Addition and subtraction

  • Neighbours
    problem

    Neighbours

    Age
    7 to 11
    Challenge level
    2 out of 3

    In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

  • Dodecamagic
    problem

    Dodecamagic

    Age
    7 to 11
    Challenge level
    2 out of 3

    Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

  • Prison Cells
    problem

    Prison Cells

    Age
    7 to 11
    Challenge level
    2 out of 3

    There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

  • How many eggs?
    problem

    How Many Eggs?

    Age
    7 to 11
    Challenge level
    2 out of 3
    Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
  • Special 24
    problem

    Special 24

    Age
    7 to 11
    Challenge level
    2 out of 3
    Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.
  • Pairs of glasses of four different colours.
    problem

    Zargon Glasses

    Age
    7 to 11
    Challenge level
    2 out of 3

    Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

  • Magic Circles
    problem

    Magic Circles

    Age
    7 to 11
    Challenge level
    2 out of 3
    Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?
  • A square wooden table.
    problem

    Arranging the Tables

    Age
    7 to 11
    Challenge level
    2 out of 3

    There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

  • Number Juggle
    problem

    Number Juggle

    Age
    7 to 11
    Challenge level
    2 out of 3
    Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
  • A Rod and a Pole
    problem

    A Rod and a Pole

    Age
    7 to 11
    Challenge level
    2 out of 3
    A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?