1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Is x! even possible?

  1. Nov 22, 2011 #1
    I have been given a problem to make a problem for x!. The only restriction is, "But omit odd numbers given x is even"

    Another is for x! is, "Omit even numbers, x is divisible by 3".

    Is it even possible? I've thought of several manners, but I don't think I'm correct.

    Thanks in advance, everyone.
     
  2. jcsd
  3. Nov 22, 2011 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    What do you mean "make a problem"? Are you supposed to design a math question?
    If I don't know your intended result I cannot help you. How would you know if you are "correct"?

    note, if n is a positive integer, then xn=2n-1 is an odd number.
    Does that help?
     
  4. Nov 22, 2011 #3

    pwsnafu

    User Avatar
    Science Advisor

    What do you mean "make a problem"? Is that a typo?

    I think what you are asking for is a formula for, say,
    [tex]1 \cdot 3 \cdot 5 \cdot 7 \cdot 9[/tex]
    Okay, start with 9!
    How do you construct the product above from 9 factorial?
     
  5. Nov 22, 2011 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    those are sometimes denoted (x)!!. If x is even it is x(x- 2)(x- 4)...(4)(2). If x is odd, it is x(x- 2)(x- 4)...(3)(1).

    Note that is x is even, say x= 2n, then we have (2n)(2n-2)(2n- 4)... (4)(2)= (2)(n)(2)(n-1)(2)(n- 2)...(2)(2)(2)(1)= n(n-1)(n-2)...(2)(1) times a power of 2.
     
  6. Feb 5, 2012 #5
    Thankyou so much everyone! This problem was a while back. I have had problems accessing this forum, that's why I haven't replied in a long time.

    If I can remember what was the problem (I don't normally forget things), as it may have been a typo, then I can reiterate the issue. I still want it solved, but till then, thanks.
     
  7. Feb 5, 2012 #6

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    omit even means only odd numbers: 1,3,5,7,9,11,13,15,17
    but only divisible by three means that 1,5,7,11,13,17... are not allowed; which leaves: 3, 9, 15, ... which is 3(1,3,5,...) ...

    i.e. it is another way of asking for the product of odd-integer multiples of three.
    So-

    If x is an odd-integer multiple of 3, then the product of odd-integer multiples of 3 up to x is given by:[tex] 3\prod_{n=1}^{x/3}(2n-1) = 3\left ( \frac{x}{3} \right )!![/tex]... isn't it?

    This sort of word problem is an exercise in curly thinking.
     
    Last edited by a moderator: Feb 6, 2012
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Is x! even possible?
  1. Is x^iy possible? (Replies: 3)

Loading...