# Communications of the ACM

Last byte

## Upstart Puzzles: Take Your Seats

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.

No entries found

### Create a Web Account

If you are already an ACM member, Communications subscriber, or Digital Library subscriber, please set up a web account to access premium content on this site.

### Join the ACM

Become a member to take full advantage of ACM's outstanding computing information resources, networking opportunities, and other benefits.

### Subscribe to Communications of the ACM Magazine

Get full access to 50+ years of CACM content and receive the print version of the magazine monthly.