What configuration of community cards and hole cards gives you the lowest possible nutted hand on the river?

#Answer

Set of Queens

Board: Q2378

Hole cards: QQ

A set is always possible on any board, so that's the lower bound on the nuts.

For a set to be the nuts, no better hand can be possible, which requires the board to have:

1. no overcards (which would make a higher set the nuts)
2. no paired cards (which would make quads the nuts)
3. no straight possibilities

The lowest set that satisfies all 3 is a set of queens