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

Showing 1,153–1,198 of 1,198

  • 9.55Equations

    Locked

    A system with reciprocals

    Difficulty 9 of 9+405 XP

  • 9.56Calculus

    Locked

    An integral with two logarithms

    Difficulty 9 of 9+405 XP

  • 9.57Arithmetic

    Locked

    Primes dividing values of a quadratic

    Difficulty 9 of 9+405 XP

  • 9.58Probability

    Locked

    Back within five steps

    Difficulty 9 of 9+405 XP

  • 9.59Algebra

    Locked

    A sum over complex roots of unity

    Difficulty 9 of 9+405 XP

  • 9.60Geometry

    Locked

    Integer triangles with a doubled angle

    Difficulty 9 of 9+405 XP

  • 9.61Arithmetic

    Locked

    Central binomial coefficients and nine

    Difficulty 9 of 9+405 XP

  • 9.62Combinatorics

    Locked

    No doubles and no triples

    Difficulty 9 of 9+405 XP

  • 9.63Algebra

    Locked

    A sequence with the integer part of a square root

    Difficulty 9 of 9+405 XP

  • 9.64Geometry

    Locked

    The smallest lattice pentagon

    Difficulty 9 of 9+405 XP

  • 9.65Arithmetic

    Locked

    The mean of odd squares

    Difficulty 9 of 9+405 XP

  • 9.66Probability

    Locked

    Until one colour runs out

    Difficulty 9 of 9+405 XP

  • 9.67Algebra

    Locked

    A sequence that grows ever more slowly

    Difficulty 9 of 9+405 XP

  • 9.68Geometry

    Locked

    A sphere touching all the edges

    Difficulty 9 of 9+405 XP

  • 9.69Arithmetic

    Locked

    A sum of integer parts

    Difficulty 9 of 9+405 XP

  • 9.70Combinatorics

    Locked

    Rooks that barely interfere

    Difficulty 9 of 9+405 XP

  • 9.71Equations

    Locked

    A triple composition with the fractional part

    Difficulty 9 of 9+405 XP

  • 9.72Calculus

    Locked

    The largest value of an integral

    Difficulty 9 of 9+405 XP

  • 9.73Arithmetic

    Locked

    A multiple of the number of divisors

    Difficulty 9 of 9+405 XP

  • 9.74Combinatorics

    Locked

    Tokens spreading along a line

    Difficulty 9 of 9+405 XP

  • 9.75Functions

    Locked

    Functions whose second iterate is a shift

    Difficulty 9 of 9+405 XP

  • 9.76Geometry

    Locked

    A sliding segment

    Difficulty 9 of 9+405 XP

  • 9.77Arithmetic

    Locked

    Ones first, then zeros

    Difficulty 9 of 9+405 XP

  • 9.78Logic

    Locked

    Dwarves and hats of five colours

    Difficulty 9 of 9+405 XP

  • 9.79Algebra

    Locked

    A polynomial in a composition equation

    Difficulty 9 of 9+405 XP

  • 9.80Geometry

    Locked

    Sides divided by distances

    Difficulty 9 of 9+405 XP

  • 9.81Arithmetic

    Locked

    A chain of divisors

    Difficulty 9 of 9+405 XP

  • 9.82Combinatorics

    Locked

    Seven numbers out of twenty-one

    Difficulty 9 of 9+405 XP

  • 9.83Functions

    Locked

    A function on the integers with a doubled argument

    Difficulty 9 of 9+405 XP

  • 9.84Geometry

    Locked

    Angle bisectors and two equal sums

    Difficulty 9 of 9+405 XP

  • 9.85Arithmetic

    Locked

    Take the root or add five

    Difficulty 9 of 9+405 XP

  • 9.86Combinatorics

    Locked

    Ten lamps and two kinds of sequences

    Difficulty 9 of 9+405 XP

  • 9.87Algebra

    Locked

    A maximum on a sphere

    Difficulty 9 of 9+405 XP

  • 9.88Calculus

    Locked

    A limit of a difference of compositions

    Difficulty 9 of 9+405 XP

  • 9.89Arithmetic

    Locked

    A product dividing a sum of squares

    Difficulty 9 of 9+405 XP

  • 9.90Probability

    Locked

    Tossing until one of two patterns

    Difficulty 9 of 9+405 XP

  • 9.91Algebra

    Locked

    A polynomial and the condition ab + bc + ca = 0

    Difficulty 9 of 9+405 XP

  • 9.92Geometry

    Locked

    A line through two centres of a triangle

    Difficulty 9 of 9+405 XP

  • 9.93Arithmetic

    Locked

    A divisor of 2ⁿ + 1

    Difficulty 9 of 9+405 XP

  • 9.94Combinatorics

    Locked

    Moving blocks to the front of a row

    Difficulty 9 of 9+405 XP

  • 9.95Equations

    Locked

    A cyclic system of three cubic equations

    Difficulty 9 of 9+405 XP

  • 9.96Calculus

    Locked

    A function with a bounded derivative

    Difficulty 9 of 9+405 XP

  • 9.97Arithmetic

    Locked

    An exponential equation with a square

    Difficulty 9 of 9+405 XP

  • 9.98Combinatorics

    Locked

    Coloured corners of a rectangle

    Difficulty 9 of 9+405 XP

  • 9.99Functions

    Locked

    A function on the integers and triples with zero sum

    Difficulty 9 of 9+405 XP

  • 9.100Geometry

    Locked

    Two cevians in an isosceles triangle

    Difficulty 9 of 9+405 XP