of 9+80 XP
4.16Algebra
Locked
Infinite nested radical √(2 + √(2 + …))
Difficulty 4 of 9+80 XP
4.17Combinatorics
Locked
Diagonals of a 12-gon
Difficulty 4 of 9+80 XP
4.18Algebra
Locked
x + 1/x = 3, find x² + 1/x²
Difficulty 4 of 9+80 XP
4.19Combinatorics
Locked
8 people seated at a round table
Difficulty 4 of 9+80 XP
4.20Arithmetic
Locked
100! mod 97
Difficulty 4 of 9+80 XP
4.21Functions
Locked
Minimum of f(x) = x² − 6x + 13
Difficulty 4 of 9+80 XP
4.22Combinatorics
Locked
Distributing 10 balls into 3 boxes
Difficulty 4 of 9+80 XP
4.23Algebra
Locked
Euler's polynomial aₙ = n² − n + 41
Difficulty 4 of 9+80 XP
4.24Algebra
Locked
Infinite nested radical √(x + √(x + …)) = 5
Difficulty 4 of 9+80 XP
4.25Algebra
Locked
Geometric sequence – find a₁
Difficulty 4 of 9+80 XP
4.26Equations
Locked
Integer solutions of x² − y² = 84
Difficulty 4 of 9+80 XP
4.27Arithmetic
Locked
Integers coprime to 30 up to 1000
Difficulty 4 of 9+80 XP
4.28Arithmetic
Locked
GCD of Mersenne numbers
Difficulty 4 of 9+80 XP
4.29Combinatorics
Locked
4-digit numbers with digit sum 9
Difficulty 4 of 9+80 XP
4.30Arithmetic
Locked
Sum of 2-digit primes with digit sum 11
Difficulty 4 of 9+80 XP

Solve problems

All problems

A tangent parallel to a side

Eighteen divisors

A product of four brackets

A price in steps of fifty cents

The foot of an altitude and a point of contact

Books as rewards

Cube roots in the denominator

A parameter from the least value

A diagonal as a diameter

Divisible by exactly one

An equation with the unknown in the denominator

The smallest triangle cut off

The common part of two discs

Terminating decimals

A sum of two cube roots

How often f(f(x)) = 0

The gap under two discs

Cards that differ by seven

Units digit of 7^100

Remainder of 2^50 divided by 7

Divisibility by 3 or 7

Sum of divisors of 360

Common ratio of geometric series

Area of triangle with sides 13, 14, 15

Logarithmic equation

Combinations – committee of 4 from 10

Probability of sum 8 on two dice

Numbers with exactly 3 divisors

Composite function f(f(2))

Largest prime factor of 2310

3-digit palindromes

Arithmetic sequence – find a₁₀

Telescoping sum

Infinite nested radical √(2 + √(2 + …))

Diagonals of a 12-gon

x + 1/x = 3, find x² + 1/x²

8 people seated at a round table

100! mod 97

Minimum of f(x) = x² − 6x + 13

Distributing 10 balls into 3 boxes

Euler's polynomial aₙ = n² − n + 41

Infinite nested radical √(x + √(x + …)) = 5

Geometric sequence – find a₁

Integer solutions of x² − y² = 84

Integers coprime to 30 up to 1000

GCD of Mersenne numbers

4-digit numbers with digit sum 9

Sum of 2-digit primes with digit sum 11