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Solve problems

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 1,105–1,152 of 1,198

9.7Equations
Locked
The product of the real roots of a quartic
Difficulty 9 of 9+405 XP
9.8Geometry
Locked
The shortest broken line
Difficulty 9 of 9+405 XP
9.9Arithmetic
Locked
The remainder of a large factorial
Difficulty 9 of 9+405 XP
9.10Logic
Locked
Both of my neighbours
Difficulty 9 of 9+405 XP
9.11Algebra
Locked
A decreasing product of cubic fractions
Difficulty 9 of 9+405 XP
9.12Geometry
Locked
A tangent at a vertex and an angle bisector
Difficulty 9 of 9+405 XP
9.13Arithmetic
Locked
Reversed digits in two bases
Difficulty 9 of 9+405 XP
9.14Combinatorics
Locked
At most half of the pile
Difficulty 9 of 9+405 XP
9.15Equations
Locked
A quadratic equation with the floor function
Difficulty 9 of 9+405 XP
9.16Geometry
Locked
A cyclic quadrilateral with two equal sides
Difficulty 9 of 9+405 XP
9.17Arithmetic
Locked
A common factor of neighbouring values
Difficulty 9 of 9+405 XP
9.18Combinatorics
Locked
As many kings as possible on a narrow board
Difficulty 9 of 9+405 XP
9.19Functions
Locked
A function on the positive integers
Difficulty 9 of 9+405 XP
9.20Geometry
Locked
A circle touching a side at its midpoint
Difficulty 9 of 9+405 XP
9.21Arithmetic
Locked
Four consecutive numbers
Difficulty 9 of 9+405 XP
9.22Combinatorics
Locked
A path without three equal steps
Difficulty 9 of 9+405 XP
9.23Algebra
Locked
The value of an integer polynomial at 7
Difficulty 9 of 9+405 XP
9.24Geometry
Locked
A triangle cut out by three cevians
Difficulty 9 of 9+405 XP
9.25Arithmetic
Locked
Digit sums of two neighbours
Difficulty 9 of 9+405 XP
9.26Combinatorics
Locked
Colouring a decagon up to rotation
Difficulty 9 of 9+405 XP
9.27Equations
Locked
A cyclic system of three quadratic equations
Difficulty 9 of 9+405 XP
9.28Geometry
Locked
A circle through two vertices and the incentre
Difficulty 9 of 9+405 XP
9.29Arithmetic
Locked
Twos in a product
Difficulty 9 of 9+405 XP
9.30Combinatorics
Locked
Merging numbers on a board
Difficulty 9 of 9+405 XP
9.31Equations
Locked
Fractional parts of a number and of its reciprocal
Difficulty 9 of 9+405 XP
9.32Geometry
Locked
A line through the antipode on the incircle
Difficulty 9 of 9+405 XP
9.33Arithmetic
Locked
A sum of two powers and the number seven
Difficulty 9 of 9+405 XP
9.34Probability
Locked
A vote count with a tie
Difficulty 9 of 9+405 XP
9.35Algebra
Locked
Fourth powers under two symmetric conditions
Difficulty 9 of 9+405 XP
9.36Geometry
Locked
A tetrahedron with equal opposite edges
Difficulty 9 of 9+405 XP
9.37Arithmetic
Locked
Euler's function and the number of divisors
Difficulty 9 of 9+405 XP
9.38Combinatorics
Locked
As few one-coloured triangles as possible
Difficulty 9 of 9+405 XP
9.39Algebra
Locked
Bounded numbers with zero sum
Difficulty 9 of 9+405 XP
9.40Geometry
Locked
Two notable centres of a triangle
Difficulty 9 of 9+405 XP
9.41Arithmetic
Locked
A Fibonacci number and a thousand
Difficulty 9 of 9+405 XP
9.42Combinatorics
Locked
Secret Santa for married couples
Difficulty 9 of 9+405 XP
9.43Functions
Locked
A non-decreasing function with a shifted argument
Difficulty 9 of 9+405 XP
9.44Geometry
Locked
The least sum of distances to the vertices
Difficulty 9 of 9+405 XP
9.45Arithmetic
Locked
Right triangles with a given perimeter
Difficulty 9 of 9+405 XP
9.46Logic
Locked
Forty coins on a balance
Difficulty 9 of 9+405 XP
9.47Algebra
Locked
A cyclic expression with zero sum
Difficulty 9 of 9+405 XP
9.48Geometry
Locked
A chain of touching circles
Difficulty 9 of 9+405 XP
9.49Arithmetic
Locked
A number made of ones
Difficulty 9 of 9+405 XP
9.50Combinatorics
Locked
No differences four or seven
Difficulty 9 of 9+405 XP
9.51Functions
Locked
An increasing function composed with itself
Difficulty 9 of 9+405 XP
9.52Geometry
Locked
The product of all sides and diagonals
Difficulty 9 of 9+405 XP
9.53Arithmetic
Locked
Doubling without changing the digit sum
Difficulty 9 of 9+405 XP
9.54Combinatorics
Locked
Two piles and a joint removal
Difficulty 9 of 9+405 XP

Solve problems

All problems

The product of the real roots of a quartic

The shortest broken line

The remainder of a large factorial

Both of my neighbours

A decreasing product of cubic fractions

A tangent at a vertex and an angle bisector

Reversed digits in two bases

At most half of the pile

A quadratic equation with the floor function

A cyclic quadrilateral with two equal sides

A common factor of neighbouring values

As many kings as possible on a narrow board

A function on the positive integers

A circle touching a side at its midpoint

Four consecutive numbers

A path without three equal steps

The value of an integer polynomial at 7

A triangle cut out by three cevians

Digit sums of two neighbours

Colouring a decagon up to rotation

A cyclic system of three quadratic equations

A circle through two vertices and the incentre

Twos in a product

Merging numbers on a board

Fractional parts of a number and of its reciprocal

A line through the antipode on the incircle

A sum of two powers and the number seven

A vote count with a tie

Fourth powers under two symmetric conditions

A tetrahedron with equal opposite edges

Euler's function and the number of divisors

As few one-coloured triangles as possible

Bounded numbers with zero sum

Two notable centres of a triangle

A Fibonacci number and a thousand

Secret Santa for married couples

A non-decreasing function with a shifted argument

The least sum of distances to the vertices

Right triangles with a given perimeter

Forty coins on a balance

A cyclic expression with zero sum

A chain of touching circles

A number made of ones

No differences four or seven

An increasing function composed with itself

The product of all sides and diagonals

Doubling without changing the digit sum

Two piles and a joint removal