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 [a₁:a₂], [a₂:a₃],..., [a_k−1:a_k] with a₁ = 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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