Generally speaking, the imposition of the full statement of a differential equation diminishes the number of Lie symmetries it possesses. Oftentimes this is to the extent of removing all Lie point symmetries and so the possibility of finding a route to the solution of differential equation using point symmetries. The extension of the class of symmetry admitted to contact, merely serves to move the goalposts rather than remove them. In his paper, the author addresses this problem in the context of ordinary differential equations. Even though the usual area of failure is taken to be partial differential equations, he shows that, even in the more comfortable area of ordinary differential equations, the problem of incompatibility with the initial/boundary conditions can be an impossible obstacle to a symmetric mode of solution. The paper concentrates on third-order differential equations, but the ideas may be extended to higher-order equations. The complexities of the calculations make the restriction to third-order differential equations pedagogically sensible. The theoretical development is restricted to symmetry conditions which can be expanded as Taylor expansions, but the suggestion of extension to Laurent and worse expansions is present. Some examples are given which makes the purpose of the method manifest. Given a third-order differential equation subject to some initial conditions (one expects that other conditions such as boundary conditions can be treated as an advanced classroom exercise after a thorough assimilation of the ideas contained in this paper), the question of symmetries of the free ordinary differential equation becomes another question. The simple example -- a good feature of this paper -- of \(y''' = 0 \) subject to \(y'' (0) = 0 \) gives eight Lie point symmetries instead of the seven of the third-order equation. There is some loss from the seven and greater gain to achieve the eight. Of course the connection between the symmetries of \(y''' = 0 \) and \(y'' = 0 \) (the imposition of \(y'' (0) = 0 \) gives the latter as the surface in phase space upon which the subsequently derived symmetries exist) follow once one admits nonlocal symmetries and so the origin of the eight is always there just as are the fates of the seven (or 10 if the contact symmetries of the third-order equation are taken into account). In this regard one may think of the symmetries under discussion and is being configurational symmetries since they belong to a differential equation subject to a constraint. The configurational invariant was advanced by \textit{L. S. Hall} [Physica 8D, 90-105 (1983)] and does not seem to have attracted much additional literature although it was/is -- to this reviewer -- an important contribution. The lack of reference to the work of Hall in the present paper suggests that the author is unaware of this seminal work. The combination of the ideas of Hall and Hydon could lead to some very nice developments in the topic of Lie point symmetries and constrained systems. Altogether this paper is clear enough to give one an immediate sense of thoughts for extension.