Working systematically

  • Gridlines
    problem

    Gridlines

    Age
    14 to 16
    Challenge level
    2 out of 3

    How many triples of points are there in this 4×4 array that lie on a straight line?

  • Scratch Cards
    problem

    Scratch Cards

    Age
    14 to 16
    Challenge level
    3 out of 3

    To win on a scratch card you have to uncover three numbers that add up to more than fifteen. What is the probability of winning a prize?

  • Small tomato seedlings in yellow pots.
    problem

    Different Digital Clock

    Age
    14 to 16
    Challenge level
    3 out of 3

    At how many times between 10 and 11 o'clock are all six digits on a digital clock different?

  • Small tomato seedlings in yellow pots.
    problem

    Medal Ceremony

    Age
    14 to 16
    Challenge level
    3 out of 3

    The teacher has forgotten which pupil won which medal. In how many different ways could he give the medals out to the pupils?

  • Small tomato seedlings in pink pots.
    problem

    Integer Indices

    Age
    14 to 16
    Challenge level
    3 out of 3

    From this sum of powers, can you find the sum of the indices?

  • Small tomato seedlings in pink pots.
    problem

    Leftovers

    Age
    14 to 16
    Challenge level
    3 out of 3

    Weekly Problem 26 - 2008
    If $n$ is a positive integer, how many different values for the remainder are obtained when $n^2$ is divided by $n+4$?

  • The Great Weights Puzzle
    problem

    The Great Weights Puzzle

    Age
    14 to 16
    Challenge level
    3 out of 3

    You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?

  • Small tomato seedlings in pink pots.
    problem

    Factor List

    Age
    14 to 16
    Challenge level
    3 out of 3

    Tina has chosen a number and has noticed something about its factors. What number could she have chosen? Are there multiple possibilities?

  • Small tomato seedlings in yellow pots.
    problem

    Phone Call

    Age
    14 to 16
    Challenge level
    3 out of 3

    How many different phone numbers are there starting with a 3 and with at most two different digits?

  • Symmetricality
    problem

    Symmetricality

    Age
    14 to 18
    Challenge level
    1 out of 3

    Five equations and five unknowns. Is there an easy way to find the unknown values?