Possible Positions Around The Round Table

What was the challenge?

If king K is sitting at the center then the youngest knight must sit to right or left of the king i.e. 2 possible positions for him.

The second youngest knight now can sit either left or right of the group of 2 made above.

The third youngest knight now can sit either left or right of the group of 3 made above.

And so on.

That is every knight has 2 possible positions except the oldest knight who will have only 1 position left.

This will be make sure each of the knight (except youngest one) has at least 1 younger neighbor (youngest one has king as one neighbor).

So after putting youngest in 2 possible ways the next youngest can be put another 2 possible ways. That is 4 possible combinations for 2.

Similarly, for arranging 3 knights' positions there can be 2^3 = 8 possible combinations.

This way for 10 knights (excluding the oldest which will have only 1 seat available at the end) there are 2^10 = 1024 possible combinations.