Addition and subtraction

  • The Patent Solution
    problem

    The Patent Solution

    Age
    11 to 14
    Challenge level
    A combination mechanism for a safe comprises thirty-two tumblers numbered from one to thirty-two in such a way that the numbers in each wheel total 132... Could you open the safe?
  • Score
    problem

    Score

    Age
    11 to 14
    Challenge level
    There are exactly 3 ways to add 4 odd numbers to get 10. Find all the ways of adding 8 odd numbers to get 20. To be sure of getting all the solutions you will need to be systematic. What about a total of 15 with 6 odd numbers?
  • Calendar Calculations
    problem

    Calendar Calculations

    Age
    7 to 11
    Challenge level
    Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
  • Spell by Numbers
    problem

    Spell by Numbers

    Age
    7 to 11
    Challenge level
    Can you substitute numbers for the letters in these sums?
  • Code Breaker
    problem

    Code Breaker

    Age
    7 to 11
    Challenge level
    This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
  • Arrange the Digits
    problem

    Arrange the Digits

    Age
    11 to 14
    Challenge level
    Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?
  • Jugs of Wine
    problem

    Jugs of Wine

    Age
    11 to 14
    Challenge level
    You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre jug is full of wine, the others are empty. Can you divide the wine into three equal quantities?
  • Homes
    problem

    Homes

    Age
    5 to 7
    Challenge level

    Six new homes are being built! They can be detached, semi-detached or terraced houses. How many different combinations of these can you find?

  • Fair Exchange
    problem

    Fair Exchange

    Age
    5 to 7
    Challenge level

    In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

  • Planet Plex Time
    problem

    Planet Plex Time

    Age
    5 to 7
    Challenge level

    On Planet Plex, there are only 6 hours in the day. Can you answer these questions about how Arog the Alien spends his day?

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