  The general position problem in graph theory asks for the largest set $S$ of
vertices of a graph $G$ such that no shortest path of $G$ contains more than
two vertices of $S$. In this paper we consider a variant of the general
position problem called the \emph{monophonic position problem}, obtained by
replacing `shortest path' by `induced path'. We prove some basic properties and
bounds for the monophonic position number of a graph and determine the
monophonic position number of some graph families, including unicyclic graphs,
complements of bipartite graphs and split graphs. We show that the monophonic
position number of triangle-free graphs is bounded above by the independence
number. We present realisation results for the general position number,
monophonic position number and monophonic hull number. Finally we discuss the
complexity of the monophonic position problem.
