1. ## number problem

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

2. perhaps you can work with series approximation such as ...i'm not sure of your question though..

3. Originally Posted by hongvo
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 $\displaystyle 3^{10000}$, try the same problem with $\displaystyle 3^n$ for some values of n that are much smaller than 10000. For example, if n = 3, then $\displaystyle 3^3 = 27$, 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.

4. Originally Posted by raa91
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.

5. Originally Posted by Opalg
Instead of attempting to look at $\displaystyle 3^{10000}$, try the same problem with $\displaystyle 3^n$ for some values of n that are much smaller than 10000. For example, if n = 3, then $\displaystyle 3^3 = 27$, 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.