Working systematically

  • No Square Sums
    problem

    No Square Sums

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    How many numbers do you need to remove to avoid making a perfect square?

  • Alberta's Age
    problem

    Alberta's Age

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    Alberta won't reveal her age. Can you work it out from these clues?

  • The Fastest Cyclist
    problem

    The Fastest Cyclist

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?

  • Relative Time
    problem

    Relative Time

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    Albert Einstein is experimenting with two unusual clocks. At what time do they next agree?

  • Alphabetical Angle
    problem

    Alphabetical Angle

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    If all the arrangements of the letters in the word ANGLE are written down in alphabetical order, what position does the word ANGLE occupy?

  • Switch On
    problem

    Switch On

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    In how many different ways can a row of five "on/off" switches be set so that no two adjacent switches are in the "off" position?

  • Gridlines
    problem

    Gridlines

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    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
    filled star filled star filled star

    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?

  • Different Digital Clock
    problem

    Different Digital Clock

    Age
    14 to 16
    Challenge level
    filled star filled star filled star

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

  • Medal Ceremony
    problem

    Medal Ceremony

    Age
    14 to 16
    Challenge level
    filled star filled star filled star

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