Conjecturing and generalising

  • Hidden Rectangles
    problem

    Hidden rectangles

    Age
    11 to 14
    Challenge level
    filled star filled star empty star
    Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
  • Threesomes
    problem

    Threesomes

    Age
    11 to 14
    Challenge level
    filled star empty star empty star
    Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?
  • problem

    Which is quicker?

    Age
    7 to 11
    Challenge level
    filled star empty star empty star

    Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

  • Largest product
    problem

    Largest product

    Age
    11 to 14
    Challenge level
    filled star empty star empty star
    Which set of numbers that add to 100 have the largest product?
  • Got It
    problem

    Got it

    Age
    7 to 14
    Challenge level
    filled star filled star empty star

    A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

  • Frogs
    problem

    Frogs

    Age
    11 to 14
    Challenge level
    filled star empty star empty star
    How many moves does it take to swap over some red and blue frogs? Do you have a method?
  • Nim-7
    problem

    Nim-7

    Age
    5 to 11
    Challenge level
    filled star empty star empty star
    Can you work out how to win this game of Nim? Does it matter if you go first or second?
  • Egyptian Fractions
    problem

    Egyptian fractions

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

    The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.

  • Cubes within Cubes
    problem

    Cubes within cubes

    Age
    7 to 14
    Challenge level
    filled star filled star filled star

    We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

  • problem

    Two primes make one square

    Age
    7 to 11
    Challenge level
    filled star filled star empty star

    Can you make square numbers by adding two prime numbers together?