Indices

  • Elevens
    problem

    Elevens

    Age
    16 to 18
    Challenge level
    Add powers of 3 and powers of 7 and get multiples of 11.
  • More Mods
    problem

    More Mods

    Age
    14 to 16
    Challenge level
    What is the units digit for the number 123^(456) ?
  • Growing
    problem

    Growing

    Age
    16 to 18
    Challenge level
    Which is larger: (a) 1.000001^{1000000} or 2? (b) 100^{300} or 300! (i.e.factorial 300)
  • Remainder Hunt
    problem

    Remainder Hunt

    Age
    16 to 18
    Challenge level
    What are the possible remainders when the 100-th power of an integer is divided by 125?
  • Thirty Six Exactly
    problem

    Thirty Six Exactly

    Age
    11 to 14
    Challenge level
    The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
  • Power Crazy
    problem

    Power Crazy

    Age
    11 to 14
    Challenge level
    What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
  • Rachel's Problem
    problem

    Rachel's Problem

    Age
    14 to 16
    Challenge level
    Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!
  • Lastly - well
    problem

    Lastly - Well

    Age
    11 to 14
    Challenge level
    What are the last two digits of 2^(2^2003)?
  • The Public Key
    problem

    The Public Key

    Age
    16 to 18
    Challenge level
    Find 180 to the power 59 (mod 391) to crack the code. To find the secret number with a calculator we work with small numbers like 59 and 391 but very big numbers are used in the real world for this.
  • Even So
    problem

    Even So

    Age
    11 to 14
    Challenge level

    Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?

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