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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 673–720 of 1,198

5.25Calculus
Locked
Series ∑ n²/2ⁿ
Difficulty 5 of 9+125 XP
5.26Arithmetic
Locked
Largest n such that (n + 10) divides n³ + 100
Difficulty 5 of 9+125 XP
5.27Algebra
Locked
x⁴ + y⁴ + z⁴ from elementary symmetric polynomials
Difficulty 5 of 9+125 XP
5.28Combinatorics
Locked
10-digit binary strings with no two consecutive 1s
Difficulty 5 of 9+125 XP
5.29Calculus
Locked
Series ∑ k/2^k
Difficulty 5 of 9+125 XP
5.30Algebra
Locked
Sum of integers n with |n² − 10n| < 5
Difficulty 5 of 9+125 XP
5.31Combinatorics
Locked
5-element subsets of {1, …, 20} with no two consecutive elements
Difficulty 5 of 9+125 XP
5.32Arithmetic
Locked
GCD of 1! + 2! + … + 10! and 10!
Difficulty 5 of 9+125 XP
5.33Functions
Locked
Real solutions of x² = 2^x
Difficulty 5 of 9+125 XP
5.34Combinatorics
Locked
Non-negative 4-tuples summing to 10 with a + b ≥ 3
Difficulty 5 of 9+125 XP
5.35Arithmetic
Locked
(1⁵ + 2⁵ + … + 100⁵) mod 4
Difficulty 5 of 9+125 XP
5.36Arithmetic
Locked
(∑_{k=1}^{100} k · k!) mod 100
Difficulty 5 of 9+125 XP
5.37Arithmetic
Locked
Sum of n where n² + 3n + 5 is a prime dividing n² + 1
Difficulty 5 of 9+125 XP
5.38Equations
Locked
Ordered pairs (x, y) with 1/x + 1/y = 1/12
Difficulty 5 of 9+125 XP
5.39Arithmetic
Locked
Sum of n ≤ 1000 with φ(n) = n/2
Difficulty 5 of 9+125 XP
5.40Combinatorics
Locked
Positive integer solutions of x + 2y + 3z = 30
Difficulty 5 of 9+125 XP
5.41Calculus
Locked
Series ∑ k(k+1)/2^k
Difficulty 5 of 9+125 XP
5.42Combinatorics
Locked
Tiling a 1 × 6 strip with red, blue, and white tiles
Difficulty 5 of 9+125 XP
5.43Algebra
Locked
Maximum of x²y³z given x + y + z = 1
Difficulty 5 of 9+125 XP
5.44Arithmetic
Locked
Largest prime factor of 101,010,101
Difficulty 5 of 9+125 XP
5.45Combinatorics
Locked
Vandermonde sum C(10,0)² + C(10,1)² + … + C(10,10)²
Difficulty 5 of 9+125 XP
5.46Combinatorics
Locked
Lattice paths from (0,0) to (10,10) passing through (5,5)
Difficulty 5 of 9+125 XP
5.47Arithmetic
Locked
Product of 4 consecutive integers – largest guaranteed divisor
Difficulty 5 of 9+125 XP
5.48Arithmetic
Locked
Wieferich primes up to 20
Difficulty 5 of 9+125 XP
5.49Calculus
Locked
Maximum area of rectangle inscribed in right triangle with legs 3 and 4
Difficulty 5 of 9+125 XP
5.50Arithmetic
Locked
Primes appearing in twin prime pairs up to 100
Difficulty 5 of 9+125 XP
5.51Algebra
Locked
Cubes of the roots
Difficulty 5 of 9+125 XP
5.52Functions
Locked
A parabola on a bounded interval
Difficulty 5 of 9+125 XP
5.53Geometry
Locked
How far apart two parallel lines are
Difficulty 5 of 9+125 XP
5.54Combinatorics
Locked
A round table without a neighbour
Difficulty 5 of 9+125 XP
5.55Equations
Locked
Powers of five in an equation
Difficulty 5 of 9+125 XP
5.56Calculus
Locked
A cycling training camp
Difficulty 5 of 9+125 XP
5.57Geometry
Locked
A centre on the x-axis
Difficulty 5 of 9+125 XP
5.58Probability
Locked
The product on two dice
Difficulty 5 of 9+125 XP
5.59Algebra
Locked
An unknown coefficient of a polynomial
Difficulty 5 of 9+125 XP
5.60Functions
Locked
The inverse of a rational function
Difficulty 5 of 9+125 XP
5.61Geometry
Locked
The area of a triangle from coordinates
Difficulty 5 of 9+125 XP
5.62Logic
Locked
When the implication fails
Difficulty 5 of 9+125 XP
5.63Equations
Locked
A system with reciprocals
Difficulty 5 of 9+125 XP
5.64Calculus
Locked
The derivative of a product at a point
Difficulty 5 of 9+125 XP
5.65Arithmetic
Locked
A deposit with taxed interest
Difficulty 5 of 9+125 XP
5.66Combinatorics
Locked
An inequality with a binomial coefficient
Difficulty 5 of 9+125 XP
5.67Algebra
Locked
A fraction and a power of the imaginary unit
Difficulty 5 of 9+125 XP
5.68Functions
Locked
Sine of a double angle
Difficulty 5 of 9+125 XP
5.69Geometry
Locked
A circle inside a rhombus
Difficulty 5 of 9+125 XP
5.70Fractions
Locked
When the result is a whole number
Difficulty 5 of 9+125 XP
5.71Equations
Locked
A square root and checking the result
Difficulty 5 of 9+125 XP
5.72Calculus
Locked
The fourth term of an infinite series
Difficulty 5 of 9+125 XP

Solve problems

All problems

Series ∑ n²/2ⁿ

Largest n such that (n + 10) divides n³ + 100

x⁴ + y⁴ + z⁴ from elementary symmetric polynomials

10-digit binary strings with no two consecutive 1s

Series ∑ k/2^k

Sum of integers n with |n² − 10n| < 5

5-element subsets of {1, …, 20} with no two consecutive elements

GCD of 1! + 2! + … + 10! and 10!

Real solutions of x² = 2^x

Non-negative 4-tuples summing to 10 with a + b ≥ 3

(1⁵ + 2⁵ + … + 100⁵) mod 4

(∑_{k=1}^{100} k · k!) mod 100

Sum of n where n² + 3n + 5 is a prime dividing n² + 1

Ordered pairs (x, y) with 1/x + 1/y = 1/12

Sum of n ≤ 1000 with φ(n) = n/2

Positive integer solutions of x + 2y + 3z = 30

Series ∑ k(k+1)/2^k

Tiling a 1 × 6 strip with red, blue, and white tiles

Maximum of x²y³z given x + y + z = 1

Largest prime factor of 101,010,101

Vandermonde sum C(10,0)² + C(10,1)² + … + C(10,10)²

Lattice paths from (0,0) to (10,10) passing through (5,5)

Product of 4 consecutive integers – largest guaranteed divisor

Wieferich primes up to 20

Maximum area of rectangle inscribed in right triangle with legs 3 and 4

Primes appearing in twin prime pairs up to 100

Cubes of the roots

A parabola on a bounded interval

How far apart two parallel lines are

A round table without a neighbour

Powers of five in an equation

A cycling training camp

A centre on the x-axis

The product on two dice

An unknown coefficient of a polynomial

The inverse of a rational function

The area of a triangle from coordinates

When the implication fails

A system with reciprocals

The derivative of a product at a point

A deposit with taxed interest

An inequality with a binomial coefficient

A fraction and a power of the imaginary unit

Sine of a double angle

A circle inside a rhombus

When the result is a whole number

A square root and checking the result

The fourth term of an infinite series