Results 1 to 3 of 3

Math Help - The old "Four numbers equal 24" problem

  1. #1
    Member Henderson's Avatar
    Joined
    Dec 2007
    Posts
    124
    Thanks
    2

    The old "Four numbers equal 24" problem

    Any time I see a question like this: http://www.mathhelpforum.com/math-he...make-24-a.html I wonder:

    Of the 9^4 possibilities of digits, how many can be solved by the four simple operations, how many can be solved if we allow other symbols, and how many are unsolvable?

    I can't come up with any way to google an answer, though I'm sure someone must have done this before. Any interest?

    I'm confident that (1, 1, 1, 1) cannot be made into 24, regardless of operations.

    Anyone want to join in to help with the other 6560 possibilities?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Jan 2009
    Posts
    32

    1,1,1,1

    (1+1+1+1)! = 24 if factorials can be used.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Mar 2008
    Posts
    934
    Thanks
    33
    Awards
    1
    Quote Originally Posted by Henderson View Post
    Any time I see a question like this: http://www.mathhelpforum.com/math-he...make-24-a.html I wonder:

    Of the 9^4 possibilities of digits, how many can be solved by the four simple operations, how many can be solved if we allow other symbols, and how many are unsolvable?

    I can't come up with any way to google an answer, though I'm sure someone must have done this before. Any interest?

    I'm confident that (1, 1, 1, 1) cannot be made into 24, regardless of operations.

    Anyone want to join in to help with the other 6560 possibilities?
    I've done this, limiting the operations to the four standard +, -, *, /. I do not have the results where I can get to them easily, and I'm not even sure I saved the files.

    However, I would like to point out another use for this type of analysis. By counting the number of solutions for each set of 4 numbers you can rank the problems by difficulty. A problem with many solutions is easier than one with few.

    There are also a couple of fine points to consider: Do you allow intermediate steps which result in negative numbers? And how about fractions-- must each step yield an integer result? My understanding, based on heresay, is that these problems ("X24") are used to drill arithmetic in elementary schools, and depending on how how much math the kids know, problems involving fractions or negative numbers might be considered to be too hard.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: August 6th 2011, 03:00 PM
  2. Replies: 2
    Last Post: April 24th 2011, 07:01 AM
  3. Replies: 1
    Last Post: October 25th 2010, 04:45 AM
  4. Dividing an "L"-shape into 4 equal pieces?
    Posted in the Geometry Forum
    Replies: 5
    Last Post: July 17th 2008, 07:54 PM
  5. how to type "not equal" in latex?
    Posted in the LaTeX Help Forum
    Replies: 4
    Last Post: June 8th 2008, 12:59 PM

Search Tags


/mathhelpforum @mathhelpforum