How many design concepts are needed?
In the real world of commercial product design it is not uncommon for (UX) designers to spend most of their time working on the nuts and bolts (pixels and screens) of a single concept.
But in order to identify the best approach to meeting the constraints of user needs, commerce and technology it is unlikely that the first concept is the optimal one. There is a reason many designers like to have a sketch books.
Furthermore, even when 3-4 concepts are sketched it is not uncommon for the final direction to be constructed from different people’s favourite parts of each of the concepts.