King Arthur and the Knights

king arthur puzzle

King Arthur and his eleven honorable knights must sit on a roundtable. In how many ways can you arrange the group, if no honorable knight can sit between two older honorable knights?


The answer is 1024 ways, up to rotation around the table. To see this, notice that the youngest honorable knight must sit right next to King Arthur - there are two possible places for him. Then, the second youngest knight must sit right next to this group of two. Once again, there are two possible places for him. Continuing like this, we see that for all honorable knights, except for the oldest one, there are two possible spots on the table. Multiplying two to the power of ten out, we get 1024.