1. A hard riddle!

Hello there!

I didn't manage to solve a specific math riddle (anyway, i'm not a maths freak), maybe you can, so here it is:

where you can notice that:
An=n
Cn=An+Bn
Σ Cn= Σ odd Cn + Σ even Cn

The "odd Cn" and "even Cn" columns must be filled respectively with odd results of An+Bn and even results of An+Bn
For instance: If the result of A6+B6 is even, place the result in "Even Cn" column in the 6th line, and you put a 0 at the "Odd Cn" column in the same line.
if the result is odd, it's the other way round.

Warning: An, Bn and Cn are natural numbers (zero excluded) !
And the result of Σ odd Cn must be also an odd number.

However , the terms B1, B2, B3, B4, ect... -of the sum ΣBn- have not to be increasing or decreasing numbers.

Accepting these instructions, how do you proceed to determine n max and replace B1, B2, B3, ect.. with number in such manner we get
ΣAn= Σ odd Cn and ΣBn= Σ even Cn at the same time?

Good luck!

2. Nice try, snowtea! but Bn can never be equal to 0, for all n,
as my instruction said, it must be a natural number.

Sorry for this ambiguity because there are 2 kinds of natural numbers, the one including 0 and another excluding 0.
I intended to deal with the second one.

3. Originally Posted by termina
Hello there!

I didn't manage to solve a specific math riddle (anyway, i'm not a maths freak), maybe you can, so here it is:

where you can notice that:
An=n
Cn=An+Bn
Σ Cn= Σ odd Cn + Σ even Cn

The "odd Cn" and "even Cn" columns must be filled respectively with odd results of An+Bn and even results of An+Bn
For instance: If the result of A6+B6 is even, place the result in "Even Cn" column in the 6th line, and you put a 0 at the "Odd Cn" column in the same line.
if the result is odd, it's the other way round.

Warning: An, Bn and Cn are natural numbers (zero excluded) !
And the result of Σ odd Cn must be also an odd number.

However , the terms B1, B2, B3, B4, ect... -of the sum ΣBn- have not to be increasing or decreasing numbers.

Accepting these instructions, how do you proceed to determine n max and replace B1, B2, B3, ect.. with number in such manner we get
ΣAn= Σ odd Cn and ΣBn= Σ even Cn at the same time?

Good luck!
Riddle me this, riddle me that,
Based on how this question is asked,
It appears to come from an assignment
That counts for a final grade. Sorry to say,
We don't help people do that thing they call cheating.

Poetry isn't my thing, but I can tell you this:
If you can prove to me this isn't an assignment
That counts for a final grade, then I will reopen the thread.
But until that time comes,