Other equations

  • Building Tetrahedra
    problem

    Building tetrahedra

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    Can you make a tetrahedron whose faces all have the same perimeter?
  • Real(ly) numbers
    problem

    Real(ly) numbers

    Age
    16 to 18
    Challenge level
    filled star filled star empty star
    If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3. What is the largest value that any of the numbers can have?