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When a shock is incident upon a corner from either the concave or convex side it is reflected by the walls forming the corner and diffracted at the edge. The mathematical problem corresponding to this phenomenon has not been solved analytically except in the following limiting two‐dimensional cases: a weak (acoustic) shock incident on any corner (Keller and Blank) and a finite shock incident either normal or parallel to a nearly flat wall (Bargmann, Lighthill, Ting, and Ludloff). In this article it is pointed out that there are certain special cases of a finite shock entering a corner from the concave side in which no diffraction occurs. In these cases it is therefore possible to solve the entire problem by using the theory of regular reflection, which yields an explicit solution by algebraic means alone.