Two Round Tables
Six people are to be seated at two identical round tables. Each table must have at least one person (a single person alone at a table is allowed), and each table can hold all six. Two seatings are the same if every person has the same left-hand neighbour in both (so rotating the people around a table changes nothing, and the tables themselves are indistinguishable), but mirror images are different. A person sitting alone counts as their own neighbour. How many different seatings are there? Give an integer.
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Source: Classic exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.