Addition and subtraction

  • Eleven
    problem

    Eleven

    Age
    11 to 14
    Challenge level
    2 out of 3

    Replace each letter with a digit to make this addition correct.

  • Clocked
    problem

    Clocked

    Age
    11 to 14
    Challenge level
    2 out of 3

    Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

  • Amazing Card Trick
    problem

    Amazing Card Trick

    Age
    11 to 14
    Challenge level
    2 out of 3

    How is it possible to predict the card?

  • Small tomato seedlings in pink pots.
    problem

    Rolling Along the Trail

    Age
    11 to 14
    Challenge level
    2 out of 3

    What could be the scores from five throws of this dice?

  • Football Sum
    problem

    Football Sum

    Age
    11 to 14
    Challenge level
    2 out of 3

    Find the values of the nine letters in the sum: FOOT + BALL = GAME

  • Pair Sums
    problem

    Pair Sums

    Age
    11 to 14
    Challenge level
    3 out of 3

    Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

  • Pairs
    problem

    Pairs

    Age
    11 to 14
    Challenge level
    3 out of 3

    Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was thinking of.

  • Cunning Card Trick
    problem

    Cunning Card Trick

    Age
    11 to 14
    Challenge level
    3 out of 3

    Delight your friends with this cunning trick! Can you explain how it works?

  • Postage
    problem

    Postage

    Age
    14 to 16
    Challenge level
    1 out of 3

    The country Sixtania prints postage stamps with only three values 6 lucres, 10 lucres and 15 lucres (where the currency is in lucres).Which values cannot be made up with combinations of these postage stamps? Prove that all other values can be made up.

  • Small tomato seedlings in pink pots.
    problem

    Pros and Cons

    Age
    14 to 16
    Challenge level
    2 out of 3

    If p is a positive integer and q is a negative integer, which of these expressions is the greatest?