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Upstart Puzzles: Take Your Seats


Take Your Seats, Figure 2

A popular logic game involves figuring out an arrangement of people sitting around a circular table based on hints about, say, their relationships. Here, we aim to determine the smallest number of hints sufficient to specify an arrangement unambiguously. For example, suppose we must seat Alice, Bob, Carol, Sybil, Ted, and Zoe. If we are allowed hints only of the form X is one to the right of Y, it would seem four hints are necessary. But suppose we can include hints that still refer to two people, or "binary hints," but in which X can be farther away from Y.

Suppose we have just three hints for the six people: Ted is two seats to the right of Carol; Sybil is two to the right of Zoe; and Bob is three to the right of Ted (see Figure 1 for this table arrangement). We see that we need only three hints to "fix" the relative locations of six people.


 

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