Factorials

  • Fac-Finding
    problem
    Favourite

    Fac-Finding

    Age
    14 to 16
    Challenge level

    Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.

  • 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)
  • SquareSearch
    problem

    Squaresearch

    Age
    14 to 16
    Challenge level
    Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
  • Forgotten Number
    problem

    Forgotten Number

    Age
    11 to 14
    Challenge level

    I have forgotten the number of the combination of the lock on my briefcase. I did have a method for remembering it...

  • Factoring factorials
    problem

    Factoring Factorials

    Age
    11 to 14
    Challenge level

    Find the highest power of 11 that will divide into 1000! exactly.

  • Powerful factorial
    problem

    Powerful Factorial

    Age
    11 to 14
    Challenge level

    6! = 6 × 5 × 4 × 3 × 2 × 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4) = 45. What is the highest power of two that divides exactly into 100!?

  • Small tomato seedlings in pink pots.
    problem

    Trailing Zeros

    Age
    11 to 14
    Challenge level

    How many zeros does 50! have at the end?

  • N000ughty thoughts
    problem

    N000ughty

    Age
    14 to 16
    Challenge level

    How many noughts are at the end of these giant numbers?

  • Factorial
    problem

    Factorial

    Age
    14 to 16
    Challenge level

    How many zeros are there at the end of the number which is the product of first hundred positive integers?

Displaying 1 - 10 of 16