Compute a way to order a given set of dominoes in such a way that they form a correct domino chain (the dots on one half of a stone match the dots on the neighbouring half of an adjacent stone) and that dots on the halfs of the stones which don't have a neighbour (the first and last stone) match each other.
For example given the stones 21
, 23
and 13
you should compute something
like 12 23 31
or 32 21 13
or 13 32 21
etc, where the first and last numbers are the same.
For stones 12, 41 and 23 the resulting chain is not valid: 41 12 23's first and last numbers are not the same. 4 != 3
Some test cases may use duplicate stones in a chain solution, assume that multiple Domino sets are being used.