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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 625–672 of 1,198

4.127Equations
Locked
A system with a single solution
Difficulty 4 of 9+80 XP
4.128Functions
Locked
The range of a shifted exponential
Difficulty 4 of 9+80 XP
4.129Geometry
Locked
A sphere around a cone
Difficulty 4 of 9+80 XP
4.130Combinatorics
Locked
Anagrams that start and end with A
Difficulty 4 of 9+80 XP
4.131Equations
Locked
Four, six and nine
Difficulty 4 of 9+80 XP
4.132Calculus
Locked
A series with sum 9
Difficulty 4 of 9+80 XP
4.133Geometry
Locked
Two space diagonals
Difficulty 4 of 9+80 XP
4.134Probability
Locked
Five numbers from their statistics
Difficulty 4 of 9+80 XP
4.135Equations
Locked
The product of sine and cosine
Difficulty 4 of 9+80 XP
4.136Functions
Locked
The greatest and the least value
Difficulty 4 of 9+80 XP
4.137Geometry
Locked
A square from a vertex and a line
Difficulty 4 of 9+80 XP
4.138Combinatorics
Locked
A coefficient in a sum of six powers
Difficulty 4 of 9+80 XP
4.139Equations
Locked
The same trinomial twice
Difficulty 4 of 9+80 XP
4.140Calculus
Locked
From arithmetic to geometric
Difficulty 4 of 9+80 XP
4.141Geometry
Locked
Where the altitudes meet
Difficulty 4 of 9+80 XP
4.142Probability
Locked
Drawing until a red one appears
Difficulty 4 of 9+80 XP
4.143Equations
Locked
The unknown in the base and the exponent
Difficulty 4 of 9+80 XP
4.144Functions
Locked
Two bacterial cultures
Difficulty 4 of 9+80 XP
4.145Geometry
Locked
The area of a plot of land
Difficulty 4 of 9+80 XP
4.146Combinatorics
Locked
A patrol without the siblings
Difficulty 4 of 9+80 XP
4.147Equations
Locked
A growing town and a shrinking town
Difficulty 4 of 9+80 XP
4.148Calculus
Locked
Regular deposits
Difficulty 4 of 9+80 XP
4.149Geometry
Locked
Two trees across a river
Difficulty 4 of 9+80 XP
4.150Probability
Locked
Four cards, four ranks
Difficulty 4 of 9+80 XP
5.1Arithmetic
Locked
Sum of integers coprime to 1000
Difficulty 5 of 9+125 XP
5.2Equations
Locked
Positive integer solutions of x² − y² = 2^100
Difficulty 5 of 9+125 XP
5.3Arithmetic
Locked
Smallest n > 1 with (n+1) dividing sum of squares
Difficulty 5 of 9+125 XP
5.4Combinatorics
Locked
Ordered triples (a, b, c) with product abc = 1000
Difficulty 5 of 9+125 XP
5.5Combinatorics
Locked
Sum of all 3-digit numbers using digits 1, 2, 3
Difficulty 5 of 9+125 XP
5.6Arithmetic
Locked
How many values of n² − n + 11 are prime for n = 1 to 10?
Difficulty 5 of 9+125 XP
5.7Arithmetic
Locked
7^(7^7) mod 100
Difficulty 5 of 9+125 XP
5.8Geometry
Locked
Lattice points in the disk x² + y² ≤ 25
Difficulty 5 of 9+125 XP
5.9Algebra
Locked
Integer part of (√2 + 1)⁸
Difficulty 5 of 9+125 XP
5.10Arithmetic
Locked
GCD of Fibonacci numbers F₁₀₀ and F₇₂
Difficulty 5 of 9+125 XP
5.11Arithmetic
Locked
Perfect sixth powers up to 10^6
Difficulty 5 of 9+125 XP
5.12Arithmetic
Locked
Sum of ⌊√k⌋ for k = 1 to 100
Difficulty 5 of 9+125 XP
5.13Arithmetic
Locked
17^17 mod 100
Difficulty 5 of 9+125 XP
5.14Combinatorics
Locked
Tiling a 2 × 10 grid with 1 × 2 dominoes
Difficulty 5 of 9+125 XP
5.15Arithmetic
Locked
Sum of n ≤ 1000 with n² ≡ 1 (mod 1000)
Difficulty 5 of 9+125 XP
5.16Combinatorics
Locked
Ordered representations of 100 as sum of 3 positive integers
Difficulty 5 of 9+125 XP
5.17Arithmetic
Locked
Integers ≤ 1000 with an odd number of divisors
Difficulty 5 of 9+125 XP
5.18Algebra
Locked
Maximum of xy + yz + zx given x + y + z = 1
Difficulty 5 of 9+125 XP
5.19Combinatorics
Locked
C(200, 100) mod 5
Difficulty 5 of 9+125 XP
5.20Arithmetic
Locked
Sophie Germain primes up to 30
Difficulty 5 of 9+125 XP
5.21Combinatorics
Locked
Partitions of 10 into distinct positive parts
Difficulty 5 of 9+125 XP
5.22Equations
Locked
Sum of integers n where n² − 19n + 99 is a perfect square
Difficulty 5 of 9+125 XP
5.23Combinatorics
Locked
Onto functions from {1,…,5} to {1,2,3}
Difficulty 5 of 9+125 XP
5.24Functions
Locked
Solutions of f(f(x)) = x for f(x) = x² − 2
Difficulty 5 of 9+125 XP

Solve problems

All problems

A system with a single solution

The range of a shifted exponential

A sphere around a cone

Anagrams that start and end with A

Four, six and nine

A series with sum 9

Two space diagonals

Five numbers from their statistics

The product of sine and cosine

The greatest and the least value

A square from a vertex and a line

A coefficient in a sum of six powers

The same trinomial twice

From arithmetic to geometric

Where the altitudes meet

Drawing until a red one appears

The unknown in the base and the exponent

Two bacterial cultures

The area of a plot of land

A patrol without the siblings

A growing town and a shrinking town

Regular deposits

Two trees across a river

Four cards, four ranks

Sum of integers coprime to 1000

Positive integer solutions of x² − y² = 2^100

Smallest n > 1 with (n+1) dividing sum of squares

Ordered triples (a, b, c) with product abc = 1000

Sum of all 3-digit numbers using digits 1, 2, 3

How many values of n² − n + 11 are prime for n = 1 to 10?

7^(7^7) mod 100

Lattice points in the disk x² + y² ≤ 25

Integer part of (√2 + 1)⁸

GCD of Fibonacci numbers F₁₀₀ and F₇₂

Perfect sixth powers up to 10^6

Sum of ⌊√k⌋ for k = 1 to 100

17^17 mod 100

Tiling a 2 × 10 grid with 1 × 2 dominoes

Sum of n ≤ 1000 with n² ≡ 1 (mod 1000)

Ordered representations of 100 as sum of 3 positive integers

Integers ≤ 1000 with an odd number of divisors

Maximum of xy + yz + zx given x + y + z = 1

C(200, 100) mod 5

Sophie Germain primes up to 30

Partitions of 10 into distinct positive parts

Sum of integers n where n² − 19n + 99 is a perfect square

Onto functions from {1,…,5} to {1,2,3}

Solutions of f(f(x)) = x for f(x) = x² − 2