Divisibility

  • Ben's Game
    problem
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    Ben's Game

    Age
    11 to 16
    Challenge level

    Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

  • Expenses
    problem
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    Expenses

    Age
    14 to 16
    Challenge level

    What is the largest number which, when divided into these five numbers in turn, leaves the same remainder each time?

  • Why 24?
    problem
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    Why 24?

    Age
    14 to 16
    Challenge level

    Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

  • Latin Numbers
    problem
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    Latin Numbers

    Age
    14 to 16
    Challenge level

    Can you create a Latin Square from multiples of a six digit number?

  • LCM Sudoku
    problem
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    LCM Sudoku

    Age
    14 to 16
    Challenge level

    Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

  • LCM Sudoku II
    problem
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    LCM Sudoku II

    Age
    14 to 16
    Challenge level

    You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

  • Prime AP
    problem
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    Prime AP

    Age
    16 to 18
    Challenge level

    What can you say about the common difference of an AP where every term is prime?

  • Novemberish
    problem

    Novemberish

    Age
    14 to 16
    Challenge level
    a) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number. (b) Prove that 11^{10}-1 is divisible by 100.
  • Check Codes
    problem

    Check Codes

    Age
    14 to 16
    Challenge level
    Details are given of how check codes are constructed (using modulus arithmetic for passports, bank accounts, credit cards, ISBN book numbers, and so on. A list of codes is given and you have to check if they are valid identification numbers?
  • Transposition Fix
    problem

    Transposition Fix

    Age
    14 to 16
    Challenge level
    Suppose an operator types a US Bank check code into a machine and transposes two adjacent digits will the machine pick up every error of this type? Does the same apply to ISBN numbers; will a machine detect transposition errors in these numbers?
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