Could anyone tell me how many odd integers are there
that are <= 1000^2000
:)
....
Re: Could anyone tell me how many odd integers are there
Quote:
Originally posted by hometown
that are <= 1000^2000
:)
....
Okay... 1000^2000 = 10^6000 = 2 * 5x10^5999
every other number is odd, so the answer is 5x10^5999.
Thank you Sir vey much for joining to solve my problem...
Sir, Could you tell me what made you think of using binary representation of that given number ? May I ask for that ? :)
Thank you....
Regards,
I would like to explain...
A.J.Gibson
Please donot get angry...I think it is not important for the answer to be correct or incorrect because there are always unexpected countless things in between, it was me who made such an unclear question. The main purpose I had when asking you again and again was nothing but just try to understand what you were really thinking when you gave me such an answer and more than that, I would like to find out why I couldnot get the answer that was the same as yours, which might partially upset you... Now I understood...Donot get angry at me hah ?:)
Your answer is absolutely correct...
What I have learnt,however, is different from the detailed result you offered and explained here...Because everytime I partition a number, I have only one choice, which means I am allowed to break only one number into its binary components at one time. Therefore, if I want to do that with another number that is next to the one I have just "devided", I will have to go back to its original position.
For example, in your case:
23
16 4 2 1
16 4 1 1 1
16 2 2 2 1
16 2 2 1 1 1
16 2 1 1 1 1 1
16 1 1 1 1 1 1 1
8 8 4 2 1 // Go back to the second position *
8 8 2 2 2 1
8 8 2 2 1 1 1
8 8 2 1 1 1 1 1
8 8 1 1 1 1 1 1 1
8 4 4 4 2 1// Go back to the postion *
.....
This is repeated until
2 2 2 2 2 2 2 2 2 2 2 1
2 2 2 2 2 2 2 2 2 2 1 1 1
2 2 2 2 2 2 2 2 2 1 1 1 1 1
......
2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
So finally there are 74 steps to finish...
Finally, I have to say that I really like your explanation, it is natural in the way of reasoning, and... that really helps...
Thank you very much...:)