How many different ways are there to fully tile a 2n x 2n grid with dominoes? Here "different" means apparently different. Further, how many unique ways are there? Here "unique" excludes all redundant configurations that are rotations and/or reflections of another. Find the different and unique ways up to 2n=8.
At first glance, this looks straightforward. Either I am missing something, or else everyone else is.
The n=1 case has two solutions.
The general case is made up by pasteing together n^2 n=1 cases. Hence, we get 2^(n^2) solutions for the general case.
To count the number of "unique" cases, examine the symmetry group and do the division.
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Posted by FrankM
on 2019-05-27 13:53:35 |
Abbreviated solution
