Consider a d-dimensional cube of side length s. Its s^d cells can be filled or empty. Let's call a specific setting of filled and empty cells a "configuration". Which configurations are there when the same number of cells must be filled in every row, column, pillar,... ?
>>> Binary Cubes
Consider n persons seated at a round table. These persons shall change places in such a way that no one is seated besides one of his former neighbours. This is repeated until everyone had everyone else as neighbour exactly once. How many ways are there to do so?