Letters in a Circle [closed]

Question

Bob drew 6 letters into a circle. A, B, C, D, E, F. I don't have a graphic, but imagine those letters into a circle, with A at the top. Bob goes clockwise through the circle, writing every third letter, that he hasn't already written down. This results in the sequence A, D, B, F, C, E. Now, Alice mixes up the letters L,M,N,O,P,Q,R,S, randomly, starting with L at the top. Bob does the same thing, and goes through the circle writing every third letter. He ends up with the sequence, L, M, N, O, P, Q, R, S. What is the order that Alice put it in, starting with L at the top.

Sorry if this is vague. I read this problem earlier, but I don't know the answer.

Answer 1

The order Alice put the letters, in clockwise order and starting from the top, in is:

L, R, O, M, S, Q, N, P

Going in order:

Put $L$ at the top
Go forwards two notches, then write $M$ on the third
Go forwards two notches again, write $N$ on the third
Go forwards two notches, we just passed $L$, so we have to add another notch, write down $O$ on the next notch
Forwards two, we passed $M$, so add another one, we can't write on the next notch because $N$ is there, so add another notch, and write $P$ on that one.
Go forwards two, add one more because we passed $L$, add as many as we need until we find an empty spot, write $Q$ on the next available.
The last two are the next available, and the last remaining.
$R$: We pass an empty spot, go forwards until we find another empty spot, and the third empty spot is going to be the first one we passed by.
$S$: It should be the last spot left.

Answer 2

The order is:

L,O,R,M,P,S,N,Q

Explanation:

Repeating the same process for the order given above we get the original order.