Given a regular octagon, in how many ways can we color one diagonal red and another diagonal blue so that the two colored diagonals cross (in the interior)? Consider rotations and reflections distinct.

Now suppose that not only must Sir Lancelot and Sir Gawain be diametrically opposite, but Sir Galahad and Sir Percival also demand to be diametrically opposite. How many seatings of the 10 knights are possible?

Thanks :) - Pushy

Edit: it you could help on this problem thanks:

How many of the 1000 smallest positive integers are congruent to 1 modulo 9?

I got 111 because 1000/9 is about 111 but that was incorrect.

PushyCake Mar 28, 2020