Place value

  • Song Book
    problem

    Song Book

    Age
    7 to 11
    Challenge level
    A school song book contains 700 songs. The numbers of the songs are displayed by combining special small single-digit cards. What is the minimum number of small cards that is needed?
  • Nice or Nasty for Two
    game

    Nice or Nasty for Two

    Age
    7 to 14
    Challenge level

    Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.

  • Cayley
    problem

    Cayley

    Age
    11 to 14
    Challenge level

    The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

  • Chocolate Maths
    problem

    Chocolate Maths

    Age
    11 to 14
    Challenge level

    Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it works?

  • Tis Unique
    problem

    Tis Unique

    Age
    11 to 14
    Challenge level

    This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

  • More Mathematical Mysteries
    problem

    More Mathematical Mysteries

    Age
    11 to 14
    Challenge level

    Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try to explain why this works.

  • Small pepper seedlings in orange pots.
    problem

    Not a Polite Question

    Age
    11 to 14
    Challenge level

    When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...

  • Writ large
    problem

    Writ Large

    Age
    11 to 14
    Challenge level

    Suppose you had to begin the never ending task of writing out the natural numbers: 1, 2, 3, 4, 5.... and so on. What would be the 1000th digit you would write down.

  • Eleven
    problem

    Eleven

    Age
    11 to 14
    Challenge level

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

  • Small tomato seedlings in pink pots.
    problem

    Back of the Queue

    Age
    11 to 14
    Challenge level

    Weekly Problem 48 - 2013
    What is the remainder when the number 743589 × 301647 is divided by 5?

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