the riddle isn't available any more, come to see answer

[HomieDolphine]

The prize isn't available anymore. DP of the tokens will be at 15:00 today (server time)
the answer: The final answer is (2N)!, which is equal to 1*2*3*...*(2N-1)*2N. the explanation: Firstly decide which guests get the white hats. we have 2N guests and N white hats, so there are 2NcN ways to do this, which is ((2N)!/(N!)^2). Now in order to define the circles, we will define two functions which are onto and one to one between the group of people with white hat and the group of people with black hat (make sure you understand why defining those functions gives all the possible circles arrangements and every arrangement is given exactly one time). The first function will be for every person with white hat to decide excactly which person with black hat will stand to his right, there are N! ways to define this function. The second function will be for every person with black hat the decide exactly which person with white hat will stand to this right, there are N! ways to define this function. so we have ((2N)!/(N!)^2)*(N!)^2=(2N)!. Final answer: there are (2N)! ways.

 

[Mukjanoo53]

No, why did you say that there are N circles?

But the answer is N right?

 

[HomieDolphine]

But the answer is N right?

No. As I have said before, the answer isn't xN for every x as real number

 

[404_NOT_FOUND]

Suck your dad's toes I'm sure it's a troll.

 

[404_NOT_FOUND]

This guy is trolling us this guy don't even have donator tag.

 

[ritikgaming]

whoever answers this riddle get 15m prison tokens:

John is having a birthday, and exactly 2N guests have arrived to John's birthday. John has N white hats and N black hats. He want his guests to dance in a number of circles (one circle or more), such that every circle contains at least 2 people, and people with the same hat color will not be nearby each other (but they can be in the same circle). Assume that all of the guests can be distinguished, and all of the hats with the same color are exactly the same, therefore, rearranging all of the white hats will not count as another arrangement and rearranging the people WILL count as another arrangement . In how many ways can John arrange this? Show your steps.

reminder: a correct answer without the steps will NOT count as solving the riddle.
gl to everybody.
note 1: I assure you that you can't find the answer on the internet. the riddle is made of another riddle that was at a certain mathematics olympiad, and has been slightly changed.
note 2: the prize was 2m tokens, now its 6m tokens.
note 3: now the prize is 15m tokens
Hint 1: the final answer is going to involve N. for example N! (1*2*3*...*N) or N^2 could be valid answers (and one of those might be correct, who knows)
Hint 2: An important part of the solution would be considering all of the combinations to assign N guests to the N white hats, and the rest to the black hats. There are exactly 2nCn ways to do it, or (2N)!/(N!)², for example if N=3 then (2N)!=6!=720, 3!=6, so there are 720/6²=20 ways to assign the guests to white hats.

my answer is
1x3x5x7x.......x(2n-1)
is it right?
if yes then send those tokens to me
my IGN: ritikgaming

 

[HomieDolphine]

my answer is
1x3x5x7x.......x(2n-1)
is it right?
if yes then send those tokens to me
my IGN: ritikgaming

This is incorrect, but the closest one yet. But you need to remember that you MUST show your steps. Namely, show how you got to this answer.

 

[Greenuel]

2n^2 (2n squared) i gotta enter more than 6 words so here i am typing more

 

[HomieDolphine]

2n^2 (2n squared) i gotta enter more than 6 words so here i am typing more

Wrong, and you MUST include your steps if you want to get the tokens. It's all written in the thread

 

[Citan]

Wrong, and you MUST include your steps if you want to get the tokens. It's all written in the thread

show us ur token bal noob

 

[HomieDolphine]

show us ur token bal noob

You could just login and see how many tokens I have in tokens top at the spawn. But because of your comment you are not allowed to participate. Namely, you won't get the prize even if you have a correct answer.