  We study the 2-offer semirandom 3-uniform hypergraph model on $n$ vertices.
At each step, we are presented with 2 uniformly random vertices. We choose any
other vertex, thus creating a hyperedge of size 3. We show a strategy that
constructs a perfect matching, and another that constructs a loose Hamilton
cycle, both succeeding asymptotically almost surely within $\Theta(n)$ steps.
Both results extend to $s$-uniform hypergraphs. Much of the analysis is done on
an auxiliary graph that is a uniform $k$-out subgraph of a random bipartite
graph, and this tool may be useful in other contexts.
