How many possible shapes can one make by rearranging $n$ square shaped blocks, with and without allowing rotational symmetry? For example, for $n = 4$, there are seven possible shapes after discounting rotational symmetry, as in Tetris.
How does this number change if one of the blocks is coloured – distinguishable from the rest? For instance, for $n = 2$ there are only two shapes one can make (with rotational symmetry admissible). However, if one block is coloured, one can make four shapes, with the second block left, right, above and below the coloured block.