Star search-A different show

An extension of the line search problem is considered in which the number of directions in which the searcher can head from the origin is arbitrary, but finite. One problem under study is when the distribution of the particle to be found has a bounded support. Sufficient conditions are established under which an optimal policy exhausts a given direction before it proceeds to another one, and the optimal order of directions in which to search is found. Special cases and some extensions are considered. A second problem has a game theoretic flavor, in particular a conjecture of Gal is partially resolved.