Problem #9
Given a set of dominoes [1:1],[1:2],...[1,n],[2,2],[2,3],...[n:n]
with no repeated tiles,
a domino circle is an ordered set [a_{1}:a_{2}],
[a_{2}:a_{3}],...,
[a_{k−1}:a_{k}] with
a_{1} = a_{k}. For example if n=3 and
k=6,[1:1],[1:2],[2:2],[2:3],[3:3],[3:1] is a domino circle.

If n is odd, a domino circle using all dominoes is possible. In how many ways
can this be done? Note that [1:2],[2:2],[2:3],[3:3],[3:1],[1:1] and [1:3],[3:3],[3:2],
[2:2],[2:1],[1:1] are each different from the domino circle above and from each other.

If n is even, what is the largest domino circle that can be constructed? How
many different sets of dominoes yield such a circle?
The solution will be posted shortly.
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