Results 1 to 5 of 5

Math Help - number problem

  1. #1
    Newbie
    Joined
    Apr 2010
    Posts
    10

    number problem

    Could anyone please help? How do you get the answer to 3 to the 10000th power (3^10000)?
    Problem:
    After figuring out 3^10000, I need to add up all its digits and thus obtain a new number. Then I need to add up the digits of this new numbers and obtain another number. I need to continue doing this until eventually I get a single digit number.

    Do I have to know the full set of 3^10000 number to end up with the single digit number after the above process?

    thanks for helping.

    hongvo
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Sep 2010
    Posts
    18
    perhaps you can work with series approximation such as ...i'm not sure of your question though..
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by hongvo View Post
    Could anyone please help? How do you get the answer to 3 to the 10000th power (3^10000)?
    Problem:
    After figuring out 3^10000, I need to add up all its digits and thus obtain a new number. Then I need to add up the digits of this new numbers and obtain another number. I need to continue doing this until eventually I get a single digit number.

    Do I have to know the full set of 3^10000 number to end up with the single digit number after the above process?
    Instead of attempting to look at 3^{10000}, try the same problem with 3^n for some values of n that are much smaller than 10000. For example, if n = 3, then 3^3 = 27, and the digits of 27 add up to 9. Do a few experiments with other small values of n and see if you start to see a pattern. Then ask yourself why this pattern should apply to big values of n like n = 10000.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Apr 2010
    Posts
    10
    Quote Originally Posted by raa91 View Post
    perhaps you can work with series approximation such as ...i'm not sure of your question though..
    Hi, thx for the tip but I've not been taught how to use the 'sigma' sign. Here I'll try to explain my question:

    Let say
    3^10000 = abcdabcdabcdabcdabcdabcd.....
    then a+b+c+d+a+b+c+d+a+b+c+d+a+b+c+d+a+...... = defghijklmn......
    then d+e+g+h+i+j+k+l+m+n+.............= pgrstu.....
    then p+q+r+s+t+u+.........=wxyz..
    then w+x+y+z+....= ABC
    then A+B+C= X (where X is a single digit number)

    I have to find X.

    Hope this is clear. Thx again.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Apr 2010
    Posts
    10

    Thumbs up

    Quote Originally Posted by Opalg View Post
    Instead of attempting to look at 3^{10000}, try the same problem with 3^n for some values of n that are much smaller than 10000. For example, if n = 3, then 3^3 = 27, and the digits of 27 add up to 9. Do a few experiments with other small values of n and see if you start to see a pattern. Then ask yourself why this pattern should apply to big values of n like n = 10000.
    Hi opalg, thanks so much. Of course, of course. Is that correct to say that I actually don't have to find out what is the answer to 3^10000 in order to arrive at my final answer to my question?
    Why don't I think outside the square? Thank you very very much.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Birthday Problem; Prime Number Problem
    Posted in the Algebra Forum
    Replies: 9
    Last Post: January 8th 2012, 11:35 AM
  2. Number problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: December 8th 2009, 07:53 AM
  3. number problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 20th 2009, 10:31 AM
  4. Replies: 2
    Last Post: December 18th 2008, 05:28 PM
  5. Replies: 6
    Last Post: March 30th 2008, 10:39 AM

Search Tags


/mathhelpforum @mathhelpforum