Inequalities

  • Rationals Between...
    problem

    Rationals between...

    Age
    14 to 16
    Challenge level
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    What fractions can you find between the square roots of 65 and 67?
  • Mediant madness
    problem

    Mediant madness

    Age
    14 to 16
    Challenge level
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    Kyle and his teacher disagree about his test score - who is right?
  • Which is bigger?
    problem

    Which is bigger?

    Age
    14 to 16
    Challenge level
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    Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?

  • Tet-Trouble
    problem

    Tet-trouble

    Age
    14 to 16
    Challenge level
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    Is it possible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units?

  • Not Continued Fractions
    problem

    Not continued fractions

    Age
    14 to 18
    Challenge level
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    Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?
  • Big, Bigger, Biggest
    problem

    Big, bigger, biggest

    Age
    16 to 18
    Challenge level
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    Which is the biggest and which the smallest of $2000^{2002}, 2001^{2001} \text{and } 2002^{2000}$?

  • Tetra Inequalities
    problem

    Tetra inequalities

    Age
    16 to 18
    Challenge level
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    Can you prove that in every tetrahedron there is a vertex where the three edges meeting at that vertex have lengths which could be the sides of a triangle?

  • Unit interval
    problem

    Unit interval

    Age
    16 to 18
    Challenge level
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    Can you prove our inequality holds for all values of x and y between 0 and 1?

  • Inner equality
    problem

    Inner equality

    Age
    16 to 18
    Challenge level
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    Can you solve this inequalities challenge?

  • Giants
    problem

    Giants

    Age
    16 to 18
    Challenge level
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    Which is the bigger, 9^10 or 10^9 ? Which is the bigger, 99^100 or 100^99 ?