I want to thank everybody for weighing in on this topic. I suspect that JohnInKansas and Jim Dixon (possibly others as well, sorry if I omitted anyone) have identified the main issue, namely that it depends on the exact (local) time at which the solstice occurs. If the solstice occurs between sunset and sunrise, I suspect (may be wrong, I suppose) that the night during which it occurs is the longest night. If the solstice occurs between sunrise and sunset, it gets more complicated. May depend on the before noon/after noon comparison, and that may depend on how you define "noon", i.e. noon on the clock vs. the time at which the sun is at its zenith.

Is it ever possible for the shortest day to be other then the day during which the solstice occurs, I wonder?

Don