A Single Gift Chain
Six friends hold a gift exchange: each person gives exactly one gift to someone else and receives exactly one gift. Call the assignment a single chain if, starting from any person and repeatedly moving to the person they give to, you visit all six people before returning to the start. How many assignments are single chains? Give an integer.
Related problems
Source: Classic counting exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.