Divisibility

  • Eminit
    problem

    Eminit

    Age
    11 to 14
    Challenge level
    The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?
  • Just Repeat
    problem

    Just Repeat

    Age
    11 to 14
    Challenge level
    Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?
  • Three times Seven
    problem

    Three Times Seven

    Age
    11 to 14
    Challenge level
    A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
  • Book Codes
    problem

    Book Codes

    Age
    7 to 11
    Challenge level
    Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
  • problem

    Gran, How Old Are You?

    Age
    7 to 11
    Challenge level

    When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

  • Adding all nine
    problem

    Adding All Nine

    Age
    11 to 14
    Challenge level

    Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

  • flow chart
    problem

    Flow Chart

    Age
    11 to 14
    Challenge level

    The flow chart requires two numbers, M and N. Select several values for M and try to establish what the flow chart does.

  • Oh! Hidden Inside?
    problem

    Oh! Hidden Inside?

    Age
    11 to 14
    Challenge level

    Find the number which has 8 divisors, such that the product of the divisors is 331776.

  • Small tomato seedlings in pink pots.
    problem

    AB Search

    Age
    11 to 14
    Challenge level

    The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?

  • Square Routes
    problem

    Square Routes

    Age
    11 to 14
    Challenge level

    How many four digit square numbers are composed of even numerals? What four digit square numbers can be reversed and become the square of another number?

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